BACHELOR’S DEGREE FINAL THESIS
Chemical Engineering Degree
Industrial Electronics and Automation Engineering Degree
TRAINING COURSE IN SIMULATION OF CHEMICAL PROCESS
CONTROL
Master thesis
Authors:
Director:
Announcement:
Alex Nogué, Pasquale Orlo
Jordi Solà, Moisès Graells
June 2020
Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Abstract
The course designed in this project allows engineers to find solutions to process control issues through
the hybrid simulation approach. The control system design relies on the use of a chemical process
simulator (Aspen HYSYS), where the process dynamics is studied, and on the use of another numerical
computing software (MATLAB-SIMULINK), where to apply the system identification method obtaining
the transfer function of the process and to obtain the performance indexes of the final responses.
Different control strategies are tested using the simulator software, which allows implementing the
Internal Model Control (IMC) method to tune the controllers. Feedback, cascade and feedforward
control schemes are simulated, starting from controlling one variable (tank liquid level, temperature in
a heat exchanger), passing through an introductory multivariable process as the heated tank (liquid
level and temperature simultaneously), and ending with a binary distillation column where 5 variables
must be controlled.
The course is organized in 8 modules with a total duration of three days. It is intended for chemical and
control engineering students willing to obtain a deeper education in process control before getting to
work or for any engineer who wishes to get started with this theme. Simulation manuals, simulation
files and other documentation were designed and produced to enhance a better course experience for
both the attendee and professor.
The project viability has been confirmed through an economic analysis, which proves that the
investment for designing this course is recovered after one year. A pilot test in the Master’s degree in
Chemical Engineering – Smart Chemical Factories (EEBE-UPC) was also carried out. The results show a
great interest and satisfaction from the attendees, who showed attraction for an advanced part,
validating the course design.
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Master thesis
Resumen
El curso diseñado en este proyecto forma a los ingenieros para encontrar soluciones a problemas de
control de procesos mediante la simulación híbrida. El diseño del sistema de control se basa en el uso
de un simulador de procesos químicos (Aspen HYSYS), donde se estudia la dinámica del proceso,
asimismo en el uso de otro software de computación numérica (MATLAB-SIMULINK), donde se aplica
la identificación de sistemas para obtener la función de transferencia del proceso, así como los índices
de rendimiento de las respuestas. Se han examinado diferentes estrategias de control usando el
programa de simulación, el cual permite la implementación del método del Internal Model Control
(IMC) para encontrar los parámetros de los controladores. Se han simulado esquemas de control en
feedback, cascada y feedforward, empezando desde el control de una variable (nivel de líquido en un
tanque, temperatura en un intercambiador de calor), pasando a un sistema multivariable introductorio
como el tanque con serpentín (control del nivel y temperatura simultáneo), finalizando con una
columna de destilación binaria donde se deben controlar cinco variables.
El curso se ha dividido en 8 módulos con una duración total de tres días. Está enfocado a estudiantes
de ingeniería química y de control que quieran formarse en control de procesos antes de trabajar o a
cualquier ingeniero que desee empezar con esta temática. Se han elaborado manuales y ficheros de
simulación, y otra documentación para mejorar el aprendizaje del asistente al curso y como soporte al
profesor.
La viabilidad del proyecto ha sido confirmada mediante un análisis económico, el cual demuestra que
la inversión realizada para diseñar el curso se recuperaría al cabo de un año. Además, se llevó a cabo
una prueba piloto en el máster de Chemical Engineering – Smart Chemical Factories (EEBE-UPC). Los
resultados muestran un gran interés y satisfacción por parte de los estudiantes, los cuales han
mostrado su disposición a realizar una parte avanzada, validando así el diseño del curso.
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Resum
El curs dissenyat en aquest projecte forma els enginyers per trobar solucions respecte a problemes de
control de processos mitjançant la simulació híbrida. El disseny del sistema de control es basa en l’ús
d’un simulador de processos químics (Aspen HYSYS), on s’estudia la dinàmica del procés, i en l’ús d’un
altre software de computació numèrica (MATLAB-SIMULINK), on s’aplica la identificació de sistemes
per a la obtenció de la funció de transferència del process així com per als indicadors de rendiment de
les respostes. S’han testejat diferents estratègies de control utilitzant el simulador, cosa que permet la
implementació del mètode de l’Internal Model Control (IMC) per a trobar els paràmetres dels
controladors. S’han simulat esquemes de control en feedback, cascada i feedforward, començant des
del control d’una variable (el nivell de líquid en un tanc, la temperatura en un intercanviador de calor),
passant per un sistema multivariable introductori com n’és el tanc amb serpentí (control de nivell i
temperatura simultani), finalitzant amb una columna de destil·lació binària on s’han de controlar cinc
variables.
El curs s’ha dividit en 8 mòduls amb una duració total de tres dies. Està enfocat a estudiants de
enginyeria química i de control que vulguin formar-se en control de processos abans de començar a
treballar o a qualsevol enginyer que desitgi començar amb aquesta temàtica. S’han elaborat manuals
i fitxers de simulació, i altra documentació per tal de millorar l’aprenentatge del participant i com a
suport pel professor.
La viabilitat del projecte ha estat confirmada mitjançant una anàlisi econòmica, la qual demostra que
la inversió realitzada per a dissenyar el curs es recuperaria al cap d’un any. A més a més, s’ha dut a
terme una prova pilot en el màster Chemical Engineering – Smart Chemical Factories (EEBE-UPC). Els
resultats obtinguts mostren un gran interès i satisfacció per part dels estudiants, els quals van mostrar
la seva disposició en realitzar una part avançada, validant així el disseny del curs.
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Acknowledgements
We would like to sincerely show our gratitude to Marc Caballero, chemical engineer and professor in
Process Control at EEBE, who helped us in the dynamic modelling and the control simulation, and at the
same time, embraced us with his positivity and motivation.
Alex Nogué, Pasquale Orlo
I would like to thank Marta, my love, for giving me strength and security when I needed it.
Finally, I would like to thank my parents who taught me never to give up, and my sister Elena who has
always believed in me.
Pasquale Orlo
I would like to thank my parents, my sisters, my uncles and aunts and my grandparents who helped and
encouraged me throughout all of the degree.
Alex Nogué
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Master thesis
Contents
ABSTRACT ___________________________________________________________ I
RESUMEN __________________________________________________________ II
RESUM_____________________________________________________________ III
ACKNOWLEDGEMENTS________________________________________________ V
1.
INTRODUCTION _________________________________________________ 3
1.1. Objectives ................................................................................................................ 4
1.2. Project scope ........................................................................................................... 4
2.
METHODOLOGY _________________________________________________ 5
2.1. Approaches to process control................................................................................ 5
2.2. Hybrid simulation..................................................................................................... 6
2.2.1.
Communication.......................................................................................................6
2.2.2.
External use .............................................................................................................7
2.3. Resolution method .................................................................................................. 8
3.
2.3.1.
Identifying the process............................................................................................8
2.3.2.
Chemical process simulation ..................................................................................9
2.3.3.
Open loop response and process dynamic analysis .............................................18
2.3.4.
Transfer function fitting ........................................................................................18
2.3.5.
Variable pairing .....................................................................................................21
2.3.6.
Selecting the control scheme and tuning the controller......................................26
2.3.7.
Control system test ...............................................................................................34
COURSE DESIGN ________________________________________________ 36
3.1. Potential attendee and educational objectives .................................................... 36
3.2. Selected cases and course schedule ..................................................................... 37
3.3. Didactic material .................................................................................................... 40
4.
CASES AND RESULTS ____________________________________________ 41
4.1. Tank liquid level ..................................................................................................... 41
4.1.1.
Mathematical modelling of the atmospheric tank...............................................41
4.1.2.
Atmospheric tank using Aspen HYSYS ..................................................................44
4.1.3.
Comparison between MATLAB and HYSYS ..........................................................54
4.1.4.
Liquid level control ................................................................................................56
4.2. Heat exchanger ...................................................................................................... 73
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
4.2.1.
Dynamic simulation of a heat exchanger............................................................. 74
4.2.2.
Disturbances and open loop responses ............................................................... 83
4.2.3.
Feedback control loop .......................................................................................... 85
4.2.4.
Cascade control loop ............................................................................................ 89
4.2.6.
Feedforward control loop .................................................................................... 93
4.2.7.
Comparison of the different control schemes ..................................................... 97
4.3. Heated tank .......................................................................................................... 101
4.3.1.
Dynamic simulation of a heated tank ................................................................ 102
4.3.2.
Disturbances and open loop responses ............................................................. 106
4.3.3.
Multiloop control................................................................................................ 110
4.4. Distillation column ............................................................................................... 120
5.
4.4.1.
Distillation column theory .................................................................................. 120
4.4.2.
Steady state simulation of a distillation column ................................................ 123
4.4.3.
Dynamic simulation of a distillation column ...................................................... 126
4.4.4.
Tray Selection for Temperature Measurements ............................................... 140
4.4.5.
Distillation column control ................................................................................. 142
4.4.6.
Multivariable control of a distillation column.................................................... 142
4.4.7.
Tuning the controllers of the distillation column .............................................. 149
4.4.8.
Testing the system.............................................................................................. 152
ECONOMIC ANALYSIS __________________________________________ 161
5.1. Investment ........................................................................................................... 161
5.2. Variable cost......................................................................................................... 162
5.3. Market study ........................................................................................................ 164
5.4. Project viability..................................................................................................... 164
5.5. Pilot test ............................................................................................................... 165
CONCLUSIONS _____________________________________________________ 173
ENVIRONMENTAL IMPACT ANALYSIS __________________________________ 175
BIBLIOGRAPHY ____________________________________________________ 177
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
1. Introduction
Since the 1950s, automatic control has become essential for chemical processing plants due to safety
and economic reasons. Without it, the plant should be controlled manually by many operators keeping
under observation many process variables, as it was done prior to 1940s [1]. Large tanks were used as
buffers, to mitigate the dynamic disturbance effects, increasing the equipment cost. Therefore, it is
crucial for process engineers to have the proper process control training.
When designing a plant, chemical and control engineers commonly work in the same team. In order to
design the right control system, it is required collaboration and knowledge sharing. However, this can
be a very hard task since their objectives and, above all, their vocabulary may be very different.
Therefore, this project intends to design a course that allows mixing both vocabularies and both
knowledge all in one figure. The course is based on the Svrcek’s approach to chemical process control,
which relies not only on the classical techniques but also on the use of professional process simulators
[2]. Svrcek (A real time-approach to process control, 2006, Preface) states:
For decades, the subject of control theory has been taught using transfer functions, frequency-domain
analysis, and Laplace transform mathematics. For linear systems (like those from the electromechanical
areas from which these classical control techniques emerged) this approach is well suited. As an approach
to the control of chemical processes, which are often characterized by nonlinearity and large doses of
dead time, classical control techniques have some limitations.
In today’s simulation-rich environment, the right combination of hardware and software is available to
implement a ‘hands-on’ approach to process control system design. Engineers and students alike are now
able to experiment on virtual plants that capture the important non-idealities of the real world, and readily
test even the most outlandish of control structures without resorting to non-intuitive mathematics or to
placing real plants at risk.
Thus, the basis of this text is to provide a practical, hands-on introduction to the topic of process control
by using only time-based representations of the process and the associated instrumentation and control.
We believe this book is the first to treat the topic without relying at all upon Laplace transforms and the
classical, frequency-domain techniques. For those students wishing to advance their knowledge of process
control beyond this first, introductory exposure, we highly recommend understanding, even mastering,
the classical techniques. However, as an introductory treatment of the topic, and for those chemical
engineers not wishing to specialize in process control, but rather to extract something practical and
applicable, we believe our approach hits the mark.
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Master thesis
1.1. Objectives
The main objective of this master thesis is to design a viable course to train engineers in the field
of chemical process control. In order to achieve this goal, these are the sub-objectives to be
accomplished:
Bases of the course and configuration







To determine the opportunities, such as the demand of this type of courses and the market
competitiveness.
To determine the profile of the attendees.
To settle the range and the scope of the course.
To establish the educational objectives.
To determine the tools to be used.
To select and design the cases to be addressed.
To state the course schedule.
Materials



To simulate the cases and provide intermediate simulations for the attendee to better
follow the course.
To draft the simulation manuals.
To draft additional documentation.
Market study



To carry out a pilot experiment.
To perform an initial and final survey.
To determine the viability of the course.
1.2. Project scope
The scope of this project consists on designing a simulation course on chemical process control,
elaborating the configuration and basis of the course, including the course materials, and simulating
and controlling the studied cases. Furthermore, a pilot test has to be done in order to obtain
feedback from potential attendees, complete the economic analysis, and check the viability of the
course.
The cases addressed in the training course, and so in this master thesis, are continuous systems
where a rigorous design of the equipment was avoided to better concentrate on the dynamic study
and control strategy. Most of the cases were simulated without dead-time as a mean of
simplification, and because they should have been selected arbitrarily, since the process simulator
does not intrinsically have time delays.
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
2. Methodology
2.1. Approaches to process control
The classical approach to process control problems is by mathematically modelling the process through
the application of the laws of conservation of mass, energy and momentum [1]. As a dynamic study is
needed, the mathematical model is in the time derivatives form. When doing so, partial differential
equations or ordinary differential equations can either be used:

A partial differential equation (PDE) is an equation that describes the evolution of a physical
quantity, not only with time, but also according to other variables, such as space. They are applied
in the distributed systems, where differential operators like the gradient, divergence curl and
Laplacian are commonly used [3].

An ordinary differential equation (ODE) is an equation that contains one or more functions of an
independent variable (time) and its derivatives [4]. Two types of ODEs can be differentiated: linear
and non-linear. If the equation contains variables only to the first power it is a linear ODE,
otherwise, it is non-linear.
Most chemical engineering systems are non-linear and can have thermal or concentration gradients in
three dimensions [5]. However, when mathematically modelling the system, some simplifications can
be carried out. The hypothesis of perfect mixing in each phase eliminates the spatial gradients, turning
the system from distributed to lumped, so only time-dependent. Moreover, there are mathematical
techniques, like the Taylor series, that allows simplifying the non-linear equations to linear ODEs.
Indeed, it must be taken into account that the simplified model provides an accurate dynamic response
of the system in some region around the steady state conditions, and the size of this region depends
on the degree of non-linearity of the process [1].
Once the process has been modelled, the set of equations must be solved. One way is by direct solution
of the differential equations working in the time-domain, obtaining as a result functions of time.
Sometimes, instead, the Laplace transforms can also be used to describe the dynamics of the system,
working in the Laplace-domain. Another option is working in the frequency-domain when the system
becomes more complex and higher in order [1].
The advances in computational power allowed computer simulation to have a vital role in the
resolution of the systems of equations obtained. This requires programming the code to solve the
equations, either by numerical integration or iterative methods [1]. It could be done using any
programming language, such as FORTRAN, VBA, Python etc... However, the MATLAB-SIMULINK
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Master thesis
software is the most commonly used, as its interface includes different types of tools and add-ins, such
as the Partial Differential Equation Toolbox, that can help in the modelling of the process.
Furthermore, there are professional chemical process simulators, such as Aspen HYSYS, Aspen PLUS,
ChemCAD, gPROMS, ProSim and many others, which can be very time-saving since they already include
the libraries for each process unit and chemical and thermodynamics properties. In particular, the
dynamic simulation aided by these software provides a deeper understanding of the process, which
helps in the control system design. In addition, they also include controller modules through which is
possible to test different control strategies with no effects on the real plants, making the control design
safer.
The combination of a chemical process simulator with another software can lead to a satisfactory
control design. This is the so called hybrid simulation, and it is the chosen method for this project. The
tools required have been decided to be Aspen HYSYS, since it is one of the most used process
simulators software and many literature can be found about it, and MATLAB, since it has additional
toolboxes and add-ins, such as the system identification toolbox and SIMULINK, which can assist the
user in the control design process.
2.2. Hybrid simulation
The hybrid simulation takes into account two software, MATLAB and HYSYS in this case, in order to
favour the strengths of both and solve a process control problem. Some examples can be [6], [7]. The
implementation of this type of simulation can be done in two main ways: by means of communication
and external use.
2.2.1.
Communication
The first approach consists on considering Aspen HYSYS as the chemical plant and MATLAB as the
control station. In this case, while HYSYS simulates the process through all the core mathematical
relations, MATLAB allows for a lot of flexibility in order to choose the type of controller that is desired.
This could also provide helpful insight on what a field test looks like where control operators are
trained. Nowadays, there are two main options in order to communicate both software. These are the
DCS and the ActiveX servers.
With the communication via DCS (Distributed Control System), both Drivers are DDE Clients that
initiate communications with DDE Servers. The DCS option in HYSYS is admitted for EXCEL and MATLAB,
allowing to build multiple controllers and export different types of variables and arrays to the selected
program.
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Figure 2.1. First Hybrid approach considered.
About the ActiveX communication, the commands are used in the MATLAB command window or
scripts, which allows controlling almost every parameter from the HYSYS simulation. In order to
transfer the values, HYSYS’ spreadsheets are used. MATLAB connects to the spreadsheet cell where
the value is stored, being able to obtain it and modify it. For the communication of both software,
special libraries already created were used [8].
In this project, the chosen communication method to test is ActiveX. This is mainly due to the DCS
protocol being not compatible with the latest versions of MATLAB, so in case it was to be used, the
MATLAB version would have to be downgraded to a much older version with less capabilities, which
would restrict the MATLAB part.
The run tests with the ActiveX communication protocol proved successful, as variables could be
exchanged between both MATLAB and HYSYS. Furthermore, the controller built in MATLAB proved to
work well enough with the HYSYS simulation. However, due to Covid-19 outbreak, the communication
tests had to be stopped as the communication could only be made with both software on local. The
documentation about the ActiveX communication can be found in Annex C7.
2.2.2.
External use
The second approach, and the one that was finally used, consists on using HYSYS for both the plant and
controller, even though, when it comes to the process control and the final tests, MATLAB-SIMULINK
is used.
In this case, MATLAB is used to perform the system identification of the process and to check that the
transfer function obtained provides a good fitting. It is also used when it comes to comparing different
tuning parameters as well as to calculate the performance criteria values.
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Master thesis
Figure 2.2. Second hybrid approach considered.
2.3. Resolution method
In order to define a pattern to solve the process control cases, there are a few steps that need to be
followed. These are:
1. Identifying the basics of the process.
2. Simulating the process.
3. Obtaining the open loop response and make a process dynamics analysis.
4. Transfer function fitting.
5. Variable pairing.
6. Selecting the control scheme and tuning the controller.
7. Testing the control system.
2.3.1.
Identifying the process
When facing a process control problem, there is a need to determine if the system is a SISO (single
input, single output) or a MIMO (multiple input, multiple output). This is essential in order to define
the process variables and the manipulated variables of the system. From a control and chemical stand
point, MIMO systems are much more complex than SISO systems because they include process
interactions that can occasionally make the system unstable.
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Figure 2.3. SISO and MIMO system block diagram.
Once the system has been defined, the next step is to identify the variables of interest (the process
variables and the manipulated variables) and to define the principal disturbances that can affect the
system. Depending on the nature of the disturbance and the place of the system where the
disturbances affect, different control schemes could prove to be more effective than others on
rejecting them. The decision about which alternative suits the problem best is better provided by
dynamic simulation.
2.3.2.
Chemical process simulation
Process simulators software have become a fundamental tool for the process engineer since they save
a lot of time in the design calculations [9] and manpower or money avoiding the physical testing of the
design idea [10]. In addition, modern versions of such software provide a very interactive experience
and intuitive environment by the modular approach simulation.
When modelling a process with a professional process simulator, there are two main types of
simulations: steady state simulation and dynamic simulation. The steady state simulation is very useful
to solve material and energy balances, obtain a first flowsheet design, and evaluate different options
for the same process. This allows a first optimization of the process through an objective function that
reduces waste and maximize production and thus benefits [5]. Nevertheless, the steady state is an
ideal situation that real plants try to reach and keep. A sudden change in feed, a failure in the supply
stream, malfunction of a valve or even a change in environmental conditions are some of the possible
causes of disturbances that can be induced in the process. Such disturbances will move some process
variables from their steady state value. In addition, start-up and shut-down can be very frequent
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Master thesis
operations. When in some of these scenarios, there is no steady state and knowledge on the transient
behaviour of the system is essential to carry out the operations in a safe and controlled way. Therefore,
dynamic simulation is also needed to perform a correct design of the process.
The difference between steady state and dynamic simulation is that the second one is time-based,
which gives a more realistic level to the simulation. Therefore, dynamic simulation enhances a better
study of the transient behaviour of the process and the effect of each disturbance. This can lead not
only to a deeper understanding of the system but also further applications than steady state
simulation. For instance, dynamic simulation is used to design the control system and test it before
even building the plant. In this field, operator training finds a good opportunity, avoiding inducing any
disturbance in the real plant. In fact, there are several OTS (operator training simulators) courses
focused on preparing the control operators for different possible plant scenarios using a dynamic
simulation [11]. Furthermore, a safety evaluation is possible by making the HAZOP analysis more
accurate [9]. Finally, it can be used to perform a more detailed optimization of the process, including
the control scheme.
In this project, the steady state simulation has been generally used to create the flowsheet and size all
the equipment, but it has been then converted to dynamics mode where the controller has been
tested. You can easily switch from steady state to dynamics mode, after making the appropriate
modifications. The Dynamic Assistant tool helps in this task providing suggestions to adapt the model
to the dynamic mode [5].
Before running a dynamic simulation in Aspen HYSYS, some dynamic features must be revised:

Pressure Flow Solver: in real life there is no flow if there is no pressure difference. In steady state
mode this relation is not taken into account, while in dynamic mode a pressure drop through the
units is necessary to have a flow. This also means that if the pressure in the output gets higher
than the input pressure, the flow is reversed. That’s why the process happens to be pressuredriven and not flow-driven. Pressure specifications are needed to solve the balances and
hydrostatic pressure is well simulated by properly modifying the height of each equipment [5].

Resistance Equations: valves turn to be essential to provide a pressure drop through which
regulate the flow of the process streams. The flow across a valve is calculated through a resistance
equation which has the following general form:
𝐹𝑙𝑜𝑤 = 𝑘 · √∆𝑃
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(Eq. 2.1)
Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Others equipment can also be modelled with the Eq. 2.1, such as the Heat Exchangers or even
each stage of a distillation column [5]. The effect and role of the k parameter will be explained in
further chapter.

Hold-up: if there is no steady state, and variables depend on time, the term of accumulation of
the balance equations turns different from zero. Information about the retained material in the
equipment is given, such as composition, temperature and rate of change. That’s why a proper
sizing of each equipment in the simulation is needed. For example, specifying the volume of a tank
is essential yet it determines the capacitance of the equipment (Volume balance equations [5]).

Capacitance: Svrcek et al. define capacitance as “the system’s ability to absorb or store mass or
energy”. They also define it as “the resistance of a system to the change of mass or energy stored
in it, i.e. inertia” [2]. This means that if there is a disturbance, a new steady state will not be
reached instantaneously, being slower as much as there is more capacitance. A big capacitance
can be a choice to improve the control strategy. Some tanks, called surge tanks, due to the volume
they hold, are sometimes used to smooth a flow disturbance coming from the previous operation,
as a kind of protection for the next one.

Dead-time: it is the delay time since a disturbance is induced in the system until the process
variable gets affected. Unlike capacitance, dead-time can be very bad for the process control,
since the disturbance is detected later and the controller will act with delay too. Anyway, the
impact of this delay depends on the relation between dead-time and process time. If dead-time
is quite smaller than the process time it won’t be difficult to control the process, but if it is similar
or even bigger than the process time, then the system can become unstable. An example could
be the flow through a long pipe. It will take some time for the material to move from the beginning
to the end of the pipe, depending on its velocity. If there is any disturbance at the beginning of
the pipe, it will arrive at the end with some delay [12]. Generally, dead-time can be minimized
with large capacitance in the process [2].
Aspen HYSYS uses the Implicit Euler method to solve both linear and non-linear ODEs, and does not
take into account PDEs [5]. The resolution method approximates the exact areas obtained through the
integrals to rectangular areas:
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Master thesis
Figure 2.4. Implicit Euler method [5].
This is an implicit method because information is required at time tn+1.
Furthermore, to reduce computational demand, Aspen HYSYS solves volume (pressure-flow), energy
and composition calculations at different frequencies [5]. However, if the system is unstable or more
precision is required, the integration step and the execution rates of the calculations can be adjusted
in the integrator tab.
When simulating, the speed can also be regulated by the Desired RealTime Factor. For example, if the
Desired RealTime Factor is set to 200, the simulation occurs 200 times faster than reality (it takes 1 min
to simulate 200 real minutes). In the same way, if it is set to 1, the simulation will occur at real time.
2.3.2.1. Control Valves
Valves are mechanical devices used to regulate flow and pressure within a process and are the most
common final control element in a control system [2].
The presence of a valve in a pipeline represents an obstacle that modifies the flow configuration,
causing turbulences and energy loss, from kinetic to friction and noise. This translates into pressure
loss between the input and output of the valve [14], [15]. Figure 2.5 shows how the stem of the valve
reduces the pass area and the vena contracta when the control valve is approximated to an orifice.
Figure 2.5. Control valve and vena contracta [16].
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
The pressure drop depends on the parameters of flow and the geometry of the valve (type, size,
manufacturer, opening). That’s why losses are known from experimental measurements. Generally,
losses are given as a quotient between the pressure drop through the element or static height (hm) and
the kinetic height of the pipeline (hL):
ℎ =
∆𝑝
𝜌𝑔
(Eq. 2.2)
ℎ =
𝑉
2𝑔
(Eq. 2.3)
ℎ
2∆𝑝
=
ℎ
𝜌𝑉
(Eq. 2.4)
𝐾=
Where K is the dimensionless coefficient of losses [17].
Table 2.1. Coefficients of losses K for open valves, elbows and tee [17].
In most valves the friction losses are minimum respect to losses due to changes in direction of the flow,
so the coefficient K can be considered independent of the Reynolds number. However, it still depends
on the opening of the valve, as Figure 2.6 shows. When the valve is wide open, the minimum losses
are observed. They increase when the opening is reduced.
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Master thesis
Figure 2.6. Coefficient of losses for different types of valve and openings [17].
As the pressure drop increases, the flow increases too but not linearly. To describe this dependence,
the flow factor Cv is used in the following equation, which derives from Bernoulli’s equation [2]:
𝑄= 𝐶
∆𝑃
𝑆𝐺
(Eq. 2.5)
Where:

Q = volumetric flow rate

ΔP = pressure drop across the valve

SG = relative density compared with water at 60 F and 14.7 psia [18]
So the Cv factor relates the capacity of the valve and the valve flow characteristics. It depends on the
type and geometry of valve, and so, as the coefficient of losses K, it is determined experimentally.
Generally, it can be defined as the number of US gallons of water at 60 F (15.5 ºC) that flow through a
control valve in 1 minute, when the pressure differential across the valve is 1 psi [2], [14], [15].
It is important not to confuse the Cv factor with the coefficient of losses K. The first has units of
gpm/√psi, while the second is dimensionless and relates the pressure drop in meters of water column
with the velocity of the fluid according to equation 2.4. In fact, by changing units, it can be derived a
formula that relates Cv and K [18]:
𝐶 = 29.84 ·
14
𝑑
√𝐾
(Eq. 2.6)
Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
There is an equivalent to metric units named Kv, obtained as [14]:
𝑚
𝐶 = 0.15 · 𝐾
ℎ
𝑏𝑎𝑟
(Eq. 2.7)
Due to the high value of the Reynolds number inside a valve, the dependence of Cv on it cannot be
appreciated. The value of Cv is a function of the valve opening. The curve giving the variation of Cv with
valve opening at high Reynolds number and at constant pressure drop is named the inherent
characteristic of the valve. The maximum value of Cv occurs when the valve is wide open and depends
on the design and size of the valve, as said before [2]. In Figure 2.7 are shown three common examples
of inherent valve characteristics: quick opening, linear and equal percentage. The Cv is represented as
percentage of the maximum flow because like this it will apply to a set of geometrically similar valves,
independent of size.
Figure 2.7. Inherent valve characteristic curves [2].
However, the pressure drop across the valve is not constant (when closing the valve it will increase),
and the variation of Cv will not follow the inherent characteristic (given by the manufacturer) but the
operating characteristic. Equal percentage will deform to a curve closest to the linear one, and the
linear to the quick opening [14].
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Master thesis
Figure 2.7 shows the differences between the three inherent characteristics, but to better appreciate
them, a gain plot versus the percentage of lift of the valve is shown:
Figure 2.8. Gain curves for the three inherent valve characteristic [2].
Comparing the slope of these curves, it can be seen how fast the Cv changes for a very small lift change
for the quick opening type, while this change decreases rapidly at opening less than 50%. The linear
has slope 0 and the variation of Cv with lift is constant, while for the equal percentage an exponential
behaviour can be observed. The Cv increases relatively slow at low lift, but increases relatively high at
higher lift.
Choosing the type of control valve depends on the specific process, but normally the following
indications can be applied [19]:

Linear: Liquid level and flow control

Equal Percentage: Temperature [20] and Pressure control

Quick opening: Pressure-relief applications
2.3.2.2. Valves in HYSYS
Sizing the valve [13] is a fundamental step to properly design the process and very important for the
control purpose. Aspen HYSYS allows sizing the valve in three different ways:

ANSI/ISA: It uses the industry-standard ANSI/ISA S75.01, considered the state-of-the-art in
valve sizing.

Manufacturer specific methods: It is possible to select a manufacturer specific method from
the Valve Vapor Flow Models list. It includes, for example, the Masoneilan, Introl, Valtek, Fisher
16
Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
methods etc… and some of these models give the possibility to choose a specific type of valve
(globe, control ball, split body, butterfly etc…)

Simple resistance equation: It uses an equation very similar to Eq. 2.1 treating the flow as
always being proportional to the square root of the pressure drop. It is not possible to select
any inherent characteristic.
The main difference between the three sizing methods are the constants and equations that model
the valve. Details about these equations and parameters can be found in the Valve section of the Aspen
HYSYS Help.
Since a detailed design of the equipment is out of scope, the sizing method used in this work is the
ANSI/ISA yet it can be applied for any valve types, style and trim once the three parameters required
are specified (Xt, FI, Fp). In all the studied cases the default values for each one of these parameters
have been used. For this method, the Cv or Cg value, depending if the stream is in the liquid or vapour
phase, must be set or can be even auto-calculated by the process simulator. The value specified or
obtained is the maximum possible conductance value, and it will decrease depending on the pressure
drop and valve opening according to the inherent characteristic chosen.
When a valve is used as an OP (controller output), another component must be considered: the
actuator. It is a device that causes the valve to move when a signal from the controller is received.
Since both valve and actuator are physical elements, it will take time to move to their specified
positions. However, Aspen HYSYS lets you decide between four actuator modes:

Instantaneous Mode: the change in the position of the actuator occurs instantaneously.

First Order Mode: The lag is modelled as a first order behaviour specifying the actuator time
constant, τ, in the following differential equation:
𝜏
𝑑(𝐴𝑐𝑡%)
+ 𝐴𝑐𝑡% = 𝐴𝑐𝑡
𝑑𝑡
(Eq. 2.8)
%

Second Order Mode: The lag is modelled as a second order behaviour.

Linear Mode: The movement of the actuator occurs at constant rate. The Actuator Linear
Rate parameter must be specified to solve the following equation:
𝐴𝑐𝑡% = (𝐴𝑐𝑡. 𝐿𝑖𝑛𝑒𝑎𝑟 𝑅𝑎𝑡𝑒)∆𝑡 + 𝐴𝑐𝑡 %
𝑢𝑛𝑡𝑖𝑙 𝐴𝑐𝑡 = 𝐴𝑐𝑡
%
(Eq. 2.9)
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Master thesis
Furthermore, it is possible to model the valve delay by specifying the time constant τsticky in the
following equation that relates it to the actuator position:
𝜏
𝑑(𝑉𝑎𝑙𝑣𝑒%)
+ 𝑉𝑎𝑙𝑣𝑒% = 𝐴𝑐𝑡% + 𝑂𝑓𝑓𝑠𝑒𝑡
𝑑𝑡
(Eq. 2.10)
The offset must be also specified.
However, as a mean of simplification, in this project the majority of the control valves have been
simulated with an instantaneous actuator and with no delay on the valve response. The details about
each control valve can be found in each case chapter.
2.3.3.
Open loop response and process dynamic analysis
Once the dynamic simulation is ready, different disturbances can be simulated in order to study the
dynamic behaviour of the process. This can aid a better understanding of the relation between the
process variables.
When knowledge on the process has been acquired, it is time to start the control simulations. In order
to do so, the first thing needed is to place a controller and select the manual mode in the HYSYS
flowsheet case. Once the connections have been configured, a step input must be applied in the
controller output. This will provide the open loop transfer function of the plant and the control valve
of the system. This function will later be used to find the control parameters.
Note that this would be the same as obtaining both valve and plant open loop responses separately: if
a step was applied in the controller output and the mass flow of the stream was measured, then the
open loop response of the valve would be obtained; if a step was applied in the stream that is used to
control the process variable and the process variable itself was measured, then the transfer function
of the plant would be obtained.
Once the response has been obtained, it is exported to MATLAB. The export method used is via .csv
spreadsheet, explained in the Exporting Data appendix.
2.3.4.
Transfer function fitting
The next step is to obtain the transfer function of the system. In order to do so, the open loop response
obtained via HYSYS is plotted in MATLAB and approximated to a certain model. This can be done
following two different approaches: using the System Identification Toolbox in MATLAB or doing it
manually with many different existent methods. The chosen method is to do it manually, as for the
course it is expected that the attendees do not know the basics of system identification. In addition,
the results obtained have been checked by using SIMULINK. Indeed, the System Identification Toolbox
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
would probably be the preferred method in an advanced course, as it is able to obtain models of
dynamic systems not easily modelled from first principles or specifications.
The three methods used in this project are fittings for first [21] and second order systems as well as an
approximation for higher order systems. Note that the result of this process is a function in the Laplace
Domain.
One of the most basic responses that can be obtained after a step input is applied is a first order system,
in which the function obtained resembles Figure 2.9. This type of function has the form shown in Eq.
2.11.
𝐺(𝑠) =
𝐾
𝜏𝑠 + 1
(Eq. 2.11)
In order to calculate the parameters for this transfer function, the first thing to do is to calculate the
gain. The gain of the system is going to be the final value of the process variable minus its initial value
divided by the step input applied.
𝐾=
𝑌
𝑈
−𝑌
−𝑈
(Eq. 2.12)
Finally, in order to obtain the time constant, it will be estimated as the time where the process variable
reaches the 63.2% of its final value. This value corresponds to point A in Figure 2.9.
𝑌(𝜏) = 𝑌
−𝑌
· 0.632 + 𝑌
(Eq. 2.13)
Figure 2.9. First order transfer function and its characteristics [22] .
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Master thesis
Another type of fairly common response in chemical processes is the second order:
𝐺(𝑠) =
𝐾
(𝜏 𝑠 + 1)(𝜏 𝑠 + 1)
(Eq. 2.14)
According to [21] the use of Eq. 2.14 as a transfer function does not cover all the possible second order
behaviour. The two limiting cases are τ2/τ1=0 where the system becomes critically damped and τ1/τ2=1,
where the system becomes a first order model.
For second order transfer functions that include time delays or that are underdamped, the transfer
function that should be used is the following:
𝐺(𝑠) =
𝐾𝑒
𝜏 𝑠 + 2𝜉𝜏𝑠 + 1
(Eq. 2.15)
The technique used to obtain the unknowns of Eq. 2.15 is called the Smith’s method [21] and it requires
the times at which the normalized response reaches the 20% and the 60% of its value. With these time
parameters, then the t20/t60 ratio is calculated. With the ratio, the parameters of τ and ξ can be obtained
from the Smith’s plot, shown in Figure 2.10.
Figure 2.10. Smith’s method plot [23].
Nevertheless, in some occasions, fitting a second order or higher order responses into a first order plus
time delay could prove useful. If this was the case, Skogestad’s half rule can be used [23], [24]. To apply
this rule, the transfer function must fulfil two requirements:
1. It has to be overdamped.
2. The largest time constant has to be 1.5 times larger than the second largest one.
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
If this was the case, the function can be approximated into a first order plus time delay (FOPDT) transfer
function, as shown in Eq. 2.16.
𝐺(𝑠) =
𝐾𝑒
𝜏𝑠 + 1
(Eq. 2.16)
An example could be done considering the transfer function shown in Eq. 2.17.
𝐺(𝑠) =
𝐾
(𝜏 𝑠 + 1)(𝜏 𝑠 + 1)(𝜏 𝑠 + 1)
(Eq. 2.17)
With 𝜏 > 𝜏 > 𝜏 in order to fit it into a FOPTD, the time constant of the resulting function is going to
be the largest time constant plus half of the second largest one.
𝜏= 𝜏 +
𝜏
2
(Eq. 2.18)
And the time delay is going to be half of the second largest one plus all the other time constants
remaining in the transfer function.
𝛳=
𝜏
+ 𝜏
2
(Eq. 2.19)
All the results provided by the system identification method can be found in Appendix B.
2.3.5.
Variable pairing
This step is only made in those cases where there are multiple process variables and multiple
manipulated variables, the MIMO systems. So, the cases where variable pairing is needed are cases 3
and 4, the Heated Tank and the Distillation Column.
In MIMO systems, there are 2 or more variables that need to be controlled, and to achieve this task
the same number of manipulated variables has to be selected for the control. Moreover, it is essential
to select the right configuration for each system as a wrong pairing could potentially turn the process
unstable because of the interactions between the process variables.
To illustrate the methods, the assumption that the system has two process variables and two
manipulated variables is made. In that case, the control strategy would be to pair each manipulated
variable with one process variable using a feedback controller [21].
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Master thesis
Figure 2.11. Heated tank MIMO system.
In the process shown in Figure 2.11, there are two control variables and two process variables, making
it a 2x2 system, where four transfer functions can be found.
𝐺
(𝑠) =
𝑌 (𝑠)
𝑈 (𝑠)
(Eq. 2.20)
𝐺
(𝑠) =
𝑌 (𝑠)
𝑈 (𝑠)
(Eq. 2.21)
𝐺
(𝑠) =
𝑌 (𝑠)
𝑈 (𝑠)
(Eq. 2.22)
𝐺
(𝑠) =
𝑌 (𝑠)
𝑈 (𝑠)
(Eq. 2.23)
The last four transfer functions can be rewritten in terms of the output values, as shown in Eq. 2.24
and Eq. 2.25.
𝑌 (𝑠) = 𝐺
(𝑠)𝑈 (𝑠) + 𝐺
(𝑠)𝑈 (𝑠)
(Eq. 2.24)
𝑌 (𝑠) = 𝐺
(𝑠)𝑈 (𝑠) + 𝐺
(𝑠)𝑈 (𝑠)
(Eq. 2.25)
If two feedback loops are used to control both multiple variables, there are two possible process
configurations: a scenario where y1 is controlled by u1 and y2 is controlled by u2, but there is another
possible scenario where y1 is controlled by u2 and y2 is controlled by u1. The first configuration is called
1-1, 2-2, while the second is called 1-2, 2-1 [21].
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Figure 2.12. Block diagram for the u1-y1, u2-y2 systems.
Figure 2.13. Block diagram for the u1-y2, u2-y1 systems.
For instance, considering 1-1, 2-2 schemes, if there was an error in one of the two controllers caused
by a set-point change in Ysp1, the controller Gc1 would adapt to that set-point change and force Y1 to
reach that value. Meanwhile, Y2 would also change due to the process interactions, and then the
controller Gc2 would have to adjust Y2 to bring it to its set-point Ysp2, but that would also affect Y1. This
process would go on until a steady-state between the two variables is reached.
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Master thesis
In order to pair the controlled variables and the manipulated variables the Relative Gain Array (RGA)
Method will be discussed [21], [25]. Bristol’s RGA Method calculates the relative gain λij, which can be
defined as the division between open-loop and the closed loop gain, intending the open-loop gain as
the one obtained when no interactions between the input variables is considered:
𝜆 =
(Eq. 2.26)
𝜕𝑦
𝜕𝑢
𝜕𝑦
𝜕𝑢
Here
is the gain between the input i and the output j when all the other inputs are held constant,
and
is the gain between input i and output j when all the other outputs are held constant. If the
relative gain for every input and every output is calculated, then the RGA can be constructed.
𝑦 𝜆
𝑦 𝜆
𝛬= ⋯
⋯
𝑦 𝜆
𝜆
𝜆
⋯
𝜆
⋯ 𝜆
⋯ 𝜆
⋯ ⋯
⋯ 𝜆
(Eq. 2.27)
The relative gains can be calculated from the steady-state data of the system or from simulated process
model. For a 2x2 systems, linearizing the model provides the following equations [21]:
𝑦 = 𝐾 𝑢 + 𝐾 𝑢
(Eq. 2.28)
𝑦 = 𝐾 𝑢 + 𝐾 𝑢
(Eq. 2.29)
In order to calculate the open-loop gain, the u2 is set to zero, so the gain equals K11 .
𝜕𝑦
𝜕𝑢
(Eq. 2.30)
=𝐾
About the closed loop gain, the first thing to do is to obtain the equation of u2 when y2 equals to zero.
𝑢 =−
(Eq. 2.31)
𝐾
𝑢
𝐾
If then it is substituted in equation 2.28, the following closed-form is achieved.
𝑦 = 𝐾 −
24
𝐾 𝐾
𝐾
𝑢
(Eq. 2.32)
Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
If now equation 2.32 is substituted into equation 2.26, where the open loop gain is divided by the
closed loop gain, the relations obtained for parameter λ are shown in Eq. 2.33 [25].
𝜆
=
1
𝐾 𝐾
1−
𝐾 𝐾
(Eq. 2.33)
The RGA has some important properties for steady state models [21], which are:
1. The matrix is normalized and the sum of the columns and rows equals to one.
2. The relative gains are dimensionless.
Taking into account these properties, the RGA can be constructed by values that are a function of λ11.
𝛬=
𝜆
1−𝜆
1−𝜆
𝜆
(Eq. 2.34)
In order to obtain the steady-state gains, it can be done with the HYSYS process model. For example,
to calculate the output gain for one variable, the input can be changed in a stepwise form while all the
other inputs are held constant.
There are five different scenarios depending on the value of λ [21]:
1. λ=1. It means that closing the loop 2 has no influence in loop 1. In this situation, y1 should be
paired with u1 and y2 with u2.
2. λ=0. In this case, it is the opposite of the first one, and means that closing loop 2 has no
influence in loop 2. Therefore, y1 will be paired with u2 and y2 will be paired with u1.
3. 0 < λ < 1. In this case, there is interaction between both loops, and depending on the degree
of interaction one situation or the other will be chosen.
4. λ>1. For this case, closing the second loop reduces the gain between y1 and u1, meaning that
both loops interact. This interaction is greater when λ is closer to infinite.
5. λ<0. When the value is negative, closing the second loop has an adverse effect in loop 1.
The conclusion is that y1 should be paired with u1 if λ >= 0.5. Otherwise, it should be paired with u2.
According to [21], the disadvantage of the RGA analysis is that dynamic considerations are not taken
into account. This is especially problematic when there is a process function with time delay or with a
very large time constant, and in some cases, if there is a really slow response of y1 to a change in u1, an
y1-u2 pairing might be more desirable.
The Singular Value Analysis (SVA) method [21], [26] is another technique that helps with the selection
of the variables, evaluates the robustness of the control strategy and determines the best multiloop
control configuration ([21], [26]).
In this project, the singular value analysis will be done with the steady-state gains. In order to do so,
the steady-state gain matrix (Eq. 2.35) is needed. It is desirable that the vectors of this matrix are
25
Master thesis
linearly independent, which means that the determinant of the matrix cannot be null. The parameters
that need to be obtained are the singular values, obtained by calculating α’, and obtaining its roots.
𝐾
𝐾
𝐾=
⋯
𝐾
𝐾
𝐾
⋯
𝐾
⋯ 𝐾
⋯ 𝐾
⋯ ⋯
⋯ 𝐾
(Eq. 2.36)
|𝐾 𝐾 − 𝛼′𝐼| = 0
𝜎 =
𝛼 ;𝜎 =
(Eq. 2.35)
𝛼
(Eq. 2.37)
With the eigenvalues, the final value that needs to be calculated is the condition number (CN):
𝐶𝑁 =
𝜎
𝜎
(Eq. 2.38)
Where the condition number is calculated by dividing the largest and the smallest singular values. If
the CN value is large, it will indicate poor conditioning, as it will mean that the large manipulated
variable will have CN times more effect on the system than the other one. The SVA is really helpful for
some cases where the RGA doesn’t indicate the poor conditioning of the system [21].
Another tool to analyse the stability of control loop pairings is the Niederlinski index [2]. This method
is used to prove that a 2x2 matrix is stable, even though, if the matrix is larger than a 2x2, it can only
be used to determine that the control loop is definitely not stable. If the NI is negative the system will
be unstable.
𝑁𝐼 =
2.3.6.
|𝐾|
∏
(Eq. 2.39)
𝑘
Selecting the control scheme and tuning the controller
The process can be controlled using different control strategies. The control schemes used in this
project are feedback, cascade and feedforward control (this last explained in chapter 4.2.6). Each
scheme provides a different response and a comparison allows picking the best one. The tuning
method depends on the control scheme and on the type of system. For example, different tuning
strategies are applied for a SISO or a MIMO system.
2.3.6.1. Feedback control
Nowadays, there are multiple control loops that can be used, but the most common and the most used
one is the feedback control. In a feedback control loop, the controller compares the measured variable
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
to the set point and takes the corrective action by calculating the controller output and transmitting
the signal to the control valve. There are many feedback controllers, and some examples are P, PI, PD
or PID. P (proportional), I (integral) and D (derivative) are the corrective actions that modify the error
to produce the controller output.
About the proportional action, the controller gain can be adjusted in order to make the changes more
or less aggressive, and the sign of the proportional gain can be adjusted to make the controller output
increase or decrease as the error signal increases. In P controllers there needs to be a bias value,
because when the controller output equals the desired value, the error is zero, thus making the
controller output also zero [27]. In this kind of controllers, the controller output is proportional to the
error signal:
(Eq. 2.40)
𝑜𝑝(𝑡) = 𝑏𝑖𝑎𝑠 + 𝐾 · 𝑒(𝑡)
The main drawback of proportional-only controllers is that an offset occurs after a setpoint change or
a disturbance, meaning that it will not reach the desired value.
Integral action provides the elimination of the offset, thus achieving to make the error value equal to
zero. When integral action is used, the output of the controller changes until it attains the value
required to make the steady-state error zero.
𝑜𝑝(𝑡) = 𝑏𝑖𝑎𝑠 +
1
𝜏
(Eq. 2.41)
𝑒(𝑡)𝑑𝑡
The basic function of the derivative action is to anticipate the future behaviour of the error signal. In
other words, the derivative action seeks to not allow rapid movements of the process variable.
𝑜𝑝(𝑡) = 𝑏𝑖𝑎𝑠 + 𝜏
(Eq. 2.42)
𝑑𝑒(𝑡)
𝑑𝑡
From the derivative action equation, it can be seen that the value of the output is equal to the bias as
long as the error is constant, which is the main reason why the derivative action is never used alone.
The PID is the combination of the three corrective actions, and it is one of the most used controllers
nowadays. The most common form of PID is the following, which is called the parallel form. The PID
controller continuously calculates the error value and applies a correction action based on the three
tuning parameters.
𝑜𝑝(𝑡) = 𝑏𝑖𝑎𝑠 + 𝐾
𝑒(𝑡) +
1
𝜏
𝑒(𝑡)𝑑𝑡 + 𝜏
𝑑𝑒(𝑡)
𝑑𝑡
(Eq. 2.43)
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Master thesis
Even though the parallel PID is among the most common forms, there are other digital versions of the
PID. These two alternatives are the position and velocity form [21]. What these two forms do is to
replace the integral and derivative terms by finite difference approximations.
𝑜𝑝 = 𝑜𝑝 + 𝐾
𝛥𝑡
𝑒 +
𝜏
𝜏
(𝑒 − 𝑒
𝑒 +
𝛥𝑡
(Eq. 2.44)
)
Where:

Δt is the sampling period or the time between two measurements.

ek is the error at the sampling instant k.
In the velocity form, the result of the equation is the change of the controller output:
𝑜𝑝 = 𝑜𝑝
+𝐾
𝑒 −𝑒
+
𝛥𝑡
𝜏
(𝑒 − 2𝑒
𝑒 +
𝜏
𝛥𝑡
+𝑒
)
(Eq. 2.45)
According to [21], the velocity form has three advantages over the position form:
1. It contains an anti-reset windup.
2. The output can be expressed in the increment form, which is useful for some final control
elements.
3. It does not require initialization of the output when transferring the controller from manual to
automatic.
2.3.6.2. Stability margins
For simplicity reasons, the margins of stability have only been calculated for simple feedback loops.
Using the block diagram of the system, the margins of stability of the controller can be calculated via
the Routh-Hurwitz criterion [28]. This will allow the engineer to know between which margins the
controller parameters values are. The block diagram a feedback control system is shown in Figure 2.14.
Figure 2.14. Feedback system block diagram.
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Two transfer functions can be obtained, one relating the output to the set-point and the other relating
the output to the disturbance. For a set-point change, the closed loop transfer function of the system
is shown in Eq. 2.46 obtained when Yd equals to 0.
(Eq. 2.46)
𝐺𝐺 𝐺
𝑌(𝑠)
=
𝑌 (𝑠) 1 + 𝐺 𝐺 𝐺
For a disturbance change, the closed loop transfer function is shown in Eq. 2.47 obtained when Ysp
equals to 0.
(Eq. 2.47)
𝑌(𝑠)
𝐺
=
𝐷(𝑠) 1 + 𝐺 𝐺 𝐺
As it can be seen, both transfer functions share the same denominator (1 + 𝐺 𝐺 𝐺 ), which means that
both functions share the same characteristic equation [21].
The Routh-Hurwitz stability criterion is an analytical technique to determine if any roots of a polynomial
have positive real parts, which would mean that the polynomial has right plane poles, making the
system unstable. The method can only be applied to systems whose characteristic equations are
polynomials in s, making it not valid for time delay transfer functions [21]. In the case of time delay
systems, either the First Order Taylor Approximation or the Padé Approximation should be used for the
time delay part.
The characteristic equation has the following form:
𝑎 𝑠 + 𝑎
𝑠
+ ⋯+ 𝑎 𝑠 + 𝑎 = 0
(Eq. 2.48)
One of the conditions in order to determine if the system is stable is that all the coefficients of the
polynomial are positive. This condition is necessary but not sufficient to determine the stability of the
function. The next thing to do is to create the Routh array:
𝑎 𝑎 𝑎
𝑎 𝑎
𝑎
𝑏 𝑏
𝑏
𝑐
𝑐
…
⋮
0
0
𝑧
0
0
1
2
3
4
⋮
𝑛+1
⋯
⋯
⋯
0
0
0
(Eq. 2.49)
In the last matrix, n is the order of the characteristic equation. Finally, the values of b and c are
calculated as it follows:
𝑏 =
𝑎
𝑎
−𝑎 𝑎
(Eq. 2.50)
𝑎
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Master thesis
𝑏 =
𝑎
𝑐 =
𝑐 =
𝑎
−𝑎 𝑎
(Eq. 2.51)
𝑎
𝑏 𝑎
−𝑏 𝑎
𝑏
(Eq. 2.52)
𝑏𝑎
−𝑏 𝑎
𝑏
(Eq. 2.53)
Nevertheless, there are some cases where the Routh array criterion might be difficulty to apply,
especially notable in MIMO systems, as in those kinds of processes, the denominator of the closed loop
transfer function includes all the transfer functions of the system, making it much more difficult to
obtain.
2.3.6.3. Cascade control
About the cascade controller, the main difference with the feedback one is that it involves two
controllers, where the output of the first one provides the set-point for the second, having one loop
nested inside the other:
Figure 2.15. Block diagram of the cascade control system.
When it comes to improving the feedback controller, the cascade scheme will outperform the feedback
one when the disturbances are associated with the manipulated variable [21].
In order to tune the cascade controller, there are few steps that need to be followed [2]:
1) Place the primary controller in manual and the second controller on the local set point. It will
break the cascade system and allow the inner controller to be tuned.
2) Tune the secondary controller.
3) Return the secondary controller to remote set point.
4) Tune the primary controller.
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Once both controllers have been tuned there shouldn’t be any interaction between them. In case there
was, it means that the primary loop is not slow enough and it overlaps with the inner loop. About
cascade controllers, there is a rule of thumb that says that in order to avoid overlapping both
controllers, the inner loop has to be at least four times faster than the primary loop [2].
2.3.6.4. IMC tuning method
When it comes to the tuning of a PID controller, there are multiple tuning rules that could be followed.
These rules can be divided in two categories: on-line and offline. The main difference between them
is that online methods are based on experimental tests to calculate a set of initial controller
parameters, whereas in offline tuning, the parameters obtained are normally reached through block
diagram algebra or via the transfer function of the process. Some examples of on-line tuning methods
could be the Ziegler-Nichols or the Tyreus-Luyben, and for off-line methods, the Direct Synthesis and
the IMC method.
In this project, it was decided to use the IMC method [7], [21], as it provides good results and has a
degree of freedom that allows the operator to achieve a faster or slower response depending on the
characteristics of the system. The IMC method [21] is based on an assumed process model that leads
to analytical expressions for the tuning of the controller. One of the main advantages of the IMC
method is that it allows trade-offs between performance and robustness (where robustness means
that the control system can provide a satisfactory performance for a wide range of process conditions
and [21]) to be considered.
Consider the block diagram shown in Figure 2.16, where 𝐺 represents the internal model that is perfect
for the system and G is the physical model of the process.
Figure 2.16. Initial block diagram of the IMC model.
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Master thesis
If the block diagram is transformed into the one shown in Figure 2.17, via block diagram algebra, the
transfer function of the controller can be obtained (Eq. 2.54).
Figure 2.17. Initial block diagram modified with block diagram algebra.
To find Q, the IMC method states that it is equal to the inverse of the stable part of the given function
multiplied by a filter (Eq. 2.54). The filter part is multiplied in order to make sure that the function
obtained is a semi-proper system, where the degree of the numerator does not exceed the one of the
denominator.
𝑄= 𝐺
·𝐹
𝑤ℎ𝑒𝑟𝑒 𝐹 =
1
𝜆𝑠 + 1
(Eq. 2.54)
Once the Q has been obtained, it can be substituted into Eq. 2.55, and matched with the transfer
function of the desired controller in order to obtain the parameters.
𝐺 =
𝑄
(Eq. 2.55)
1−𝑄· 𝐺
For the three main transfer function shown in chapter 2.3.4 (first order, second order, first order plus
time delay), the tuning parameters are shown hereafter. For a detailed explanation on how to obtain
them, refer to the IMC Manual in Appendix C5.

First order
𝐾 =
𝜏
𝐾 ·𝜆
𝜏 = 𝜏
32
(Eq. 2.56)
(Eq. 2.57)
Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Where Eq. 2.56 and Eq. 2.57 can be substituted into Eq. 2.58.

𝐺 (𝑠) = 𝐾
1+
𝐾 =
2𝜉𝜏
𝐾 ·𝜆
1
𝜏𝑠
(Eq. 2.58)
Second order
(Eq. 2.59)
𝜏 = 2𝜉𝜏
(Eq. 2.60)
𝜏
2𝜉
(Eq. 2.61)
𝜏 =
Where Eq. 2.59, Eq. 2.60 and Eq. 2.61 can be substituted into Eq. 2.62.
𝐺 (𝑠) = 𝐾

1+
1
(𝜏 𝑠 + 1)
𝜏𝑠
(Eq. 2.62)
First order plus time delay
𝐾 =
𝜏
𝐾 · (𝜆 + 𝛳)
(Eq. 2.63)
(Eq. 2.64)
𝜏 = 𝜏
Where Eq. 2.63 and Eq. 2.64 can be substituted into Eq. 2.65.
𝐺 (𝑠) = 𝐾
1+
1
𝜏𝑠
(Eq. 2.65)
If the parameters for different transfer functions such as first order or first order plus time delay are
obtained, one of the main disadvantages that can be seen is that the integral part of the controller
doesn’t change with the tuning parameter. This makes it easier to tune but can be a problem if the
system has slow dynamics or a large dead-time. In this case the integral time will have a disproportional
value. Nevertheless, in order to mitigate this effect, the Skogestad’s theorem [23] that allows obtaining
smaller integral parts. It states that for large values of the time constants or systems with large deadtimes, the value of τI, will be the minimum of either the process time constant or 4 times the tuning
value plus the time delay.
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Master thesis
𝜏 = min{𝜏, 4(𝜆 + 𝛳)}
(Eq. 2.66)
2.3.6.5. Multivariable systems
When the system to control is a multivariable one the approach is quite different. There are two
options: a multivariable controller and a multiloop controller. In this project, multiloop controllers have
been used for cases 3 and 4, as they are easier to understand and require less parameters to tune.
About the tuning, there are multiple methods that can be used [21]:

Detuning method: each controller is designed ignoring process dynamics. Then, the process
interactions are taken into account by detuning the controllers until the result achieved is
satisfactory.

Sequential loop method: the controller for a selected process variable and manipulated variable
is tuned and that loop is closed, then the second controller is tuned and its loop is closed too, and
so on for every controller in the process. The main advantage is that it is a simple method, while
the main disadvantage is that it is heavily reliant on the first controller tuned.

Independent loop method: each controller is designed based on the open-loop transfer functions
of each process.
2.3.7.
Control system test
Once the control system has been designed and tuned, it must be tested in order to prove its efficiency.
It can be done by simulating a wide variety of set-point changes and disturbances. For the same case,
different control schemes were tested. To better compare them, the Event Scheduler tool provided by
HYSYS has been used. This tool allows programming the disturbances and makes it easier and faster to
reproduce them at the same specific simulation time. The set-point changes and the disturbances are
equal for all the parameters tested.
In order to objectively verify which response is better, some indicators can be used [29]. These are the
IAE (Integral of the absolute value), ISE (Integral of the squared error) and ITAE (Integral of the timeweighted absolute error).
34
𝐼𝐴𝐸 =
|𝑒(𝑡)|𝑑𝑡
𝐼𝑆𝐸 =
𝑒(𝑡) 𝑑𝑡
(Eq. 2.67)
(Eq. 2.68)
Training Course in Simulation of Chemical Process Control
𝐼𝑇𝐴𝐸 =
𝑡|𝑒(𝑡)|𝑑𝑡
Alex Nogué, Pasquale Orlo
(Eq. 2.69)
The IAE integrates the error over time without adding weight to the errors. ISE integrates the square
of the error over time, which penalizes large errors. While the ITAE integrates the absolute error
multiplied by the time, which weights errors that exist after a long time more heavily than those at the
start of the response [30].
It is desired that these indicators have a value as small as possible, which would mean that the errors
obtained are really small. In some cases, it could happen that different responses obtain better results
on different indicators, this would mean that the response performs better on what that indicator
values the most.
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Master thesis
3. Course design
The aim of this course is to train engineers in facing the process control issue by the use of a
professional process simulator, taking advantage of the big computational power nowadays available.
Once attended the course, knowledge about both process control and dynamic simulation will be
acquired. Through this, the engineer can afford solving control design tasks in a relatively quick way,
with no need of performing experimental disturbances in the real plant, making it safer. Furthermore,
the engineer will be able to compare different control schemes and choose the one which best suits
the problem.
There are many other similar training courses on this topic. Inprocess, Chemstations and PSE, are some
examples of companies that offer these services. Each one uses a process simulator (Aspen Hysys,
ChemCad, gPROMS) to accomplish different educational objectives, which include initiation to process
simulation, modelling advanced reactor or designing control systems among others. Many kinds of
training courses are given frequently, which means that there is a good demand for this product.
The current course may differ from the others in the difficulty level, since it pretends to be a basic
course. The idea is to design a course not only for chemical engineers, but for whoever may want to
approach process control and, above all, for non-experienced engineers. In order to do so, the course
has been organized in cases of increasing difficulty, where the knowledge acquired through one case
is then integrated in the next one to make a further step. Like all the courses, the teaching language is
English, since it allows further market opportunities.
3.1. Potential attendee and educational objectives
Any engineer whose role includes process control tasks could be interested in this course. The following
potential attendee profiles can be considered:


Chemical or control engineering student wishing to educate deeply in process control before
getting to work.
Any engineer wishing to get started with chemical process control or interested in this kind of
approach.
The knowledge and skills provided by this course are summarized through the following educational
objectives:

To identify the process variables, the input variable, the set-point and the control element given
a certain process to be controlled.

To learn the basic control theory.

To learn the basic process dynamic concepts.
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo

To understand the effect of different disturbances in a process and how to reduce them.

To learn to perform dynamic simulations and control them in Aspen HYSYS.

To apply the system identification method, obtaining the transfer function of the process.

To analyse and tune control alternatives for the same process.

To perform a multivariable control.
Anyway, in order to make sure that the attendee will be able to accomplish all these objectives, some
few requirements are needed. Familiarity with the steady state simulation and MATLAB environment
is recommended. In addition, a basic knowledge about the classical techniques and mathematical
modelling could provide a richer experience for the attendee.
3.2. Selected cases and course schedule
The intention is to facilitate everyone’s approach to the course by starting with an easy case where no
specific process knowledge or experience is needed. The control of the tank liquid level is a good
starting point since it only needs the conservative principle of matter to be applied. In addition, it only
has one variable to be controlled and the process dynamic is very intuitive. The simplicity of this case
allows an easier introduction on control theory, process dynamics and types of control valves, and
alternative control strategies (feedback with different MV and cascade control loop). Furthermore, it
is used to compare the mathematical modelling with the professional chemical process simulators
approach, highlighting the benefits provided by the last one.
Then, another process with only one variable to be controlled is faced. The heat exchanger is a very
common unit in chemical plants and allows introducing the temperature control, which is directly
linked to plant safety and production objective. In this case, the system requires knowledge about the
heat transfer phenomena and the design parameters of the equipment. However, through a brief
introduction on the heat exchangers and the dynamic analysis of the process, even the attendee who
does not have a chemical engineering education will be able to accomplish all the course objectives
planned for this case. Furthermore, as the attendee has already used more than one control strategy
in the first case, the heat exchanger case is used to introduce the feedforward control loop. Once again,
a comparison between the possible control schemes helps the attendee to decide which one is the
best option for the proposed problem.
The third case serves as an introduction to multivariable control, taking advantage of the tools acquired
through the previous two cases. The heated tank is a process with two variables to be controlled: the
liquid level and the temperature. Moreover, the two variables are not independent. For instance, if the
temperature increases the water density increases too and the liquid level rises. On the other hand, if
the liquid level decreases, the heat is absorbed by a smaller amount of liquid, so the temperature
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Master thesis
increases. The principles behind this process have already been analysed in the first two cases, which
makes it easier to introduce the RGA and SVA methods and the multiloop tuning.
By the moment, the cases have been selected in order to have a smart increasing difficulty level. The
last case reunites the knowledge acquired through all the other cases all in one, but still adding some
more difficulty due to a higher process dynamic complexity and number of variables. The distillation
column is a very common separation unit in chemical plants. Since the separation strategy involves
thermodynamic concepts, a brief theoretical introduction about distillation process is included. The
dynamic analysis helps understanding the relation between the many process variables, stating clearly
that the dynamic simulation, and so the course approach, is very useful to get a deeper view in process
control.
The course has been organized in three days. Here is the schedule and timing:
Module
Content Description
Time
Day
Introduction to the control problem
1
Tank Liquid Level open loop example using mathematical
modelling approach (MATLAB and SIMULINK).
Introduction to control terminology (set point, process
variable, disturbance etc…).
2h
Initiation to Dynamic Simulation
2
Tank Liquid Level open loop example by simulation using
Aspen HYSYS. Steady state simulation and transition to
dynamics mode. Dynamics concepts (pressure driven
process, control valves, resistance equation, capacitance,
hydrostatic pressure etc…). Stripcharts. Benefits of the
capacitance on controllability. Comparison between the
two approaches and difference analysis.
2h
Liquid Level Control
3
38
Tank Liquid Level closed loop. Exporting Data from HYSYS
and application of the system identification method. PID in
HYSYS. Feedback and cascade control loop. IMC tuning of
PID. Controller test using the Event Scheduler tool.
3h
DAY 1
Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Dynamic Simulation of a Heat Exchanger
4
Heat transfer concepts and dynamic simulation of a heat
exchanger. Analysis of the effect of the volume on the heat
transfer. Dynamic analysis of the open loop responses to
temperature and flow disturbances.
2h
Temperature Control Loops
5
Feedback, Cascade and feedforward + feedback control
loop for temperature control in a heat exchanger.
Comparison using the Event Scheduler and evaluation of
the best control strategy.
2h
DAY 2
Initiation to Multivariable Control
6
Dynamic simulation of a tank constantly heated using
steam passing through the tube bundle. Dynamic analysis
to study the dependent variables and their relations.
Simultaneous temperature and level control. Introduction
to RGA and SVA for the variable pairing. Introduction to
multiloop tuning.
3h
Distillation Column Simulation
7
Distillation theory and VLE concept introduction. Shortcut
and steady state simulation for a binary distillation column
of n-butane and n-pentane. Dynamic simulation of a
distillation column adding equipment by equipment.
Dynamic analysis to better understand the relation
between all the variables.
2.5 h
DAY 3
Distillation Column Control
8
Degrees of freedom and possible control schemes. RGA
analysis. Tuning of the controllers. Comparison between
the proposed control strategies selecting the one which
best suits the process requirements.
3.5 h
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Master thesis
3.3. Didactic material
The professor will guide the attendees in the cases resolution, solving the case himself/herself. In
addition, the attendee can rely on simulation manuals for each case, where the resolution is guided
step by step. Furthermore, intermediate simulation files are provided for the attendee to have many
starting points and maintain the class rhythm in case of necessity. This is also useful in case the
attendee wanted to repeat the cases once the course is over. Further documentation available for this
course is:

IMC tuning method document: an introduction to the IMC method and a demonstration of how
to obtain the controller parameters.

Event scheduler manual: a step by step guide to the use of Event Scheduler tool applied to a
general case.

Data export by .csv: a brief explanation on how to export data from HYSYS to use it elsewhere.

Piping and instrumentation diagram (P&ID) document: an introduction to the drawing of P&ID,
explaining the basic standards for the representation of each control system element.
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
4. Cases and results
This chapter shows all the selected cases that are going to be addressed to the course. For each one of
them, the most relevant aspects of the dynamic simulation have been explained and, in order to
concern the attendee with the process dynamics, the open loop behaviour of each system has been
analysed under the effect of many disturbances. Finally, each chapter reports the results for different
control strategies, each one tested under the same conditions.
4.1. Tank liquid level
The first case regards the control of the liquid level in an atmospheric tank. It was decided to simulate
the system in both MATLAB-SIMULINK, using the mathematical model, and HYSYS. Finally, the open
loop responses have been compared in order to state the differences between the two results and the
benefits or disadvantages of each approach.
4.1.1.
Mathematical modelling of the atmospheric tank
The proposed system is a tank open to the atmosphere with only two streams, as shown in Figure 4.1.
When in steady state, the inlet flow (Fi) equals the outlet flow (Fo) and the liquid level is fixed to a value.
Figure 4.1. Flow diagram of the tank.
By applying the material balance to this process, the transient behaviour can be modelled. This
equation [31] states that the inlet flow minus the outlet flow equals the rate of accumulation in the
tank.
𝐹 − 𝐹 =
𝑑𝑉
𝑑𝑡
(Eq. 4.1)
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Master thesis
So, if the inlet flow is higher than the outlet flow, the rate of accumulation will be positive and the
liquid level rise, while if it is lower, the rate of accumulation will be negative causing the level to drop.
Considering a vertical cylindrical tank, the hold-up volume is the base area of the tank multiplied by
the height of liquid (F is the volumetric flow):
𝐹 − 𝐹 = 𝐴·
(Eq. 4.2)
𝑑ℎ
𝑑𝑡
The outlet flow depends on the valve opening, the valve unknown constant and on the hydrostatic
pressure. The latter causes the height of the liquid inside the tank to be proportional to the square root
of the height of liquid inside the tank. So, the material balance turns to be:
𝐹 − 𝑘 · 𝑉𝑎𝑙𝑣𝑒𝑂𝑝𝑒𝑛𝑖𝑛𝑔 · √ℎ = 𝐴 ·
𝑑ℎ
𝑑𝑡
(Eq. 4.3)
If the terms of the equation are rearranged, Eq. 4.4 is obtained:
𝑑ℎ
𝐹 − 𝑘 · 𝑉𝑎𝑙𝑣𝑒𝑂𝑝𝑒𝑛𝑖𝑛𝑔 · √ℎ
=
𝑑𝑡
𝐴
(Eq. 4.4)
In order to calculate the unknown constant of the valve (k), the equation has to be considered in
steady-state, in which the derivative term is equal to zero. The initial value of the height is 1.024 m
(50% of total height) and the valve opening is 50%:
𝑘=
𝐹𝑖
√ℎ · 𝑉𝑎𝑙𝑣𝑒𝑂𝑝𝑒𝑛𝑖𝑛𝑔
=
0.002495
√1.024 · 0.5
= 4.93𝑒 − 3
(Eq. 4.5)
Simulating this system in SIMULINK with the calculated k value demonstrates that the system is at
steady state. Figure 4.2 shows that the graphic of the liquid height over time is flat, hence the liquid
level has remained constant at 1.024 m.
In order to observe a change in the height value, a positive disturbance has been introduced in the
input flow. The liquid level rises until a new equilibrium is reached at a higher height value. The
response obtained is a first order type, which demonstrates that the model could be approximated to
a linear ODE.
42
Alex Nogué, Pasquale Orlo
Height (m)
Training Course in Simulation of Chemical Process Control
Figure 4.2. Steady state simulation.
Open Loop Response to a Step Disturbance
1.6
1.5
Height Value
Height (m)
1.4
1.3
1.2
1.1
1
0
50
100
150
200
250
300
Time (minutes)
Figure 4.3. Open loop response of the system to a flow disturbance.
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Master thesis
4.1.2.
Atmospheric tank using Aspen HYSYS
In order to simulate an atmospheric tank in HYSYS, a steady state simulation has been performed first.
It has then been converted to a dynamic simulation making the proper modifications explained here.
For more details about the simulation see Simulation Manual – Tank Liquid Level in Appendix C1, where
you will find a step by step simulation guide for this case.
The tank feed has the following specifications:
Table 4.1. Tank feed specifications.
Temperature
Pressure
Std. ideal Liquid Vol. Flow
Molar fraction H2O
Molar fraction N2
Molar fraction O2
FEED
25 ºC
140 kPa
9 m3/h
1.00
0.00
0.00
The need of nitrogen and oxygen will be discussed later. The fluid package used for the system H2ON2-O2 is Peng-Robinson.
The steady state simulation only requires 3 material streams and a vessel, which only needs connection
information.
Figure 4.4. Tank Liquid Level: Steady state flowsheet.
The results are resumed in Figure 4.5. As expected, all the water that enters the system exits from the
bottom of the tank and there is no flow through Vapour stream. As it can be seen, the simulation can
be done without knowledge of the liquid level.
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Figure 4.5. Tank Liquid Level: Steady state worksheet.
Even if the material balance is correct, this simulation does not provide a faithful reproduction of
reality. If you observe the pressure values, there is no pressure drop along the system. This is wrong
for two reasons:

No pressure drop means that there is no flow through the tank.

In a half-filled tank, there is a column of liquid that contributes to the pressure, so the pressure
at the bottom of the tank should be higher than the one at the liquid surface.
Furthermore, considering that every vessel in HYSYS is closed, there is no information about the 50%
tank volume left. To simulate an open tank there should be air at atmospheric conditions entering or
exiting depending on whether the liquid level drops or rises respectively.
4.1.2.1. Dynamic simulation
In order to convert the simulation to a dynamic one, many modifications must be made. First of all, the
vessel must be sized. This allows having information about the liquid height and the residence time of
the hold-up liquid. A flat vertical cylinder tank is chosen with a 3 m3 volume. Aspen HYSYS automatically
calculates a diameter and a height:
Figure 4.6. Tank Liquid Level: Tank sizing.
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Master thesis
Then, to better model this system, a valve is added to each stream obtaining the following flowsheet:
Figure 4.7. Tank Liquid Level: Steady state flowsheet with valves.
Each valve has a linear inherent characteristic (liquid level control) but they have been sized differently:

Feed valve (VLV-100): It has a 50% opening and the pressure drop equals the difference
between FEED pressure (140 kPa) and the inlet pressure to the tank (101.3 kPa = 1 atm). With
these data and the flow passing through the valve, the Cv can be obtained by auto-sizing with
the ANSI/ISA method.

Liquid valve (VLV-102): It also has a 50% opening but the pressure drop is calculated differently.
As the steady state simulation does not take into account hydrostatic pressure, the pressure
at the bottom is not real. The pressure due to the liquid height can be calculated through the
following equation:
∆𝑝 = 𝜌𝑔∆ℎ
(Eq. 4.6)
The density can be obtained by the Liquid stream properties, while the height of liquid depends
on the liquid level desired. In this case, the height of the tank is 2.048 m and, as the liquid level
wanted is 50%, Δh will be 1.024 m. Considering that the outlet pressure is the atmospheric
one, this pressure differential will be equal to the pressure drop in the Liquid valve:
∆𝑝 = 1007
𝑘𝑔
𝑚
1 𝑘𝑃𝑎
· 9.81 · 1.024 𝑚 ·
= 10.12 𝑘𝑃𝑎
𝑚
𝑠
1000 𝑃𝑎
(Eq. 4.7)
Once again, with this data and the flow through the valve, the Cv value is obtained by autosizing.

Vapour valve (VLV-101): This valve does not exist in the real process, but here it has been
included for integration purposes. So, there should be no resistance through this valve, that’s
why the opening is set to 100% and the Cv to 1E+05, a very high conductance value.
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Training Course in Simulation of Chemical Process Control
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Unlike the steady state mode, the dynamics mode allows simulating reversal flows with components
that are not entering the system. This feature has been employed to simulate the air dynamics. In the
Vapour 2 stream, in the Product Block section, it has been specified that for reversal flows, a stream
containing 0.79 N2 and 0.21 O2 at 25ºC should enter the system.
In order to reproduce the reality properly, one last feature must be considered: the height of the
equipment. As hydrostatic pressure is taken into account, the height difference between a valve and
the connection to the tank could lead to pressure loss. That’s why it is very important to select the
vessel nozzles heights first:
Figure 4.8. Tank Liquid Level: Nozzles height.
The Feed inlet is set to 100% of the total tank height because, in this way, the water always enters the
tank at atmospheric pressure, even if the liquid level exceeds the 50%. If the feed nozzle would be at
40%, the pressure would be higher due to hydrostatic pressure. For similar reasons, the liquid nozzle is
maintained to 0% of tank height in order to have the maximum possible pressure at the bottom in
every scenario. The Vapour nozzle is maintained to 100% because, for lower heights, there could be
liquid loss. Finally, to avoid additional pressure loss, the valves heights are set equal to the tank nozzles
ones.
Through these modifications, the process modelling has been improved and made much more realistic.
However, before performing a dynamic simulation, other features must be revised. As explained in
chapter 2.3.2, in dynamics mode the solver is a pressure-flow solver. This means that it needs pressure
specifications in order to determine the stream flows. The Dynamics Assistant is a very useful tool that
can help in setting these specifications. Figure 4.9 shows the suggestions for the steady state
simulation:
Figure 4.9. Tank Liquid Level: Dynamics Assistant suggestions.
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Master thesis
The HYSYS manual suggests setting the pressure specifications in every boundary stream and avoiding
the flow specifications. In Figure 4.7, these specifications are better visualized through the colour code:
green streams have pressure specification only, yellow streams have flow specification only, blue
streams have no specification, while red streams have both pressure and flow specification.
All the dynamics specifications can be modified in the Dynamics tab of each equipment. To correctly
solve the integration, the valves should also have the pressure-flow relation activated (default option).
If this option is not selected, the pressure drop, and so the Cv, are not allowed to change losing realism
in the simulation.
Figure 4.10. Tank Liquid Level: Valves dynamics specifications.
The starting point can also affect the dynamics behaviour. As a continuous process is to be simulated,
the initial liquid level must be 50%:
Figure 4.11. Tank Liquid Level: Tank starting point.
Note that the static head contribution must be enabled in the integrator tab. The progress of the
dynamic simulation can be monitored through the Strip Chart, which are graphics where the chosen
variables actualize their value as time passes by. Running the simulation during 200 minutes provides
the following results:
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Figure 4.12. Tank Liquid Level: Dynamic simulation results (200 min).
Figure 4.12, at the beginning, shows an incoherent behaviour which has to be ignored: Liquid
volumetric flow decreases and then increases in a short period of time, which leads to a liquid level
rise. This is due to an initial phase where pressures need to stabilize, yet at time 0 static head
contribution is taken into account and there is a rapid change in the pressure at the bottom of the tank.
Finally, the output flow equals the input flow (FEED volumetric flow) and the liquid level stabilizes at
50%. No more change is observed, which means that a steady state has been reached.
Figure 4.13. Process pressures in dynamic simulation (200 min).
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Master thesis
Observing the process pressures in the flowsheet, it can be seen how the bottom pressure raised due
to the hydrostatic pressure.
Figure 4.14. Process mass flows in dynamic simulation (200 min).
Observing the process mass flows in the flowsheet, it can be seen that a negative flow is in the head of
the tank, which means that air is entering. However, it is negligible respect to the inlet and outlet flows.
4.1.2.2. Open loop response in HYSYS
In order to obtain the system open loop response, a feed flow disturbance is induced in the process.
To do so, a pressure change in FEED stream is done: from 140 kPa to 160 kPa, and then from 160 kPa
to 120 kPa. Changing the inlet pressure will affect the pressure drop and so the flow passing through
the system. It also could be done by forcing a flow specification; however, the pressure change method
is more realistic.
The first disturbance causes a FEED flow increase. The FEED flow changes instantaneously from 9 m3/h
to 11.08 m3/h, being a step disturbance. The tank begins to accumulate water and liquid level rises.
Consequently, hydrostatic pressure increases and so does the Liquid flow. A new steady state is
reached when Liquid flow equals FEED flow.
The second disturbance causes a FEED flow decrease. Again, it is a step disturbance, but as the outlet
flow is higher than the inlet flow, the liquid level drops until the flows are equals and equilibrium is
reached again at a difference liquid level.
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Training Course in Simulation of Chemical Process Control
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Figure 4.15. System response to FEED flow disturbances.
A mass flow Stripchart has been created to see what happens to Vapour Flow:
Figure 4.16. Vapour flow response to disturbance.
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Master thesis
At the beginning there is a relatively great increase in the flow outside of the tank. This is due to the
liquid level rise. By rising, water displaces the air above it. As the rising rate decreases with time, the
Vapour flow starts to decrease until becoming approximately null. The opposite happens with the
second disturbance. As Liquid Level drops, more air enters the tank. When the dropping rate begins to
decrease, the vapour flow returns to an approximately null value.
Figure 4.17. Pressure response to disturbance.
The same behaviour observed in Figure 4.15 is in Figure 4.17, yet flows depend on pressure. Only
Vapour pressure does not change because the tank is open to the atmosphere. The flow is only due to
the liquid displacement.
4.1.2.3. Capacitance effect
In order to better study the capacitance effect on the system response, the same process was
reproduced but a tank volume of 9 m3 was used this time. The feed stream is exactly the same, the only
difference is in the diameter of the tank, yet the height was fixed at 2.048 m as the first tank, to avoid
hydrostatic pressure differences. Both systems were studied for disturbances in the feed flow (dashed
lines represent the bigger, B, tank variables):
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
Figure 4.18. Capacitance study: Stripchart legend.
Figure 4.19. Capacitance study: Open loop response (160kPa and 120kPa).
The system behaviour is the same as explained before. It can be seen how the bigger tank reaches the
same final value but in much more time being the liquid level change smoother. For example, for the
first disturbance, the stabilization time was 150 minutes for the smaller tank against the 400 minutes
for the bigger tank. A further analysis can be done inducing a flow disturbance with consecutives
positive and negative steps:
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Master thesis
Figure 4.20. Capacitance study: Open loop response (Consecutive disturbances).
Pressure changes from 160 kPa to 120 kPa were performed each 5 minutes. It can be seen how the
bigger tank response is smoother all the time. The liquid level is maintained to low values and the outlet
liquid flow oscillates less. This proves why capacitance improves the process controllability. The reason
is that “the same force” is trying to move a bigger mass of water. As the inertia is higher, the
acceleration is lower and the system behaves smoother.
4.1.3.
Comparison between MATLAB and HYSYS
Once the system has been simulated in both MATLAB and HYSYS, the open loop responses are
compared. In order to do so, the same feed flow disturbance has been induced. In HYSYS a pressure
change from 140 kPa to 160 kPa leads to a flow increase of 2.09 m3/h, which is the step input
introduced in MATLAB. Exporting the HYSYS experimental results into MATLAB, it can be seen that
both responses are identical:
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Training Course in Simulation of Chemical Process Control
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Comparison of Open Loop Responses
1.7
SIMULINK Values
HYSYS Values
1.6
Height (m)
1.5
1.4
1.3
1.2
1.1
1
0
50
100
150
200
250
300
Time (minutes)
Figure 4.21. Comparison of the HYSYS and MATLAB open loop response to a pressure disturbance.
To further test the system, a set-point disturbance was induced to see how both systems behave and
to see if when facing another type of change they would still be similar.
Comparison of Open Loop Responses
1.4
SIMULINK Values
HYSYS Values
1.35
1.3
Height (m)
1.25
1.2
1.15
1.1
1.05
1
0
50
100
150
200
250
300
Time (minutes)
Figure 4.22. Comparison of HYSYS and MATLAB open loop response to a set-point change.
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In Figure 4.22, it can be seen again that both curves are almost identical, which demonstrates that the
MATLAB and HYSYS models are able to achieve the same responses.
If one compares the simulation requirement for each program, the MATLAB model can be the best
option if the liquid level response is the only objective, since it’s time-saving and only needs an
equation, which is the material balance. In contrast, HYSYS requires simulating the air dynamics, the
selection of a fluid package, the proper sizing of the valves and the selection of the equipment height.
It takes into account the air-water interaction, water vaporization, frictional temperature changes, and
pressure-flow relations making the simulation much more complex than in MATLAB.
For this specific case, all these aspects were negligible and maybe HYSYS is not necessary. Nevertheless,
if the system changes, this statement can turn to be false. For instance, if the liquid was not water but
acetone instead, its volatility is not negligible and air interaction is very important. The same would
happen if a phase mixture feed entered the tank or if the temperature is much higher than the ambient
one. Moreover, the nozzles location makes the simulation more realistic, yet if the feed nozzle is below
the liquid level, the water would enter the tank at a different pressure due to the static head
contribution, which could affect the inlet and outlet flow. In addition, HYSYS allows a holdup analysis
that for more complex systems, with different composition, could be very useful.
It is possible to reproduce in MATLAB the same response as in HYSYS for any process. However, this
means adding many and many equations such as Peng-Robinson state equation, resistance equations
for valves or heat exchangers, material and energy balances for all the equipment, sizing relations, etc…
For all these reasons, the next cases will be simulated in Aspen HYSYS, yet all the equations are already
integrated and is much more interactive thanks to the software design.
4.1.4.
Liquid level control
By the moment, the tank has been simulated as an open loop system. As there is no feedback action,
the loop is very sensitive to noise and disturbances.
Figure 4.23. Open loop system.
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Training Course in Simulation of Chemical Process Control
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If a controller and a sensor were introduced and the control loop was closed, the process variable
would be used to differentiate the set-point with the output, comparing both values to achieve a better
control of the system.
Figure 4.24. Closed loop system.
From a control stand point, the objective is to maintain a constant liquid percent level inside the tank,
which is the desired value or set-point (SP). To perform this task, a controller must be added to the
system in order to regulate the opening of one of the valves depending on the current level value and
the set-point introduced. In that case, the valve opening would be the OP of the process.
There are multiple options when choosing the type of control to be used because, for most tanks, the
precision might not be the most important feature. In some cases, it might be a good option to tradeoff some precision for an easier control. If that is the case, an option could be using a proportional-only
controller. By doing so, the cancellation of the error might never be achieved, but the error would be
between the margins specified.
Another option would be using a PI controller, which is among the most popular for tanks level control
and all control systems in general. By using this type of controller, the cancelation of the error would
be achieved, as the proportional control would obtain a good result in decreasing the error and the
integral part would take it to the set-point.
The last option argued in this document is shown in [6], where two proportional controls and one PI
control have been used. High gain proportional controls are used when the level reaches its 90% and
10%, while in between this margin the Proportional-Integral is used.
In this case, it was decided to use the proportional and integral controller, since its implementation is
not the most complicated between the options mentioned, and because no off-set provided by a Ponly controller is desired.
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For the tank considered, there are two possible options to achieve the control objective: output and
input streams as manipulated variables. Both are acceptable and can provide good results. The only
difference between both control schemes is the transfer function of the process and the action of the
controller.
About the first scheme, the transfer function of the process is going to have a negative gain. This
happens because if the valve opens, the level is going to drop, meaning that one of the variables
involved in the gain calculation must be negative. The controller action must be direct because if the
level rises and it is greater than the set-point, the output valve must open for the level to reach the
desired value again.
Figure 4.25. Liquid tank control scheme using the output flow valve.
About the second scheme, shown in Figure 4.26, the transfer function of the process is going to have
a positive gain instead. This happens because if the valve opens, the level rises, and both parameters
involved in the gain calculation are positive. In terms of the control action taken by the controller, it
must be a reverse action. If the level rises and it is greater than the set-point, the valve must close.
In order to demonstrate the differences between both system and that both schemes can be
implemented obtaining good results in both set-point tracking and disturbance rejection, both cases
have been simulated.
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Training Course in Simulation of Chemical Process Control
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Figure 4.26. Liquid tank control scheme using the input flow valve.
4.1.4.1. PID Controller in HYSYS
The controlled in HYSYS can be added from the model palette together with all the other modules. It
first requires 2 connections: the PV, the variable that is going to control, and the OP that is the variable
that is changed to reach the SP. In each case of this project, the OP is the valve opening of the control
valve.
Figure 4.27. HYSYS controller “Connections” tab.
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Master thesis
Once these variables have been selected, the next step is to configure the parameters tab:
Figure 4.28. HYSYS controller “Parameters” tab.
As Figure 4.28 shows, it can be set if the controller has a Direct or Reverse action. Then, the set-point
mode can be chosen to be on Local, if the set-point is given by the user, or on Remote, if it is given by
another controller. In the Mode specification, several can be chosen:





Off: The controller doesn’t track the PV.
Manual: The controller is not running but the OP can be changed from the controller tab.
Automatic: The OP is set by the PID algorithm selected.
Casc: For the cascade mode. It is only available when another controller is attached.
Indicator: PV tracking is enabled, but the OP is static.
In the PV range, both maximum and minimum values must be specified. In order to determine the
range, general rules have to be followed. For example, for liquid levels, the percentage will go from 0
to 100 %, but in flow controllers the minimum will be the flow passing through the valve when it is
completely closed (0 kg/h) and the maximum will be the flow when the valve opening is 100%. It is
encouraged for these tests to be performed when the system is operating in nominal conditions.
Several PID algorithm types can be chosen, such as HYSYS, Honeywell, Foxboro, Yokogawa, but for all
the cases in this project, the default option has been used (HYSYS algorithm) [5]. The algorithm subtype
indicates the form of the PID controller. Different types can be chosen but for each case the Velocity
form has been selected as it contains some advantages that other forms don’t, as it was already argued
in chapter 2.3.6.1.
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Training Course in Simulation of Chemical Process Control
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4.1.4.2. Feedback control: Output flow
If the outlet flow is selected as MV, the OP is the valve opening of the output valve while the PV is the
liquid level inside the tank. Figure 4.29 shows the block diagram of the process, where two transfer
functions are obtained. These functions are the relation between the height of the system and the setpoint, and between the same process variable and the main disturbance of the system.
Figure 4.29. Staring block diagram of the liquid tank control scheme.
Following the methodology explained in chapter 2.3.4, from the open loop response of the tank, a first
order model has been obtained.
𝑌 (𝑠)
−2.35
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠]
=
𝑈(𝑠)
25.12𝑠 + 1
(Eq. 4.8)
About the disturbance, if a step input is applied in the pressure, the transfer function in Eq. 4.9 is
obtained:
𝑌 (𝑠)
1.23
%
=
𝐷(𝑠)
23.44𝑠 + 1 𝑘𝑃𝑎
(Eq. 4.9)
With both transfer functions calculated, the final block diagram is shown in Figure 4.30.
Figure 4.30. Block diagram of the tank.
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As already stated in Chapter 2.3.6, the characteristic equation obtained for the system, is the same one
for the set-point and disturbance closed loop transfer functions, and because of this the Routh-Hurwitz
criterion can be applied in order to obtain the margins of stability for the controller.
1 + 𝐺 𝐺 𝐺 = 25.12𝑠 + 𝑠(1 − 2.35𝐾 ) − 2.35𝐾 = 0
(Eq. 4.10)
If the Routh array is constructed, the following matrix is obtained:
𝑠
𝑠
𝑠
(Eq. 4.11)
25.12 −2.35𝐾
1 − 2.35𝐾
0
−2.35𝐾
0
Since all the parameters must be positive, the limit parameters for the controller are going to be:
𝐾 < 0.43
(Eq. 4.12)
𝐾 <0
(Eq. 4.13)
Where KI = KC/τI. So, the Routh criterion states that the proportional gain should be smaller than 0.43,
which means that it will more likely be negative in this system. The integral gain needs to be negative,
which means that the proportional gain and the τI have opposite signs in order for the system to be
stable.
When applying the IMC tuning method, different values of λ will be tested in order to show the
difference between a faster and a lower response. The Skogestad’s theorem has also been applied to
work with a different value of τI.
Table 4.2. Controller parameters obtained for the different tuning parameters.
Kc
τI
IMC (λ = 3)
-3.56
25.12
IMC (λ = 20)
-0.53
25.12
SKO (λ = 3)
-3.56
12
In order to test the system, different SP changes and disturbances have been applied and the responses
obtained have been compared to appreciate the differences. The introduced disturbances are:
1.
2.
3.
4.
5.
Pressure change from 140 kPa to 160 kPa in minute 100.
Set Point change from 50% 30% in minute 500.
Pressure change from 160 kPa to 140 kPa in minute 900.
Set Point change from 30 %to 80% in minute 1300.
Set Point change from 80 % to 50% in minute 1700.
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Tank level case disturbances
200
Pressure disturbance
Set-point disturbance
190
100
90
180
80
170
70
160
60
150
50
140
40
130
30
120
20
110
10
100
0
200
400
600
800
1000 1200 1400 1600 1800 2000
0
Figure 4.31. Test disturbances applied in the system.
The level and controller output responses to those disturbances are shown in figures 4.32 and 4.33
respectively.
Figure 4.32. Response obtained for the different tuning parameters.
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Master thesis
Figure 4.33. Valve response to the different disturbances tested.
From Figures 4.33 and 4.34, it can be seen that the values obtained with the Skogestad limit value are
the best in both set-point tracking and disturbance rejection, however, they produce really high
changes in the control valve in a very short time, which in some systems might be a problem.
In order to objectively define which system obtains the best responses, the IAE, ISE and ITEA
performance criteria have been applied. The results are shown in Table 4.3.
Table 4.3. IAE, ISE and ITAE indexes obtained for the responses simulated.
IAE
ISE
ITAE
IMC (λ = 3)
1928.10
27257.70
16.10
IMC (λ = 20)
3746.40
49608.80
31.20
SKO (λ = 3)
920.30
15544.00
7.70
Where the units used for level are the percentage (%) and for time are minutes (min).
From the last table, it can be seen that the tuning parameters that provide a better response are the
ones obtained with the Skogestad method, which outclasses both other sets of parameters in all three
performance indexes. However, these parameters produce really aggressive changes to the control
element, which might put a lot of stress in the valve. So, the tuning that would be chosen for the tank
level case, depends on what it is pretended to achieve. For example, if a fast response and minimum
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Training Course in Simulation of Chemical Process Control
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error are needed, the parameters obtained with the limit of value would fit best. However, if a fast
response is not needed, it might be useful to considerate the IMC with a constant of 20.
4.1.4.3. Feedback control: Input Flow
If the manipulated variable is the input flow, the OP is the inlet valve this time. If the open loop
response is simulated, the transfer function of the system is the one shown in Eq. 4.14. As it can be
seen, it has a positive gain, unlike the one shown in the output flow control.
𝑌 (𝑠)
2.2
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠]
=
𝑈(𝑠)
23.44𝑠 + 1
(Eq. 4.14)
The block diagram of the system is the following.
Figure 4.34. Block diagram of the level tank.
With the block diagram, the closed loop transfer function can be obtained:
1 + 𝐺 𝐺 𝐺 = = 23.44𝑠 + 𝑠(1 + 2.2𝐾 ) + 2.2𝐾 = 0
(Eq. 4.15)
If the Routh array is constructed, matrix xx is obtained, and the limit parameters for the controller are
Eq. 4.17 and Eq. 4.18.
𝑠
𝑠
𝑠
23.44 +2.2𝐾
1 + 2.2𝐾
0
+2.2𝐾
0
(Eq. 4.16)
𝐾 > −0.45
(Eq. 4.17)
𝐾 >0
(Eq. 4.18)
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Master thesis
In this case, it can be seen that the value of the proportional gain will be positive, as well as the integral
part of the controller.
Again, if the IMC rules are applied into the calculation of the proportional and integral terms, the
following parameters are obtained:
Table 4.4. Controller parameters obtained for the different constant values.
λ
Kc
τI (w/limit of value)
4
2.64
16
5
2.12
20
6
1.77
23.44
In this case, as the difference between faster and slower parameters was already seen in the output
flow control, it was opted to use similar tuning parameters in order to observe the slight differences
between them. To test this simulation, the same disturbances used in the previous case have been
introduced
Tank level response for different tuning parameters
80
Level percentage (%)
70
60
50
IMC (lambda = 4)
IMC (lambda = 5)
IMC (lambda = 6)
40
30
20
0
200
400
600
800
1000 1200 1400 1600 1800 2000
Time (min)
Figure 4.35. System response for different parameters for the disturbances tested.
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Training Course in Simulation of Chemical Process Control
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Figure 4.36. Valve response of the different tuning parameters.
It can be seen that the control obtained for this process is really good as the tuning parameters are
small obtaining a really fast control with good disturbance rejection as well as set-point tracking. No
much difference can be appreciated between them.
Table 4.5. IAE, ISE and ITAE indexes obtained for the responses simulated.
IAE
ISE
ITAE
IMC (λ = 4)
99.46
168.97
8.28
IMC (λ = 5)
106.24
174.40
8.85
IMC (λ = 6)
120.80
181.14
10.07
The performance criteria confirm that each one of the three sets of parameters obtain good results,
being the ones obtained with the IMC for a tuning parameter of 4 the fastest in the group. Even though,
as already stated, all three controller parameters could be used as they obtain really good results in
the three indexes.
4.1.4.4. Cascade control
Even though the results obtained in both input and output flow cases provide a good control, it has
been simulated a cascade control scheme in order to test how much it improves disturbance rejection.
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Master thesis
In the cascade scheme, the PV of the primary controller is the liquid level inside the tank, while for the
secondary, the PV is the mass flow on the input stream. When it comes to the set-point, the set-point
of the primary controller will be given by the user, but for the secondary controller, the set-point will
be given by the primary.
Figure 4.37. P&ID of the cascade control scheme for the tank.
As it can be seen in the block diagram shown in Figure 4.38, the secondary process or the inner loop
process consists on the valve transfer function, which will be scaled to % in order to tune the controller.
Figure 4.38. Block diagram of the cascade control system.
As explained in the methodology, the first loop that has to be tuned is the inner loop, which is the flow
loop. The following graphic is obtained when a change in the controller output is applied while it is in
manual mode. It has been necessary to model the actuator with a first order model because an
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Training Course in Simulation of Chemical Process Control
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instantaneous response, as it was in the previous cases, would not provide a transfer function. A time
constant of 0.2 minutes was set arbitrarily. It does not really affect the main system since it is very small
compared to the large tank dynamics.
Flow resposne to step change
11000
10500
10000
9500
9000
8500
8000
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Time (min)
Figure 4.39. Inner loop response to the set-point change.
The transfer function of the system is:
𝑃(𝑠)
179.45
𝑘𝑔
0.99
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠]
=
=
𝑈 (𝑠)
0.2𝑠 + 1 ℎ · %
0.2𝑠 + 1
(Eq. 4.19)
The mass flow has been scaled in order to obtain the transfer function and the controller parameters.
The maximum and minimum parameters (PV range) are the ones obtained when the valve is fully
opened and fully closed. This range goes from 0 kg/h to 17960 kg/h.
If the Routh array is built for the inner loop controller, the margins of stability obtained are:
𝐾 > −1
(Eq. 4.20)
𝐾 >0
(Eq. 4.21)
In order to tune the first controller, the IMC method has been used for a lambda parameter of 3:
𝐾 = 0.15
(Eq. 4.22)
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Master thesis
(Eq. 4.23)
𝜏 = 0.20
About the tuning of the master controller, the slave controller has been put in cascade mode with the
set of tuning parameters already placed in the flow controller. A step change has been introduced in
the master controller output and the open loop response has been obtained.
Level resposne to step change in cascaded controller
90
85
Experimantal Values
First Order Approximation
Second Order Approximation
80
75
70
65
60
55
50
45
0
20
40
60
80
100
120
140
160
180
200
Time (min)
Figure 4.40. Fitting of the primary loop.
As it can be seen in Figure 4.40, the open loop response obtained resembles a second order model (Eq.
4.25), even though, as the second time constant of the system is really small, it could be also fitted into
a first order one (Eq. 4.24).
𝐻(𝑠)
2.30
=
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠]
𝑈 (𝑠)
24.12𝑠 + 1
(Eq. 4.24)
𝐻(𝑠)
2.30
=
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠]
𝑈 (𝑠)
25𝑠 + 26𝑠 + 1
(Eq. 4.25)
In this case, if the first order model is chosen, the IMC controller is built like in the previous cases.
Otherwise, if the second order model is chosen, the IMC controller incorporates a derivative
component.
About the tuning of the first order transfer function, if a parameter of 5 is selected, the parameters
obtained are the ones shown in equations 4.26 and 4.27.
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𝐾 = 2.09
(Eq. 4.26)
𝜏 = 20
(Eq. 4.27)
About the tuning of the second order transfer function, for the same constant value, the parameters
obtained are the following:
𝐾 =
2𝜉𝜏
2 · 2.6 · 5
11.30
=
=
= 2.26
𝜆·𝐾
𝜆 · 2.30
𝜆
𝜏 = 2𝜉𝜏 = 2 · 2.6 · 5 = 26
𝜏 =
𝜏
5
=
= 0.96
2𝜉 2 · 2.6
(Eq. 4.28)
(Eq. 4.29)
(Eq. 4.30)
In this case, the cascade scheme has been compared to the feedback scheme shown earlier; in order
to test it, two separate categories have been created, one consisting of set-point tracking, and the
other one consisting of disturbance rejection.
The set-point disturbances introduced to the system are:
1.
2.
3.
4.
From 50 % to 65 % in minute 100.
From 65 % to 25 % in minute 300.
From 25 % to 45 % in minute 500.
From 45 % to 50 % in minute 700.
The pressure disturbances introduced are:
1.
2.
3.
4.
From 140 kPa to 170 kPa in minute 100.
From 170 kPa to 150 kPa in minute 300.
From 140 kPa to 120 kPa in minute 500.
From 120 kPa to 140 kPa in minute 700.
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Master thesis
Temperature (ºC)
Figure 4.41. Different control schemes response to set-point tracking.
Figure 4.42. Different control schemes response to disturbance rejection.
From Figure 4.41, it can be seen that the three control systems are almost equally good at set-point
tracking, the main difference being in that the regular feedback produces less overshoot. Instead,
Figure 4.42 shows that the cascaded schemes perform much better at feed flow disturbance rejection
in both PI and PID cases than the feedback controller. The reason lies in the fastest detection of the
flow change due to the slave controller, so it mustn’t wait for a PV variation to start actuating.
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4.2. Heat exchanger
Another important variable to control in chemical processes is temperature. Reactor or column feeds
must enter at a specific temperature for the process to work optimally. Moreover, the temperature
must be controlled for safety reasons. For instance, in an exothermic reactor, a too high reactor
temperature could lead to a dangerous conversion rate, activating secondary reactions, producing gas
and increasing the pressure. If there is not a good control system, this can translate into a reactor
explosion [32].
The chosen case study to get started with the temperature control is the heat exchanger. It is a very
common unit in chemical plants which allows energy integration and is used, for example, to
condensate a stream or just to change its temperature to fit the requirement of the next process unit.
Each heat exchanger has a hot stream that will be cooled down and a cold stream that will warm up.
The heat transfer depends on the available transfer area A, the overall heat transfer coefficient U, and
the temperature gradient. The following equations describe the heat exchanger system:
𝑄 = 𝑈 · 𝐴 · 𝐹 · ∆𝑇
(Eq. 4.31)
𝑄= Ḟ
· 𝑐𝑝
· ∆𝑇
(Eq. 4.32)
𝑄= Ḟ
· 𝑐𝑝
· ∆𝑇
(Eq. 4.33)
Where:

Q is the heat transfer, which is the same for both fluids if heat loss is negligible.

ΔTml is the logarithmic mean temperature difference through the heat exchanger, determined
by the two temperature profile, the cold fluid one and the hot fluid one.

Ft is a correction factor of the ΔTml which depends on the configuration of the heat exchanger
(counter or co-current).

Ḟ is the molar or mass flow of the hot or cold stream.

cp is the specific heat capacity, assuming as a simplification that it does not vary with
temperature in the temperature range of the process.

ΔT is the temperature difference between the outlet and inlet stream.
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Master thesis
In the proposed case, the process stream is hot water at 60ºC and 180 kPa, with a flow of 100 kg/h
which must be cooled down to 40ºC. The available coolant is water at 5ºC and 180 kPa. The hot stream
enters the tube side while the coolant goes through the shell. Figure 4.43 shows the steady state
flowsheet:
Figure 4.43. Steady state flowsheet.
The PV is the temperature of the Hot OUT stream and the SP is 40ºC. In such a system there could be
many disturbances that will make the PV move from its desired value:

Process stream (hot fluid) flow disturbance

Process stream (hot fluid) temperature disturbance

Utility stream flow disturbance

Utility stream temperature disturbance

Fouling can decrease the overall heat transfer coefficient [33]

Strong changes in the environmental conditions increase the heat loss
4.2.1.
Dynamic simulation of a heat exchanger
As for the open tank, a steady state simulation has been performed and then properly converted to a
dynamic one. Here are the main aspects of the simulation remarking the differences between steady
state and dynamic simulation. For more details about the simulation see Simulation Manual - Heat
Exchanger in Appendix C2, for a step by step guide.
The only component used is water and the fluid package is ASME Steam. In order to run the steady
state simulation a heat exchanger configuration must be selected and the system fully specified. The
configuration used is a two tube passes and one shell pass, being the first a counter current pass. In
Figure 4.44, it can be seen how this configuration allows having a relatively high temperature
difference, which is the driving force of the heat transfer, all along the tube path.
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Figure 4.44. Heat Exchanger with U-tube configuration. [34]
The specifications applied are the following:

UA to 440 kJ/h·ºC

Pressure drop in tube-side and shell-side to 30 kPa

Hot OUT temperature to 40ºC
As a rigorous design of the equipment is out of scope for this project, all the design parameters are left
to their default options. The steady state simulation returns the following results:
Figure 4.45. Steady state simulation results.
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Master thesis
As expected, the duty exchanged (8371 kJ/h) is the exact one to bring 100 kg/h of water from 60ºC to
40ºC, as equation 4.32 estimates. The used specifications allow the calculation of the Ft Factor and the
Cold stream flow. So, 53.57 kg/h is the amount of coolant needed to achieve the process objective.
A valve has been added to each inlet stream for control purposes discussed further in this chapter. In
steady state mode the pressure drop specification is used, while a Cv value is needed in dynamics mode.
For each valve, the Cv has been obtained by auto-sizing with the ANSI/ISA method, with a 50% opening
and Equal Percentage inherent characteristic since a temperature control is to be performed. The only
difference is the flow passing through each valve and the pressure drop. About the utility valve, a higher
pressure drop has been selected in order to give it a higher flow range, since it is going to be the OP
(see chapter 4.2.3). Specifically, for the process stream valve (VLV-100) the pressure drop has been set
to 50 kPa, while for the utility stream valve (VLV-101) it has been set to 100 kPa.
The Dynamics Assistant makes the following suggestions:
Figure 4.46. Dynamics Assistant suggestion.
The first two suggestions refer to pressure specifications for all boundary streams and no more
specifications. The last two refer to the heat exchanger. As the valve, the heat exchanger is a resistance
element and need pressure-flow specifications and two conductance values, one for both tube and
shell paths (k parameter in Eq. 2.1). It is possible to auto-calculate the conductance value, but first of
all it is important to set the heights of the equipment and activate the static head contribution in the
integrator as hydrostatic pressure can affect the flow through the heat exchanger. The stream nozzles
of the heat exchanger have been set as shown in Figure 4.47:
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Figure 4.47. Nozzles height of the Heat Exchanger.
In this configuration, the hot fluid enters from above and exits at the bottom, while the cold fluid does
the opposite. The default maximum height is 1 m, so the process stream valve (VLV-100) height has
been set to 1 m, while the utility valve height to 0 m.
In the Dynamics Specs tab of the heat exchanger it is possible to visualize the dynamic specifications
and obtain the k values:
Figure 4.48. Conductance parameters k and pressure flow equation specification.
When simulating a heat exchanger in dynamics mode, three models are available: basic, intermediate
and detailed. The main difference is the possibility of specifying more or less geometry details. For this
project, the basic model is enough. This model allows selecting the tube and shell volume and the
overall UA only:
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Master thesis
Figure 4.49. Dynamic model of the Heat Exchanger.
The volume of the equipment is essential to determine the rate of accumulation and the hold-up of
the heat exchanger. To better visualize the importance of these specifications, two simulations have
been done. The first using the default tube and shell volume (0.1 m3 both) and the second one reducing
the tube volume to a ten part of its default value (0.01 m3). The results are shown using a strip chart
for the process temperatures and another strip chart for the enthalpies or duties of the process.
Figure 4.50. Temperature Stripchart Legend.
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Figure 4.51. Temperature Stripchart (tube volume = 0.1 m3).
The expected behaviour was a flat Stripchart since no disturbance was induced to the process.
However, the temperatures of the outlet streams move from their steady state value until they reach
a new equilibrium.
Figure 4.52. Enthalpy Stripchart (tube volume = 0.1 m3).
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Master thesis
Figure 4.53. Enthalpy Stripchart Legend.
Figure 4.54. Flowsheet DYN1.
The Exchanger Cold Duty and Hot Duty are the steady state duties, while s_Shell duty and s_Tube duty
are the real ones. It can be seen how they decrease rapidly at the beginning and then increase until
they stabilize to a lower value. This means that the exchanged energy is lower than in steady state
simulation. This explains why, at the exit of the heat exchanger, the hot fluid temperature increases
while cold one decreases. The reason behind this behaviour is in the accumulation inside the heat
exchanger, as the energy balance in the heat exchanger demonstrates:
𝑄
= 𝐻
−𝐻
−𝑄
−𝑄
(Eq. 4.34)
As much more accumulation, less heat exchanged. When switching to Dynamics Mode the volumes
are taken into account but the dynamic calculation is not initialized yet and there is not any option to
set a starting scenario. So, when running the simulation, the tube and shell of the heat exchanger start
filling up. Hence, the rate of accumulation at the beginning is maximum and then decreases with time,
which explains the great decrease of the duty exchanged and then its slower increase in the Enthalpy
strip charts.
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Figure 4.55. Temperature Stripchart (tube volume = 0.01 m3).
Figure 4.55 shows the same behaviour as Figure 4.51 but with a lower deviation of the outlet
temperatures. By reducing the tube volume, the accumulation in the tube side is reduced. The
exchanged energy (8084 kJ/h) is still lower than in the steady state simulation (8371 kJ/h), but higher
than in the previous case (7966 kJ/h). Even when the rate of accumulation is 0 and the system reaches
the equilibrium, the heat exchanged is lower than the calculated in steady state simulation. This is due
to the big difference between the residence time in tube and shell. A proper design would reduce the
duty deviation, however, the effect on the PV is negligible yet the temperature difference is less than
1 ºC (see Figure 4.57, PV=40.69ºC). In addition, it must be considered that the shell volume should be
designed with some tolerances since more coolant could be needed for control purposes.
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Master thesis
Figure 4.56. Enthalpy Stripchart (tube volume = 0.01 m3).
Figure 4.57. Flowsheet DYN2.
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4.2.2.
Alex Nogué, Pasquale Orlo
Disturbances and open loop responses
A set of disturbances was applied to the simulation in order to analyse the process dynamics.
1. 300-400 minutes: hot stream inlet pressure change from 180 kPa to 220 kPa. This is a flow
disturbance of 20 kg/h more approximately.
2. 400-600 minutes: hot stream inlet temperature change from 60ºC to 70ºC.
3. 600-800 minutes: cold stream inlet pressure change from 180 kPa to 160 kPa. This is a flow
disturbance of 5 kg/h less approximately.
4. 800-1000 minutes: cold stream inlet temperature change from 5ºC to 10ºC.
Figure 4.58. Temperature Stripchart: Open Loop response.
Observing Figure 4.58 and 4.60, the following conclusions can be done:

Disturbance 1: A higher flow means higher heat capacity and higher exchanged duty.
However, as this duty is going to be transferred by a greater amount of hot fluid than before,
the temperature difference will decrease and the PV will increase. The exchanged duty
increases at the beginning but then decreases when a new steady state is going to be reached,
since the temperature difference becomes lower.
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Master thesis

Disturbance 2: A higher temperature will increase the driving force obtaining a higher heat
transfer. However, this kind of disturbance will also make the outlet temperatures to be
higher than before (PV increases). The heat exchanged increases very fast at the beginning
but then falls smoothly until a new steady state is reached due to the decrease of the
temperature difference.

Disturbance 3: A coolant flow decrease means a heat capacity decrease which translates into
a lower exchanged duty. This leads to higher outlet temperatures (PV increases).

Disturbance 4: If the coolant enters the heat exchanger at a higher temperature, the driving
force will decrease and so does the exchanged duty. The outlet temperature will increase until
a new equilibrium is reached (PV increases).
Figure 4.60. Enthalpy Stripchart: Open Loop response.
The effect of each disturbance on the process variable depends on the type and on its magnitude.
However, if it is considered that the simulated disturbances are the limit cases for this process, the
temperature disturbance on the hot stream happens to be the most influent disturbance.
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4.2.3. Feedback control loop
In the heat exchanger, the process variable is the process stream output temperature and the
manipulated variable is the service stream input, which will be modulated through a valve in order to
face the disturbances previously mentioned. The proposed control scheme for the feedback controller
is shown in Figure 4.61, where the transmitter is placed in the process stream output, and it is
controlled with the valve in the service stream input.
Figure 4.61. P&ID of the feedback control scheme for the heat exchanger.
Once the open loop response has been obtained, the process transfer function can be fitted into a first
order obtaining Eq. 4.35.
𝑇 (𝑠)
−0.624
º𝐶
=
𝑈(𝑠)
64.35𝑠 + 1 %
(Eq. 4.35)
Now, in order to scale the transfer function obtained, the PV range must be known. In heat exchangers
set-point changes are not usual and in case they are demanded, the changes is really small. So, the
range selected is within 10 ºC of the nominal value and the range goes from 35 ºC to 45 ºC.
𝑇 (𝑠)
−6.24
%
=
𝑈(𝑠)
64.35𝑠 + 1 %
(Eq. 4.36)
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The block diagram of the feedback control loop for the heat exchanger is almost the same as the
control loop for the tank liquid level, where only the process stream input disturbance has been
considered.
Figure 4.62. Block diagram of the heat exchanger feedback system.
The closed loop transfer functions of set-point change and disturbance are Eq. 4.37 and Eq. 4.38, which
again, have the same denominator.
𝐺 𝐺𝐺𝐺
𝑇(𝑠)
=
𝑇 (𝑠)
1+𝐺 𝐺 𝐺
(Eq. 4.37)
𝑇(𝑠)
𝐺
=
𝑇 (𝑠)
1+𝐺 𝐺 𝐺
(Eq. 4.38)
Both functions have the same characteristic equation, which means they both have the same margins
of stability that have been calculated via Routh-Hurwitz method.
1 + 𝐺 𝐺 𝐺 = 64.35𝑠 + 𝑠(1 − 6.24𝐾 ) − 6.24𝐾 = 0
(Eq. 4.39)
With the Routh array, the margins obtained are Eq. 4.41 and Eq. 4.42.
𝑠
𝑠
𝑠
86
64.35 −6.24𝐾
1 − 6.24𝐾
0
−6.24𝐾
0
(Eq. 4.40)
𝐾 < 0.16
(Eq. 4.41)
𝐾 <0
(Eq. 4.42)
Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
In order to obtain the tuning parameters, the IMC method has been used again for different values of
λ:
Table 4.6. Controller parameters obtained for different methods used.
Kc
τI
IMC (λ = 5)
-2.06
64.35
SKO (λ = 5)
-2.06
20
SKO (λ = 7)
-1.47
28
Several set-point changes and disturbances have been added to test the different set of tuning
parameters:
1. Set-point change from 40 ºC to 42 ºC in minute 100.
2. Process stream input temperature change from 60 ºC to 70 ºC in minute 400.
3. Set-point change from 42 ºC to 38 ºC in minute 700.
4. Process stream input temperature change from 70 ºC to 60 ºC in minute 1000.
5. Set-point change from 38 ºC to 40 ºC in minute 1300.
Figure 4.63. Test disturbances for the feedback control system.
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Temperature(ºC)
Master thesis
Figure 4.64. Different tuning parameter responses to the disturbances introduced.
From Figure 4.64, some conclusions can be drawn. The first is that the fastest responses, which are the
ones obtained via the Skogestad’s method value present a light overshoot. This is due to big Kc value.
In this case, the values obtained without Skogestad’s limit provide the worst response due to the large
Valve Opening (%)
integral time, which makes the system really slow in both set-point tracking and disturbance rejection.
Figure 4.65. Valve response for the different tuning parameters.
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About the valve response, as it could be expected, the most aggressive responses are obtained for the
IMC where the limit value has been used.
In order to objectively compare the three tuning parameters proposed, the IAE, ISE and ITAE
performance criteria will be used again:
Table 4.7. IAE, ISE, ITAE obtained for the heat exchanger control system.
IAE
ISE
ITAE
SKO (λ = 5)
190.92
303.71
1.59
IMC (λ = 5)
366.88
451.30
3.05
SKO (λ = 7)
237.87
366.87
1.98
The performance criterion confirms that the IMC with the limit value and the tuning parameter of 5
obtains the best performance out of the three tested, closely followed by the one with the tuning
parameter of 7.
4.2.4. Cascade control loop
In a cascade control system, the main difference with the feedback control is that the output of the
temperature controller is fed into another controller instead of going directly to the valve. This second
loop, is responsible for ensuring that the flow rate of the cold liquid doesn’t change due to faults that
cannot be controlled, for example, irregularities in the cold liquid distribution. In this cascade scheme,
the process variable of the primary controller is the process stream output temperature, while the PV
of the second controller is the input mass flow of the service stream.
Figure 4.66.P&ID of the cascade control for the heat exchanger.
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Master thesis
By implementing cascade control, the flow controller will adjust the valve position in case that a
disturbance occurs in the service stream input. For instance, due to other users’ demands, the pressure
could drop leaving the system with less flow than usual. In a feedback control, in order to counter that
disturbance, the system would wait until the process variable has been modified, while in a cascade
control, the second controller would act immediately modifying the control valve stem position.
If the open loop response of the flow controller is obtained, it can be seen that the obtained transfer
function consists on the transfer function of the valve:
𝐹(𝑠)
2.19
%
=
𝑂𝑃(𝑠)
0.2𝑠 + 1 %
(Eq. 4.43)
Building the Routh array for the first controller provides the margins of stability:
𝐾 > −0.45
(Eq. 4.44)
𝐾 >0
(Eq. 4.45)
Before obtaining the open loop response of the primary controller, the secondary one has to be tuned
first and closed. In order to do so, the IMC method for a first order transfer function has been used
with a tuning parameter of 0.6, obtaining Eq. 4.46 and Eq. 4.47.
𝐾 = 0.15
(Eq. 4.46)
𝜏 = 0.20
(Eq. 4.47)
Once the inner loop has been closed, a step input can be introduced in the system and the open loop
response of the primary loop can be obtained. For this loop, the transfer function is Eq. 4.48 and the
fitting is shown in Figure 4.67.
𝑇(𝑠)
−2.30 %
=
𝑂𝑃(𝑠)
55𝑠 + 1 %
90
(Eq. 4.48)
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System response to a master controller change
41.5
Experimental Values
First Order fitting
41
40.5
40
39.5
39
38.5
0
50
100
150
200
250
300
350
400
Time (min)
Figure 4.67. Primary loop fitting of the set-point change response.
Different constants have been tested for the IMC controller, obtaining the parameters shown in the
Table 4.8.
Table 4.8. Controller parameters obtained for the primary controller in the cascade scheme.
Kc
τI
SKO (λ=7)
- 3.41
28
SKO (λ=10)
- 2.39
40
IMC (λ=15)
- 1.60
55
About the testing of the cascade loop, the disturbances and SP change introduced in the system are:
1.
2.
3.
4.
Set-point change from 40 ºC to 42 ºC in minute 100.
Cold input pressure changes from 180 kPa to 210 kPa in minute 300.
Set-point change from 42 ºC to 40 ºC in minute 500.
Hot input temperature change from 60 ºC to 65 ºC in minute 700.
From the responses obtained for the different parameters it is clear that the ones that achieve the
fastest response are the two parameters that use the limit value of the integral constant. These
perform well in both set-point tracking and disturbance rejection; the only downside is that they
present overshoot.
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Temperature (ºC)
Master thesis
Figure 4.68. Tuning parameters response to the tests introduced.
In terms of valve opening, as expected, the IMC with the limit value for the tuning parameter of 7
Valve Opening (%)
obtains the most aggressive valve openings.
Figure 4.69. Valve opening of the different tuning parameters for the cascade loop tests.
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If the performance criterion is used the results shown in Table 4.9 are obtained. It can be seen that, as
expected, the Skogestad obtains the best performance followed by the IMC with a constant of 15.
Table 4.9. IAE, ISE, ITAE obtained for the different cascade parameters performance.
IAE
ISE
ITAE
SKO (λ = 7)
42.55
33.02
0.35
SKO (λ = 10)
53.09
38.64
0.44
IMC (λ = 15)
78.48
59.75
0.65
4.2.6. Feedforward control loop
Generally, feedforward control can be used when feedback cannot effectively control a process
variable. As previously said, a feedback controller must wait until disturbances affect the process
variable before actuating, but with feedforward control loop the controller can compensate this
disturbance before the process is affected.
In this case, a feedforward controller based on the steady-state energy balance of the heat exchanger
will be built [35]. It consists on calculating the valve opening as a function of the flow passing through
it. In order to implement this in HYSYS, the spreadsheet must be used to calculate the result of the
equation and export it to the valve.
Figure 4.70. Feedforward control block diagram.
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Master thesis
Figure 4.71. P&ID of the feedback plus feedforward control scheme.
In this case, it is desired to control the process stream output temperature, which will be named THout.
In order to maintain THout at a SP, the control valve will be open or closed depending on the required
action. The main disturbance considered is a temperature fluctuation in the process stream input (THin).
In order to determine the OP, the controller requires SP and THin.
The steady-state energy balance relates the stream flow to the disturbance of the process.
𝐹
𝐶
(𝑇
− 𝑆𝑃 ) − 𝐹
𝐶
(𝑇
−𝑇
)=0
(Eq. 4.49)
Isolating FCin:
𝐹
=
𝐶
𝐶
(𝑇
(𝑇
− 𝑆𝑃)
· 𝐹
−𝑇 )
(Eq. 4.50)
A graphic of the valve opening vs the flow rate is obtained and, as Figure 4.72 shows the relation is
non-linear, an approximation to the third order has been done. Table 4.10 shows the numerical values
of the valve opening for each different flow value.
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Table 4.10. Mass flow and Valve Opening relation for the feedforward valve.
Valve Opening (%) Flow rate (kg/h)
0
0
10
0.47
20
3.76
30
12.61
40
29.25
50
53.59
60
80.73
70
103.20
80
117.60
90
125.00
100
129.80
Valve Opening vs Mass Flow
1
0.9
0.8
Valve Opening
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Mass flow (m3/h)
Figure 4.72. Valve opening and mass flow relation of the control valve.
By using the least squares method, a relation between x and y has been obtained:
𝑂𝑃(%) = (0.08 + 2.29 𝑥 − 3.99 𝑥 + 2.62 𝑥 ) · 100
(Eq. 4.51)
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Relation between the mass flow and the valve opening
1
0.9
Experimental values
Least squares fitting
0.8
Valve Opening
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Mass flow (m3/h)
Figure 4.73. Valve opening relation with mass flow curve fitting.
If in Eq. 4.51 the x is substituted by the mass flow, Eq. 4.52 is reached:
𝑂𝑃 (%) = 100 ·
0.08 + 2.29
𝐹
𝐹
− 3.999
129.8
129.8
+ 2.618
𝐹
129.8
(Eq. 4.52)
However, mostly, feedforward-only control is not the best option because an accurate model of the
process is needed and sometimes it’s not available. The equation that relates the output of the valve
to the flow rate is not one hundred percent accurate, which leads to an offset between the control
valve desired percentage and the real mass flow passing through the valve.
In order to eliminate the offset, a feedback controller will be used in conjunction with the feedforward
controller. The feedback controller used will have the same tuning parameters as the normal feedback
controller already calculated (IMC with λ = 7). In order for the variable to reach the set-point, its output
value will be reduced to create a positive offset that allows the feedback controller to act and reach
the set-point.
In order to test the feedback controller, different disturbances will be introduced into the system:
1. Disturbance of 10ºC in the input flow temperature (from 60 to 70ºC).
2. Disturbance of 5ºC in the input flow temperature (from 70 to 65ºC).
3. Disturbance of 5ºC in the input flow temperature (from 65 to 60ºC).
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Temperature(ºC)
Training Course in Simulation of Chemical Process Control
Figure 4.74. Feedforward plus feedback controller response to temperature disturbances.
From the last graphic it can be seen that the feedforward plus feedback controller does a good job at
the input disturbance rejection, even though it takes a long time for the temperature to stabilize.
4.2.7. Comparison of the different control schemes
In order to compare the different control systems, three different tests have been carried out. These
have been classified as set-point changes, temperature disturbances and flow disturbances.
About the set-point changes:
1.
2.
3.
4.
5.
Set-point change from 40 ºC to 43 ºC in minute 100.
Set-point change from 43 ºC to 41 ºC in minute 400.
Set-point change from 41 ºC to 37 ºC in minute 700.
Set-point change from 37 ºC to 39 ºC in minute 1000.
Set-point change from 39 ºC to 40 ºC in minute 1300.
About the temperature disturbance:
1.
2.
3.
4.
5.
Temperature change from 60 ºC to 55 ºC in minute 100.
Temperature change from 55 ºC to 58 ºC in minute 400.
Temperature change from 58 ºC to 68 ºC in minute 700.
Temperature change from 68 ºC to 64 ºC in minute 1000.
Temperature change from 64 ºC to 60 ºC in minute 1300.
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About the flow disturbance:
1.
2.
3.
4.
5.
Pressure change from 180 kPa to 250 kPa in minute 100.
Pressure change from 250 kPa to 210 kPa in minute 400.
Pressure change from 210 kPa to 160 kPa in minute 700.
Pressure change from 160 kPa to 260 kPa in minute 1000.
Pressure change from 260 kPa to 180 kPa in minute 1300.
For this test, the parameters for the three controllers have been selected to be not the most aggressive,
choosing more conservative approaches instead.
Table 4.11. Tuning parameters used for the comparison.
τI
Feedback
-1.47
28
Cascade (Primary loop)
-2.39
40
Feedforward (feedback controller)
-1.47
28
Temperature (ºC)
Kc
Figure 4.75. Different control schemes response to set-point changes.
About the response to SP changes, it can be seen that the most effective is the feedback controller,
followed closely by the cascade controller, which has a bit more of overshoot and a longer stabilization
time.
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Table 4.12. IAE, ISE and ITAE obtained for the SP disturbances introduced.
IAE
ISE
ITAE
Cascade
138.66
203.78
1.15
Feedback
95.14
135.88
0.79
Feedforward
310.35
400.59
2.50
Temperature (ºC)
The temperature results are shown in Figure 4.76.
Figure 4.76. Different control schemes response to temperature disturbances.
About the temperature response, it can be seen that even though the feedforward plus feedback
controller obtains good results in the rejection of the temperature disturbance, it is the control
scheme with a longer stabilization time, which penalizes the control scheme when it comes to the
performance criteria.
Table 4.13. IAE, ISE and ITAE obtained for the temperature disturbances.
IAE
ISE
ITAE
Cascade
80.60
59.57
0.67
Feedback
53.95
32.62
0.44
Feedforward
99.10
54.46
0.82
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Temperature (ºC)
The responses obtained to the flow disturbances are shown in Figure 4.77.
Figure 4.77. Different control schemes response to flow disturbances.
It can be seen that the cascade controller achieves the best performance, obtaining much better
results than both the feedforward and the feedback controller.
Table 4.14. IAE, ISE and ITAE obtained for the flow disturbances introduced.
IAE
ISE
ITAE
Cascade
1.86
0.03
0.02
Feedback
16.39
1.33
0.136
Feedforward
53.25
6.785
0.44
For the heat exchanger studied in this case, the results have proven that the best control schemes
are the feedback and the cascade control loops, obtaining good results in the three tests. The final
decision should be made considering if utility stream disturbances happens frequently and taking
into account the budget available. Actually, one of the advantages that feedback controllers have
over cascade ones is that they are less expensive because they need one less controller.
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4.3. Heated tank
The third case consists on a tank heated by steam passing through a coil. This is a system that could be
used for preparing the outlet stream before entering the next unit when some more capacitance than
the one provided by a heat exchanger is wanted. In such a system, the feed enters the tank at a certain
temperature, while the hold-up liquid in the tank is at a higher temperature provided by steam
condensation. Accepting the perfect mixing hypothesis inside the tank, the outlet stream has the same
temperature than the hold-up liquid. There are two PV: the liquid level and the temperature of the
tank. A change in one of them can affect the other. On one hand, if the temperature increases, the
water density increases too and the liquid level rises. On the other hand, if the liquid level decreases,
the heat is absorbed by a smaller amount of liquid, so the temperature increases.
In the proposed case, the feed is water entering the tank at 25ºC and 140 kPa. The tank is open to the
atmosphere and the SP for the liquid level is 50%, while the temperature desired is 50ºC. The utility
stream is steam at 250 kPa (2.5 bar).
Figure 4.78. Heated Tank: Flowsheet in Aspen HYSYS.
In such a system there could be many disturbances that will make the PV move from their desired
value:
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
Feed flow disturbance.

Feed temperature disturbance.

Utility stream flow disturbance.

Utility stream pressure disturbance.

Steam quality change.

An ambient temperature decrease could increase the heat loss.
4.3.1.
Dynamic simulation of a heated tank
The tank is the same as in the first case, with the same geometry, feed and open to the atmosphere.
The coil was simulated using the tube bundle. The first part of the simulation is simulating the tank.
The steps are exactly the same as for the Tank Liquid Level case, but in this case the Separator vessel
module was used since it is the only one to support the tube bundle option. The second part is
simulating the tube bundle. For details about the steps of the simulation see Simulation Manual Heated Tank in Appendix C3.
The components used are water, nitrogen and oxygen and the fluid package is Peng-Robinson. The
separator was run in dynamics mode until the SP (50% liquid level) is reached.
Since the tube bundle is only available in dynamics mode, the simulation has been quite different to
the previous ones. In fact, when in dynamics mode, the material streams added are given automatically
some specifications just to get them initialized. For instance, pressure and temperature are given
ambient default values (1 atm and 25ºC) while the composition is equally distributed. Probably these
specifications will not be the correct ones, but they can be changed to have a desired initial point.
The steam has been simulated at 250 kPa and fully saturated. To obtain the utility requirement, the
modelling was done at the maximum conditions for the nominal feed, in order for the process to be
able to heat the hold-up liquid up to 87ºC approximately. The steam inlet valve was simulated wide
open and a 1000 kg/h flow was set. Then, when the simulation converged to the equilibrium, the valve
opening was reduced until the vessel temperature was 50ºC (SP value).
Figure 4.79 shows a typical tube bundle:
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Figure 4.79. Tube Bundle for heated tanks. (Source: Cooney [36]).
In the simulation, it was placed at the bottom of the tank. As the heat exchanger, it is another resistance
element and requires sizing. The specifications used when preparing the simulation for the maximum
conditions are the following:
Figure 4.80. Tube bundle specifications.
The selection of the heat transfer coefficients depends on the tube material and chemical species
inside and outside the tubes. In order to avoid such details, as a mean of simplification, these
coefficients were left at their default values. The tube volume, heat transfer area and the tube pressure
drop were specified instead. This allows the global UA calculation. As the simulation has not been run
yet, the Tube liquid volume percent is 0, so the tube is empty. For the same reason, the shell duty does
not have a value yet.
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Further relevant details about this simulation are:

The dynamic specifications were set in order to force a certain flow through the tube bundle.
The flowsheet with the dynamic colour code is shown in Figure 4.81. The Steam IN stream has
both pressure and flow specifications and VLV-104 has the Total Delta P specification instead
of the Pressure Flow Relation. The tube bundle has a delta P specification too as shown in
Figure 4.80, so the VLV-105 does not need any specification since the pressure has been fixed
both before and after it. This method is necessary since these material streams have been
initialized in dynamics mode.

VLV-104 has an Equal Percentage Operating Characteristic since it is going to control
temperature and has been auto-sized at the maximum steam flow condition scenario.

All the other valves, including VLV-105, are linear valves and have been auto-sized excluding
the vapour valve and the liquid outlet valve.

The Cv for the liquid outlet valve (VLV-102) has been obtained by simulating a stream with the
same flow but at 50ºC and 111.3 kPa passing through a linear valve with 50% opening, and a
pressure drop equal to the hydrostatic pressure of 1.024 m of water at 50ºC (9.94 kPa).
Figure 4.81. Heated Tank: Flowsheet at intermediate simulation.
The final results of the simulation are shown in Figure 4.82 and 4.83:
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Figure 4.82. Heated Tank: Final flowsheet.
It can be seen that both SP are reached and the utility requirement for that objective is 367 kg/h of
saturated steam at 250 kPa. The worksheet shows that the steam exits the tube totally condensed and
sub-cooled down to 27.2 ºC. This means that the global UA is very high. However, for the case purposes
it can be accepted.
Figure 4.83. Heated Tank: Worksheet results.
The process has been modelled taking into account one important simplification: the heat loss to the
environment is null and all the heat goes to the hold-up liquid. However, as the vessel is closed, Aspen
HYSYS calculates a temperature increase also for the air above the liquid surface (1.5 m3 at SP
conditions). By analysing the hold-up material, it can be considered that all the heat goes to the liquid
water since the vapour amount is negligible compared with the aqueous amount (Moles column):
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Figure 4.84. Heated Tank: Vessel holdup.
4.3.2.
Disturbances and open loop responses
A set of disturbances is simulated in order to analyse the dynamic behaviour of the system:
1. 9500-9700 minutes: feed inlet pressure change from 140 kPa to 160 kPa. This is a flow
disturbance of 2 m3/h more approximately.
2. 9700-9900 minutes: feed temperature change from 25ºC to 15ºC.
3. 9900-10100 minutes: steam inlet valve opening change from 64.72% to 90%. This simulates a
valve malfunctioning.
The results are shown using three different strip charts. Figure 4.86 shows the liquid percent level
together with the vessel flows. Figure 4.87 shows the process temperatures and the duty exchanged,
while Figure 4.88 shows steam mass flows and pressures. Figure 4.89 is a zoom of the Steam Stripchart
to better visualize the effect of the second disturbance on the steam pressure and flow.
Figure 4.85. Temperature Stripchart Legend.
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Figure 4.86. Liquid level Stripchart: open loop response.
Figure 4.87. Temperature Stripchart: open loop response.
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Figure 4.88. Steam Stripchart: open loop response.
Figure 4.89. Steam Stripchart: open loop response zoom in disturbance 2.
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Figure 4.90. Steam Stripchart Legend.

Disturbance 1: When the feed flow increases, the level rises until a new equilibrium is reached.
This means that the hold-up amount also increased and, as the amount of steam is the same,
the same heat will be absorbed by more mass of water. This leads to a lower tank temperature.

Disturbance 2: When the feed enters the tank at a lower temperature there is a rapid change
in the heat exchanged. This is due to the mixing of the colder feed with the hold-up liquid. The
driving force, so the temperature difference, is higher now and maximum at the beginning,
decreasing with time until a new steady state is reached. This explains why the duty drops but
to a higher value than before. However, the duty is not enough to maintain the tank
temperature to the previous value. Instead, it decreases down to 37ºC approximately. The
condensed water exits the tube bundle at a lower temperature too, yet more heat is being
exchanged. This disturbance has much more effect on the temperature than on the liquid
level. As the feed stream is now at 15ºC, the density is higher and more water is entering the
tank, which justifies the small feed and liquid flow increase. This scenario, should lead to a
liquid level increase, however, as the holdup liquid passes from 45ºC to 37ºC its density
decreases too occupying less volume, which means that the liquid level drops. Figure 4.89
shows the condensed steam behaviour to disturbance 2. It can be seen that during 5 minutes
the aqueous phase flow and steam out flow oscillate, showing rapid positive and negative
accumulation inside the tube bundle. This can be due to the rapid increase of the heat
exchanged and its relatively fast stabilization. This leads to a rapid change in the tube hold-up
temperature and its density.

Disturbance 3: If the steam valve suddenly opens, more steam will enter the tube bundle. This
means that more latent enthalpy is available, which justifies the great increase in the heat
exchanged. When the valve opens, the pressure drop decreases, which makes Steam IN 2
pressure higher. When talking about a saturated steam, a pressure increase means a saturated
temperature increase, increasing the driving force of the heat transfer. The result is a vessel
temperature increase, which causes the water density to be lower and occupy more volume,
so the liquid level to drop.
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4.3.3.
Multiloop control
In order to control this process, multiloop techniques must be used. In this case, the output variables
are going to be the vessel temperature (y1) and the liquid percent level (y2). The manipulated variables
are going to be the tube bundle input stream (u1) and the tank output stream (u2), as shown in the
diagram below.
Figure 4.91. Heated tank P&ID.
4.3.3.1. Variable pairing and system identification
As it is a MIMO system, the changes on both input streams values affect both process variables. This
means that in the process there are four transfer functions, as it is a 2x2 system. Gp11 is the transfer
function of the vessel temperature variable when a change is applied in the tube bundle input stream.
Gp12 is the transfer function of the vessel temperature variable when a change in the outlet flow is
applied. Gp21 is the transfer function of the tank liquid level when a change in the tube bundle input
stream is applied, and Gp22 is the transfer function of the tank liquid level when a change in the tank
outlet flow is applied.
In this case, in order for the attendee to be aware on different pairing methods, RGA, SVA, and NI will
be used.
It is important to remark that, for this case, the gains of the transfer function had to be obtained in
dynamics mode, because the steady state mode does not support the tube bundle module.
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Table 4.15. Transfer function gains.
K11 [%/%]
K12 [%/%]
K21 [%/%]
K22 [%/%]
2.45
2.6e-3
0.1
-1.5
It can be seen that with a λ being really close to 1, the pairing for the variables obtained with the RGA
method is the 1-1, 2-2 configuration.
𝜆=
1
1
=
= 0.99
0.0026 · 0.1
1.0001
1−
2.448 · (−1.5)
(Eq. 4.53)
𝜆
1−𝜆
(Eq. 4.54)
1−𝜆
𝜆
=
0.99
0.01
0.01
0.99
If the Niederlinski index is calculated a positive value is obtained, which means that it cannot be
concluded if the system will be stable or not.
𝑁𝐼 =
|𝐾|
∏ 𝑔
=
(Eq. 4.55)
−3.6723
= 0.99
−3.672
In case that the singular value analysis is used, the first thing to do is to see if the gain matrix is linearly
independent.
|𝐾 − 𝛼𝐼| =
2.448 − α
0.1
0.0026
= 𝛼 − 0.948𝛼 − 3.66 = 0
−1.5 − α
(Eq. 4.56)
(Eq. 4.57)
𝛼 = 2.44; 𝛼 = −1.49
From equations Eq. 4.56, as the values obtained were different than 0, it can be stated that the gain
matrix is linearly independent.
In order to calculate the singular values, the eigenvalues of the KTK matrix must be obtained.
𝐾 𝐾=
2.44
0.0026
𝐾 𝐾−𝛼 𝐼=
0.1 2.13
−1.5 0.1
5.19 − 𝛼
−0.14
0.0026
5.19
=
−1.5
−0.14
−0.14
=𝛼
2.25 − 𝛼
−0.14
2.25
− 7.44𝛼 + 11.65
(Eq. 4.58)
(Eq. 4.59)
And the values obtained are σ1 (Eq. 4.61) and σ2 (Eq. 4.62).
𝛼 = 5.19; 𝛼 = 2.24
(Eq. 4.60)
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𝜎 =
𝛼 = 2.28
(Eq. 4.61)
𝜎 =
𝛼 = 1.49
(Eq. 4.62)
Finally, the CN number is shown in Eq. 4.63.
𝐶𝑁 =
𝜎
2.28
=
= 1.5
𝜎
1.49
(Eq. 4.63)
With the SVA, in this case, as the value is really close to one, it can be said that the 2x2 matrix is really
well conditioned.
About the transfer function of the vessel temperature, when a change is applied in the tube bundle
input stream a second order identification has been selected (Eq. 4.64).
𝑌 (𝑠)
2.44
%
1.22
º𝐶
=
=
𝑈 (𝑠)
11.05𝑠 + 10.64𝑠 + 1 %
11.05𝑠 + 10.64𝑠 + 1 %
(Eq. 4.64)
Instead, when a change is applied in tank output flow stream, a first order fitting has been used (Eq.
4.65).
𝑌 (𝑠)
0.0026
%
0.0013 º𝐶
=
=
𝑈 (𝑠)
9.9𝑠 + 21.8𝑠 + 1 %
21.52𝑠 + 1 %
(Eq. 4.65)
In the case of the transfer function of the liquid percent level, when a change is applied to the heat
exchanger input stream, a second order fitting has been obtained (Eq. 4.66).
𝑌 (𝑠)
0.1
=
𝑈 (𝑠)
15.73𝑠 + 1
%
%
(Eq. 4.66)
Instead, when a change is applied to the output flow stream, a first order model has been selected (Eq.
4. 67).
𝑌 (𝑠)
−1.53
%
=
𝑈 (𝑠)
28.80𝑠 + 1 %
(Eq. 4.67)
So, taking into account the RGA, SVA, and NI results, the selected pairings for this case are y1-u1 and y2u2, and it can be concluded that the system is stable, obtaining a 1-1, 2-2 configuration. In this case, the
dynamic considerations are not a key factor in pairing the variables because there is not a great
difference in the time constants obtained.
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Figure 4.92. Block diagram of the heated tank.
According to [21] the characteristic equation of the 2x2 system is the following.
1+𝐺 𝐺
1+𝐺 𝐺
−𝐺 𝐺 𝐺 𝐺
=0
(Eq. 4.68)
Eq. 4.68 can be simplified considering that the gains of the transfer functions Gc12 and Gc21 are really
small and thus the controller parameters can be approximated considering that both transfer functions
are 0.
Note that to obtain the stability parameters, both controllers have been considered to be PI.
1+𝐺 𝐺
= 11.05𝑠 + 10.64𝑠 + (1 + 2.44𝐾 )𝑠 + 2.44𝐾 = 0
(Eq. 4.69)
With the Routh-Hurwitz method, the limit parameters for the first controller are Kc1 and KI1.
𝐾
>
2.53𝐾 − 1
2.44
𝐾 >0
(Eq. 4.70)
(Eq. 4.71)
For the second controller:
1+𝐺 𝐺
= 28.80𝑠 + (1 + 𝐾 ) − 1.5𝐾 = 0
(Eq. 4.72)
And the final limit parameters for the controller are going to be Kc2 and KI2.
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𝐾
< 0.66
𝐾 <0
(Eq. 4.73)
(Eq. 4.74)
4.3.3.2. Tuning the controllers
In order to obtain the controller parameters of the system, the independent loop method explained in
chapter 2.3.6.5 will be used. In this method, both controllers are tuned based on their open loop
responses.
The IMC method will be used and, in this case, as the temperature loop is a second order function, a
PID will be obtained. However, in order to compare the PID with the PI, the transfer function will be
approximated to a first order plus time delay in order to obtain a PI controller.
The P&ID diagram of the Heated Tank is shown below, where the two controllers can be seen in action.
Tuning the first controller
In the temperature controller, using a tuning parameter equal to 5 the proportional, integral and
derivative parts obtained are shown in Eq. 4.75, Eq. 4.76, Eq. 4.77, respectively.
𝐾𝑐 =
2𝜉𝜏
%
= 0.90
𝐾𝜆
%
𝜏 = 2𝜉𝜏 = 10.64
𝜏 =
𝜏
= 1.03
2𝜉
(Eq. 4.75)
(Eq. 4.76)
(Eq. 4.77)
In order to obtain the PI controller, as said earlier, Skogestad’s half rule has to be used, but first, the
denominator of Eq. 4.64 has to be rearranged in the form of Eq. 4.78.
𝑌 (𝑠)
1.22
º𝐶
=
𝑈 (𝑠)
(9.47𝑠 + 1)(1.16𝑠 + 1) %
(Eq. 4.78)
The next step is to transform the two time constants into one, so the new time constant will be
obtained by adding the largest time constant plus half of the next largest:
𝜏 = 9.47 +
114
1.166
= 10.06
2
(Eq. 4.79)
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Alex Nogué, Pasquale Orlo
And the time delay is going to be the second largest time constant divided by 2 plus all the other time
constants, but in this case there are none.
𝛳=
(Eq. 4.80)
1.166
= 0.58
2
The resulting FOPTD transfer function is shown in equation 4.81:
𝑌 (𝑠)
1.22
=
𝑒
𝑈 (𝑠)
10.06𝑠 + 1
.
(Eq. 4.81)
º𝐶
%
In order to tune a first order plus time delay system, the equations shown in appendix C5 can be used,
with a tuning parameter of 4. The PI values obtained are:
𝐾 =𝐾 =
(Eq. 4.82)
𝜏
10.06
=
= 0.90
𝐾 · (𝜆 + 𝛳) 2.44 · (4 + 0.58)
(Eq. 4.83)
𝜏 = 𝜏 = 10.06
Tuning the second controller
For the second controller, the first order equations of the IMC method have been used. For this case,
several tests will be performed with different values of λ. The Skogestad controller parameters have
also been calculated for the case when the tuning constant is equal to 5.
Table 4.16. Controller parameters obtained for the liquid level controller.
Kc
τI
IMC (λ = 5)
-3.84
28.8
IMC (λ = 10)
-1.92
28.8
IMC (λ = 15)
-1.28
28.8
Skogestad (λ = 5)
-3.84
20
4.3.3.3. Testing the control system
In order to test the control parameters obtained for the first controller, different set-point changes and
disturbances were introduced to the system with both loops closed. In this case, as the RGA pointed
out, the interaction between both loops is minimal. However, to test the first controller, the
parameters used for the second one were Kc2 = -3.84 and τI2 = 20. The final disturbances applied were:
1. Set-point change from 50 ºC to 70 ºC in minute 0.
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2. Pressure disturbance in the tube bundle input steam from 250 kPa to 280 kPa in minute 300.
3. Temperature disturbance in the Feed stream from 25 ºC to 20 ºC in minute 600.
4. Set-point change from 70 ºC to 50 ºC in minute 900.
Temperature (ºC)
5. Pressure disturbance in the tube bundle input steam from 280 kPa to 250 kPa in minute 1200.
Temperature (ºC)
Figure 4.94. Different control schemes response to different disturbances.
Figure 4.95. Valve response of the PID obtained with the IMC method.
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From the Figure 4.94, it can be seen that both PI and PID parameters obtain very good and very similar
results. In Figure 4.95, it can be seen the oscillation of the controller output when the derivative action
is added. In this case, as in the simulation there is no noise it is not critical, but in other cases where in
the plant there is external noise or interferences that cannot be shielded off, the derivative action
should never be added. Another characteristic of the derivative action that can be seen in the graphic
is the derivative kick, around 600 minutes. The derivative kick occurs because the value of the error
changes suddenly when the set-point is adjusted, thus causing a really large error and saturating the
Temperature (ºC)
controller output. In Figure 4.96, the controller output of the PI shows a much smoother response.
Figure 4.96. Valve Opening response for the PI obtained with the IMC method.
Table 4.17. IAE, ISE and ITAE obtained for the first controller.
IAE
ISE
ITAE
PI
243.93
223.52
2.03
PID
258.23
231.29
2.15
As expected, as the two controllers behave really similar, the performance parameters are identical.
Due to the small oscillations in the PID controller output, for the tests of the liquid level controller, the
PI was used.
In the liquid level loop, the different set-point changes and disturbances were:
1. Set-point change from 50 % to 70% in minute 0.
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Input disturbance from 140 kPa to 170 kPa in minute 300.
Heat exchanger set-point change from 50 ºC to 60 ºC in minute 600.
Set-point change from 70 % to 50% in minute 900.
Input disturbance from 170 kPa to 140 kPa in minute 1200.
Liquid Level (%)
2.
3.
4.
5.
Figure 4.97. Different responses for the test disturbances proposed in the liquid level loop.
From the last graphic, it can be seen that the best response of all the tuning parameters are the ones
obtained with the Skogestad tuning method.
Outflow valve responses to disturbances
100
IMC (lambda = 5)
IMC (lambda = 10)
IMC (lambda = 15)
SKO (lambda = 5)
90
80
70
60
50
40
30
20
10
0
0
500
1000
1500
Time (min)
Figure 4.98. Valve opening responses for the tuning parameters.
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From the valve graphics, it can be seen that the Skogestad and the IMC for a constant of 5 give the
most aggressive controller outputs, especially when a set-point change occurs. On the other hand, the
other two tuning methods are not as much aggressive.
The performance criteria return the results shown in Table 4.18. It can be seen that the Skogestad
parameters obtained are the best in terms of the error, as they achieve better results in all the
categories, followed by the IMC when a constant of 5, and with the last being the IMC with the higher
constant.
Table 4.18. IAE, ISE and ITAE obtained for the second controller.
IAE
ISE
ITAE
IMC (λ = 5)
713.90
3123.30
5.94
IMC (λ = 10)
951.30
5150.90
7.92
IMC (λ = 15)
1437.90
8954.30
11.98
SKO (λ = 5)
496.70
2514.50
4.13
So, attending the results obtained, the controllers selected are the PI option for the temperature
control and IMC with a tuning parameter of 5 with the Skogestad limit of value for the tank level loop.
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4.4. Distillation column
The final case reunites all the knowledge assimilated by the moment, adding some more difficulty in
both process simulation and control. The process chosen is a binary distillation column for a nonazeotropic mixture with a total condenser. For such a system, there are 5 PV to be controlled and so 5
OP to be chosen. The selection process will be discussed later in chapter 4.4.5. As all these variables
affect each other, a multivariable control will be performed and, as the relation between each variable
can be more troublesome, a brief distillation theory review is presented in chapter 4.4.1.
4.4.1.
Distillation column theory
The distillation is a separation process based on the volatility of the chemical species. Disregarding the
nature of the mixture to separate (binary or multicomponent, azeotropic or non-azeotropic), the
separation is easier if the relative volatility is higher. The mixture is heated up to its boiling point
obtaining a vapour with a higher composition of the component with the lower boiling temperature,
being the heat provided the separator agent. The system obtained is a two-phase system described
by the vapour-liquid equilibrium (VLE), which can be represented with the diagram in Figure 4.99b.
(a)
(b)
Figure 4.99. Continuous distillation with reflux and total condenser (a) [33], VLE diagram description (b) [37].
The simplest case for a continuous distillation column is the one shown in Figure 4.99a. Inside the tower
there is an ascending vapour flow and a descending liquid flow which are brought into contact on
plates. Figure 4.100a shows the control volume for plate n and Figure 4.100b how the purification takes
place. Two streams enter plate n: the liquid coming from the above stage (Ln-1) and the vapour coming
from the previous plate (Vn+1). These two streams are not in equilibrium and, when brought into
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contact, they try to reach it exchanging heat of vaporisation, which allows the transport of the volatile
component from the liquid to the vapour. As Figure 4.100b shows, the result is a higher molar fraction
of the light component in the vapour and a lower molar fraction in the liquid (x is the molar fraction of
component A in the liquid phase, y is the molar fraction of component A in the vapour phase). A
composition gradient is obtained in the column where the molar fraction of the heavy component
decreases while the molar fraction of the light component increases from the bottom to the top of the
column.
(a)
(b)
Figure 4.100. Material balance in stage n (a) and rectification in stage n (b) [38].
Obtaining high purity components depends on many variables and design parameters:

Stage efficiency: the contact between the two phases is crucial to have a maximum mass
transport. This happens when the equilibrium is reached. However, in real plates, equilibrium is
never truly reached and the separation degree is lower. In the designing procedures, it is common
to consider stage efficiency equal to 1, the maximum value, and sometimes it can be a very good
simplification for real processes.

Stage number: as more plates are in the column, the separation degree is higher since more
contact phases are added. However, adding plates means increasing equipment cost.

Feed stage number: it is very important for the feed to enter the column in a plate where the
conditions (composition, temperature) are as similar as possible. The feed can enter the tower in
four different scenarios: at its boiling point, sub-cooled liquid, saturated vapour or mixture of
liquid and vapour phase. Depending on this condition, the amount of liquid or vapour in the
column will be higher or lower since the liquid fraction will go down to the bottom while the
vapour fraction will go up to the top.

Reflux ratio: it is the relation between the flow returned to top of the column (L) and the distillate
product extracted (D). For each distillation column there is a minimum reflux ratio at which the
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number of plates required to accomplish the separation objective is infinite. As much more reflux,
more liquid is returned to the column and more contact is allowed between the phases. This
achieves higher purities or reduces the stage number requirement for the same separation
objective. Nevertheless, this equipment cost saving is countered by an increase in utility needs,
yet there is more mass in the tower and the reboiler (the heat exchanger placed at the bottom of
the column) needs more heat to maintain the boiling temperature. There exists a relation for
selecting the optimal reflux ratio that states that it should lie between 1.2 and 1.5 times the
minimum reflux ratio [33].

Pressure: the VLE changes at different pressures, which makes it essential to work at constant
pressure. Normally, the operating pressure is referred to the pressure at the top of the column.
Its selection will depend on the dew point of the top vapour to condensate. As pressure increases,
the dew point also does, which allows using a coolant stream at a higher temperature.
Environmental changes must be taken into account when designing the condenser yet the
maximum summer temperature of cooling water is 30ºC [33].
In such a system, the degrees of freedom can be determined by the phase rule [33]:
𝐹 =𝐶−𝑃+2
(Eq. 4.84)
Where:

F is the number of degrees of freedom

C is the number of components of the system (binary = 2)

P is the number of phases of the system (vapour and liquid = 2)
Which results into 2 degrees of freedom. Considering the steady state material balance in the column
in Figure 4.99a, these 2 degrees of freedom can be assigned to achieve the separation objectives:
𝐹 =𝐷+𝐵
(Eq. 4.85)
𝐹·𝑥 =𝐷·𝑥 +𝐵·𝑥
(Eq. 4.86)
Where:

F is the feed flow.

D is the distillate flow.

B is the bottom flow.

xi is the molar fraction of the light component in each stream.
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4.4.2.
Alex Nogué, Pasquale Orlo
Steady state simulation of a distillation column
The chosen case is the distillation of n-butane and n-pentane mixture, a common process in oil refining
[39]. The feed stream has the following specifications:
Table 4.19. Feed specifications.
Vapour / Phase Fraction
Pressure
Molar Flow
Molar fraction n-butane
Molar fraction n-pentane
FEED
0.0000
520 kPa
800 kmol/h
0.55
0.45
The 0.00 specification in the vapour phase fraction indicates that the feed enters at its boiling point.
The objective of the separation is obtaining a distillate product with a 98% n-butane purity and a
bottom product with a 98% n-pentane purity. The operating pressure has been decided to be 500 kPa,
which assures a dew point of the top vapour mixture around 50ºC (Source: Aspen HYSYS). This makes
it possible to condensate the vapour using water at 5ºC.
Figure 4.101a shows the VLE for the n-C4 and n-C5 mixture at different pressures (units in lb/in2) [40].
Even if the chosen operating pressure is not represented (100 lb/in2 = 689.5 kPa), the graphic shows
that the mixture is not azeotropic. The Peng-Robinson fluid package was selected to model the VLE and
the thermodynamics properties of the system, as suggested by HYSYS through the Method Assistant.
In Figure 4.101b, it is shown how this fluid-package predicts the VLE for the binary mixture at 500 kPa.
(a)
(b)
Figure 4.101. VLE data (a [40]) and VLE obtained through a HYSYS case study (b).
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In order to design the column, the Shortcut module was implemented. However, there are graphical
methods such as the McCabe-Thiele one that can also be used for a binary mixture [38]. Estimating a
pressure drop of 40 kPa along the column, the number of plates, the reflux ratio and the feed stage
have been obtained (Figure 4.102). These results have been used to simulate the Distillation Column
module.
Figure 4.102. Shortcut Column: Performance tab.
Once the plates have been set to be 21 and the feed stage to 10, as said in the previous chapter, there
are 2 degrees of freedom to be specified in order to determine the separation degree. In this case, the
reflux ratio and the distillate flow were specified, both coming from the Shortcut calculation. The
steady state simulation converged to a result shown in Figure 4.103. It can be seen how the separation
objective is achieved and the column design correct.
Figure 4.103. Distillation Column: Results.
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Further analysis implies plotting the temperature and composition profiles. In Figure 4.104, it can be
seen how the temperature changes at each stage proving that every stage is working and separation
is taking place in all of them. This means that there is not an excessive number of stages and, as the
98% of purity objective has been reached, no more stages are needed.
The same can be observed in the composition plot. As said before, the separation takes place in every
stage. In a distillation column, changes in temperature mean changes in composition as the VLE
diagram in Figure 4.100b shows.
Figure 4.104. Distillation Column: Temperature Profile.
Figure 4.105. Distillation Column: Composition Profile.
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4.4.3.
Dynamic simulation of a distillation column
In order to perform a dynamic simulation of this process a different methodology was used. Instead of
converting the current steady state simulation into a dynamic one, the column was assembled starting
from a tower and the material streams, adding the required equipment one by one (sump, reflux drum,
pump and heat exchangers). The Absorber module was used in this case. The tray diameter was
changed from 1.5 to 2.5 m, just to give some more slack to the system, and the flow path was set to 2,
in order to allow 2 paths through the plates instead of only 1. In the next chapter, a brief description
about each equipment is presented. For more details about the steady state and dynamic simulation
see Simulation Manual - Distillation Column.pdf in Appendix C4.
4.4.3.1. Equipment Analysis
Assembling the column from zero implies properly designing both bottom and top recycle loops. In
Appendix A4, details about the design decisions and calculations are shown. The bottom recycle loop
extracts the liquid from the column and returns it as vapour after passing through a heat exchanger
(the reboiler). The following equipment are required:

Sump: it is a vessel added at the bottom of the column that assures that there is always some
liquid in the column and adds inertia to the system as a disturbance prevention. A vertical flat
cylinder Separator was used with a diameter of 2.5 m and a height of 4 m. The design liquid level
is at 65%. The Boilup stream enters the sump at 90% of total height, which is a way to assure that
the vapour does not mix directly with the hold-up liquid.
Figure 4.106. Distillation Column: SUMP.

Reboiler: it is the heat exchanger used to vaporise the liquid exiting from the Sump for then
returning it to the column. The utility stream is saturated steam at 7.5 bar and goes tube-side
while the cold stream goes shell-side. The same model as in the Heat Exchanger case was used.
The tube volume is of 0.535 m3 while the shell volume is 1.605 m3.
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Figure 4.107. Bottom recycle loop: reboiler and divisor tee.

Divisor Tee: it is a module which allows the separation of the liquid stream coming from the Sump
into the bottom product and the Boilup streams. The flow of the outlet streams depends just on
the pressure difference when in dynamics mode.
The top recycle loop extracts the vapour from the last stage and brings it to the ground level where it
is totally condensed. This is then accumulated in a closed vessel called Reflux Drum. The liquid exiting
from the bottom of this vessel goes to a pump, necessary to bring it back to 14 m high. The outlet
stream is then divided into two streams, the distillate product and the reflux stream, using the Divisor
Tee module. Figure 4.108 shows the flowsheet for this loop. Some information about each equipment
is resumed below:

Condenser: it is the heat exchanger used to condensate all the vapour exiting the top of the
column. The coolant is water at 5ºC. Again, the hot fluid goes tube-side while the coolant goes
shell-side. The tube volume was designed to be 0.94 m3, while the shell volume is of 2.09 m3.

Reflux Drum: a flat horizontal cylinder Separator was used with a total volume of 30 m3. The HYSYS
relation between height and diameter returns a height of 2.942 m. The designed liquid level is
50% [2]. In Figure 4.108, it can be seen that there is a purge stream. However, it is just a simulation
building feature yet the vessel must have two outlet streams. Actually, the vessel is closed and
pressurized when switching to dynamics mode.
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Figure 4.108. Top recycle loop.

Pump: it is necessary to gain the pressure to reach the top of the column from the ground level.
The head specification together with speed and efficiency specifications allow the creation of
pump curves, which add a more realistic point to the simulation since the head supplied by the
pump will vary with the flow passing through it. The curve can be seen in Appendix A4 (Figure A5).
All the equipment height was defined at ground level, except for some valves where the height has
been set equal to the nozzle height of the previous or next unit. It should be noted that there are many
valves and sometimes also 2 valves in series. However, the majority of them are simulation building
choices in order to facilitate the integration task. For instance, when there is a height change or an
equipment change, the valve can help dividing the pressure calculation into two more points, the inlet
point and the outlet point. For such valves, a big value of Cv was selected (1E+05) or a very small
pressure drop (0.001 kPa) for then obtaining the Cv through auto-sizing. Some valves show a pressure
drop, but it is only due to the hydrostatic pressure for the height change. The only valves that can be
used as OP are the following:

Feed (VLV-100), Reflux (VLV-113), Bottoms (VLV-103) and Distillate (VLV-112) valves: as they are
going to be OP for flow or level control, they have been set with a Linear operating characteristic.

Steam (VLV-105) and Coolant (VLV-108) valve: as they are going to be OP for pressure or
temperature control, the Equal Percentage operating characteristic was selected.
4.4.3.2. Transition to Dynamics Mode
This chapter serves to highlight the most important features when switching from steady state to
dynamics mode:

Integrator: as the simulation is much more complex than the previous ones, a smaller integration
step is required. Instead of the default one (0.5 s), a 0.2 s step was used. Furthermore, it has been
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necessary to bring the execution frequencies to the lower value, solving all the calculations
simultaneously. This is due to the amount of flash processes and composition change tray by tray.

Dynamic specifications: as in the previous cases, the pressure specification was left in each
boundary stream and each valve has got the pressure flow relation active. About the heat
exchangers, the conductance values were obtained by auto-sizing after specifying the flow and
the steady state pressure drop estimated. The same was done for the valves.

UA and k reference flows: a new feature has been implemented for this case. Once the dynamic
simulation reached the equilibrium, the two heat exchangers were given flow reference values.
The UA reference flow is used to model the UA variation with flow through the tubes or shell. The
following equation describes the relation [5]:
𝑈𝐴
= 𝑈𝐴
𝑚𝑎𝑠𝑠 𝑓𝑙𝑜𝑤
·
𝑚𝑎𝑠𝑠 𝑓𝑙𝑜𝑤
,
(Eq. 4.87)
The reference flows were set as the steady state values. If the flow gets higher, the UA will also
be higher, while the opposite happens if the flow drops. The k reference flow is important for
start-up and shut-down operations yet it provides a more linear relation between flow and
pressure at low flow region. The k reference flows were set at 40% of the steady state flow, as
recommended in the HYSYS Help. The relation that will be applied only in the case that the flow
is lower than the reference flow is the following:
𝑘

= 𝑘
·
|𝐹𝑙𝑜𝑤|
𝑅𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝐹𝑙𝑜𝑤
(Eq. 4.88)
Controllers: in order to make the simulation converge and reach the equilibrium, another
common building feature has been implemented. The controllers help in stabilizing the system
that without this help would probably not converge due to the big differences between steady
state simulation and dynamic simulation. The feed controller is absolutely artificial. In real plants,
the feed flow and pressure is determined by the previous unit, a reactor or another distillation
column for example, but here there is no another unit. If the feed is set to be free, it will change
if there is a change in the pressure profile inside the column, and as the boundary pressure has
been specified, the pressure drop will vary and so does the flow. The vessels controllers are added
to stabilize the system, which would be very difficult for the big inertia of these equipment. The
last is the reflux controller, which helps in getting the desired distillate, and so the bottom,
product.
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Figure 4.109. Distillation Column: Dynamic Simulation Flowsheet.
All these controllers are just PI controllers. As no tuning has been done yet, they have been given
common parameters. The flow controllers were set to reverse action, yet if the flow increases, valve
must close, and with K=0.1 and Ti=0.25. The level controllers were set to direct action with K=2 and
Ti=10 [5].
4.4.3.3. Results Analysis
The simulation reaches the equilibrium and the results show that the separation objective is achieved
(98% purity). A further analysis can be done by comparing the dynamic simulation results with the
steady state ones:
Table 4.20. Steady state vs Dynamics.
Distillate
Distillate purity
Bottoms
Bottoms purity
Recovery n-C4
Recovery n-C5
Reflux Ratio
Qreboiler
Qcondenser
Top stage pressure
Inlet stage pressure
Bottoms pressure
Stages
Inlet stage
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Steady State
441.9 kmol/h
97.98%
358.1 kmol/h
98.02%
98.40%
97.50%
1.373
2.152E+07 kJ/h
2.072E+07 kJ/h
500 kPa
520 kPa
540 kPa
21
10
Dynamics
442.5 kmol/h
98.03%
357.5 kmol/h
98.28%
98.59%
97.60%
1,371
2.168E+07 kJ/h
2.101E+07 kJ/h
503.5 kPa
516.9 kPa
549.6 kPa
21
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The great difference resides in the column pressure. Even if at the top of the column the difference is
relatively small, it affects directly to the vapour-liquid equilibrium and so to the temperatures and
compositions. It is also relevant that the feed enters at a lower pressure than in the steady state
simulation, yet the temperature and vapour phase condition will be different. The pressure profile in
the column has changed and this is due to the hydrostatic pressure, caused by the liquid inside the
column and the adding of the sump, and the resistance of each stage. As the heat exchangers and the
valves, the stages of a distillation column have a resistance equation associated as well. Figure 4.110
shows the conductance values for each plate. These values have been obtained automatically,
however, if it is necessary, they can be set to other values.
Figure 4.110. Trays conductance values.
If the temperature profiles of both columns are compared it can be seen how similar they are and no
visible difference can be distinguished between Figure 4.104 and 4.111. Globally, the results are a little
better in the dynamic simulation, but they are very similar to the steady state results. Hence, it can be
said that the column was properly simulated in dynamic mode and reliable results can be obtained.
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Figure 4.111. Distillation Column: Dynamic Temperature Profile.
4.4.3.4. Disturbances, Open Loop Responses and Process Variables Relation
As said at the beginning of Chapter 4.4, the distillation column is a more complex case of multivariable
control. So, in order to study the process variables relation, a set of disturbances is induced to the
system and the open loop responses are analysed. This is a clear circumstance in which the dynamic
simulation enhances a deeper understanding of the process and the relation of its variables.
Usually, previous to the distillation column, there is a reactor or another distillation column. A
disturbance in this unit will modify the feed conditions inducing a disturbance in the distillation unit.
So, possible disturbances are:

Feed flow disturbance.

Feed composition disturbance.

Feed temperature disturbance.
Other possible disturbances are:

Valve malfunctioning: it could happen in many process spots (bottoms, distillate, reflux, utility
streams).

Environmental changes: if there is no protection against summer temperature, the coolant will no
longer be available at 5ºC.
Before analysing the disturbances effect, some concepts must be revised. The pressure inside the
column is due to the amount of vapour inside of it. As more vapour, more pressure. The amount of
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vapour can be reduced by reducing the heat supplied or increasing the heat absorbed by the coolant.
In fact, the reflux temperature can cause a higher or lower heat transfer between the liquid and
vapour inside the column. For instance, if the reflux returns with a lower temperature, more vapour
will be condensed and the pressure drops.
Next, the first three types of disturbances are tested and the system responses are shown in three
different Stripcharts to better appreciate the results. In order to get the open loop response, all the
controllers were set on off mode, except for the feed stream. This controller is in fact used to simulate
a feed flow disturbance through a SP change.
Figure 4.112. Stripchart legend.
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Master thesis

Feed flow disturbance from 800 to 850 kmol/h
Figure 4.113. Feed flow disturbance: Open loop response (flows, liquid levels, temperature).
A higher feed flow means that more matter enters the column. According to the conservation of the
matter, the system will tend to an equilibrium where what goes out equals what goes in. However,
the sum of the output flows (Distillate Out and Bottoms Out) does not equal the feed flow. The reason
is that the liquid level of the reflux drum is still changing, which means that there is still some
accumulation in the process. With some more simulation time, equilibrium will be reached.
As the heat supplied is the same but the heat capacity has increased, the steam is not enough to
vaporise the proportional quantity of inlet stream and the column results in having more liquid than
vapour than before. The Boilup flow increase demonstrates it, together with the great liquid level rise
of the sump. This greater amount of liquid causes a Bottoms Out flow increase. If compared with the
Distillate Out flow, the variation has been much higher, however, the distillate flow also increases a
little since some more volatile component enters the column. The Reflux flow presents a very small
increase due to the additional amount of vapour exiting the column from the top. However, this top
flow increase affects the liquid level in the reflux drum, causing a positive accumulation. As said
before, as the heat supplied is fixed, the temperature measured in stage 17 is lower than before.
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Figure 4.114. Feed flow disturbance: Open loop response (flows, composition, pressures).
The liquid level increase will cause the bottom pressure of the sump to increase. Furthermore, as there
is more vapour than before, the top pressure increases changing the pressure profile of the column.
This explains why the feed pressure also changes. Generally, as the heat supplied is not enough to
provide the right temperature, the separation quality gets worse and both distillate and bottoms purity
are lower than before.
The resulting temperature profile (Figure 4.115) shows some differences with Figure 4.111: in the
rectifying zone (above the feed stage), the temperature has increased, which indicates a higher
presence of the heavy component; in the stripping zone (below the feed stage), the temperature has
decreased due to a higher amount of light component. Both phenomena demonstrate the purity loss
caused by this type of disturbance.
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Figure 4.115. Feed flow disturbance: Temperature profile inside the column.

Feed composition disturbance from 55% to 70% of n-C4
Figure 4.116. Feed composition disturbance: Open loop response (flows, liquid levels, temperature).
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The simulated disturbance consists on entering more volatile component (and so less heavy
component) than before. In this case, the feed flow is constant, so if the outlet flows vary is due to
column internal changes.
As before, the heat supplied is fixed but, this time, the amount of matter inside the column does not
change. Nevertheless, there is a top flow increase due to the generation of vapour. This is due to the
greater amount of light component, which allows the steam to vaporise more mixture than before.
For the same reason, the liquid amount decreases and so does the Boilup flow. This causes a liquid
level drop in the sump leading to a higher flow in the bottom. The Reflux flow is not really affected by
this disturbance having all the vapour amount exiting through the distillate output.
Figure 4.117. Feed composition disturbance: Open loop response (flows, composition, pressures).
As said before, firstly there is a net evaporation due to the higher amount of n-butane. This causes the
top pressure to increase changing the pressure profile inside the tower. As expected, the distillate
product is purer than before, however, the light component is not fully recovered in the top of the
column. A significant part of it exits through the bottoms, making this product much less pure. This
explains why the reflux drum level drops and the sump bottom pressure does not vary significantly.
As the composition varies a lot, the temperature of each outlet stream also changes, which has a direct
impact on the density. If the density increases, the liquid level drops.
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Figure 4.118 shows a very different temperature profile from the one shown in Figure 4.111. The next
three stages below the feed plate show a very small temperature difference, which means that they
are not needed or that the feed should enter another stage.
Figure 4.118. Feed composition disturbance: Temperature profile inside the column.

Feed temperature disturbance from 66.97 to 80ºC (0.002 to 0.1087 vapour phase)
Figure 4.119. Feed temperature disturbance: Open loop response (flows, liquid levels, temperature).
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A higher feed temperature was set in order to simulate a change in the feed condition. In particular,
the feed now enters the column with more vapour fraction than before.
As more vapour enters the column, a light top pressure increase should be registered, but above all a
flow increase exiting the top of the column. This translates into a distillate flow increase. The vapour
phase oscillation is due to pressure changes induced by the disturbance itself. As the amount of matter
inside the column is the same (feed flow is the same), less liquid than before enters the column. This
leads to a sump liquid level drop and the bottoms flow to increase consequently. However, both outlet
flows come back to their initial values approximately. This can be due to a reflux flow increase, which
reduces the top pressure restoring the initial pressure profile more or less.
Figure 4.120. Feed temperature disturbance: Open loop response (flows, composition, pressures).
As the feed enters the column at a different temperature, it is to expect that the temperature profile
changes. As a higher part of the inlet stream is already vapour, the heat supplied can be used to
vaporise a greater amount of mixture than before. The vapour is richer in the light component,
resulting in a purer distillate product, while the bottoms purity decreases below the 97%. This is due
to the higher temperature of the inlet liquid that goes to the bottom of the column. In Figure 4.121, it
can be seen how the temperature is a little bit higher in the stripping zone than in Figure 4.111. Instead,
as expected, a high purity is accompanied by lower temperatures in the rectifying zone.
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Figure 4.121. Feed temperature disturbance: Temperature profile inside the column.
Among all these scenarios there is an important feature to be highlighted. The vessels take a very long
time to stabilize due to their big volumes, and so to their inertia. This demonstrates that the system
has a big amount of capacity to face disturbances.
4.4.4.
Tray Selection for Temperature Measurements
As previously said, if the pressure is constant, the temperature is an indicator of the mixture
composition. In most of the cases, an online composition measurement (such as chromatography) is
not available, and temperature measurements turn to be essential to have information about the
separation quality. Indeed, it is important to select the right location for the temperature sensor.
E. S. Hori and S. Skogestad suggest to locate the measuring point at the stage were the slope is steep.
By calculating the temperature difference between consecutive stages, the graph in Figure 4.122 is
obtained. A further analysis can be done by measuring the temperature gain to a reflux flow step [41].
In order to do so, the steady state simulation was used. The gain is calculated by dividing the
temperature difference between the nominal temperature in a stage and the one after the step
change. The results are shown in Figure 4.123.
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Temperature slop
4.5
IncT/IncN
4
IncrementT/IncrementN
3.5
3
2.5
2
1.5
1
0.5
0
0
2
4
6
8
10
12
14
16
18
20
22
Stage
IncrementT/IncrementL
Figure 4.122. Temperature slop for consecutive stages.
Figure 4.123. Steady state gain for each stage.
Both graphics show a maximum for stage 17. This means that this stage is the most sensitive to changes
in the composition, yet it provides a faster temperature response. So, all the control schemes proposed
have got the temperature measurement point at stage 17, as a composition indicator. The SP is just
decided to be equal to the value obtained in the dynamic simulation once the equilibrium has been
reached (TSP, Stage 17 = 83.64ºC).
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4.4.5.
Distillation column control
As explained in chapter 4.4.1, in a distillation column with a total condenser and two product streams,
there are two degrees of freedom in steady-state, which needs to be specified in order to determine
the top and bottom compositions. In dynamics, the number of degrees of freedom turns to be 5. The
new three degrees of freedom need to be specified to define the column inventory variables within
the column. These variables are the pressure, the condenser level (reflux drum) and the column base
level (sump). In a real plant, the 5 degrees of freedom (5 PV) are specified through 5 valves opening (5
OP), as shown in Figure 4.124.
Figure 4.124. Distillation column P&ID with the five valves used for the control.
Each valve determines a flow that controls one or more process variable. In fact, in this case, multiple
configurations are possible and multiple variable pairings can be used in order to obtain good results.
Hence, the RGA method already presented in case 3 will be used in order to determine the best pairing.
4.4.6.
Multivariable control of a distillation column
In this case, the RGA will be used to find the most appropriate pairing for the five process variables in
the distillation column. However, in order to control the pressure, the manipulated variable used will
be the coolant flow rate in the condenser. There are other ways, but this is a very common strategy
[2].
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The four process variables are:




Bottom composition.
Top composition.
Condenser level.
Column base level.
The four manipulated variables are:




Reboiler duty QR
Reflux flow L
Distillate flow D
Bottom product flow B
In order to build the distillation column control, the example shown in [2] was followed, where a similar
distillation column was shown and it explained simple guidelines on how to obtain the variable pairing.
In this case, the reason why the reflux ratio is not considered a manipulated variable is because of the
ratio. Modifying the ratio implies modifying two flows, losing controllability.
As there are 4 PV and 4 MV, there are 24 (4!) possible configurations shown in Table 4.21, even though,
only three of those twenty-four are viable. Generally, PV and MV cross between top and bottom of the
column must be avoided.
Combinations 1, 3, 5, 9, 11, 13, 15, 19, 20, 23, 24 were discarded since they involve control of the
column base level with the reflux or distillate flows, which in reality is not viable because those streams
cannot provide good control of that variable.
Combinations 6, 8, 14 and 19 were discarded since they involve manipulating flow rate of the bottom
product or reboiler heat to control the liquid level in the reflux drum, which again, is not viable because
those streams cannot provide good control of that variable.
Combinations 21 and 22 were discarded since they do not regulate the material balance.
Combinations 2, 12 and 17 were discarded since each involves the control of one or both compositions
at the end of the column using a manipulated variable at the other end of the column.
That leaves only case 4, 10 and 18 as possible options to evaluate.
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Table 4.21. All the possible options for the control of the distillation column [2].
In order to obtain the RGA, the steady-state gains for the compositions will be used, and the best
controller pairings will be determined for the bottoms and the distillate composition. Since the
inventory loops can be considered as independent on the quality level, the multiloop is a 2x2 system.
The initial steady state simulation will be used to calculate the open loop gain and the closed loop gain.

Case 4
In this case, the MV to control top and bottom composition are the distillate flow and the heat supplied
by the reboiler respectively. In order to obtain the open loop gain (K11), the steady state simulation was
given the distillate flow and the reboiler duty as specifications. Then, a step (+60 kmol/h) was made in
the distillate flow to see how top composition changes. About the closed loop, it was simulated
specifying the bottom composition (as a controller was fixing it) and the distillate flow. The same step
was introduced and the variation of the molar fraction of the volatile component is calculated, for then
obtaining the closed loop gain (K11*).
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Figure 4.127. Distillation column control scheme (case 4).
The open loop gain is:
𝐾
=
∆𝑥
0.8755 − 0.9798
=
= −1.74 · 10
∆𝐷
501.9 − 441.9
(Eq. 4.89)
For the closed loop gain and the λ:
𝐾∗ =
∆𝑥
0.8649 − 0.9798
=
= −1.92 · 10
∆𝐷
501.9 − 441.9
𝜆
=
𝐾
−1.74 · 10
=
𝐾∗
−1.92 · 10
= 0.91
(Eq. 4.90)
(Eq. 4.91)
Finally, the RGA can be built (Eq. 4.92). It can be seen that case 4 is a strong contender when it comes
to paring the variables, as the value obtained is really close to 1.
𝜆
1−𝜆
1−𝜆
𝜆
=
0.91
0.09
0.09
0.91
(Eq. 4.92)
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
Case 10
In this case, the MV are the reflux flow and the bottoms flow. In order to obtain the open loop gain,
the steady state simulation was given the reflux and bottoms flows as specifications. Then, a step (+60
kmol/h) was made in the reflux flow and, as before the variation of top composition is calculated. About
the closed loop, it was simulated specifying the bottom composition and the reflux flow. The same step
was introduced to calculate the closed loop gain.
Figure 4.128. Distillation column control scheme (case 10).
The open and closed loop gains are the following:
=
∆𝑥
0.9869 − 0.9798
=
= 1.18 · 10
∆𝐿
666.6 − 606.6
(Eq. 4.93)
𝐾∗ =
∆𝑥
0.9904 − 0.9798
=
= 1.77 · 10
∆𝐿
666.6 − 606.6
(Eq. 4.94)
𝐾
𝜆
146
=
𝐾
1.18 · 10
∗ =
𝐾
1.77 · 10
= 0.67
(Eq. 4.95)
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The RGA matrix shows worse results than case 4 (λ farer from 1), which indicates that case 10 should
not provide the best pairing for the controller.
𝜆
1−𝜆

1−𝜆
𝜆
=
0.67
0.33
0.33
0.67
(Eq. 4.96)
Case 18
In this case, the MV are the reflux flow and the heat supplied by the reboiler. In order to obtain the
open loop gain, the steady state simulation was given the reflux and reboiler heat specifications. Then,
a step (+60 kmol/h) was made in the reflux flow. About the closed loop, it was simulated specifying the
bottom composition and the reflux flow. The same step was introduced to calculate the closed loop
gain.
Figure 4.129. Distillation column control scheme (case 18).
The open and closed loop gain are:
𝐾
=
∆𝑥
0.9958 − 0.9798
=
= 2.67 · 10
∆𝐿
666.6 − 606.6
(Eq. 4.97)
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Master thesis
𝐾∗ =
∆𝑥
0.9904 − 0.9798
=
= 1.77 · 10
∆𝐿
666.6 − 606.6
𝜆
=
𝐾
2.67 · 10
∗ =
𝐾
1.77 · 10
= 1.51
(Eq. 4.98)
(Eq. 4.99)
Finally, the RGA matrix can be constructed. The results show a worse pairing than the other two cases:
𝜆
1−𝜆
1−𝜆
𝜆
=
1.51
−0.51
−0.51
1.51
(Eq. 4.100)
In order to test the validity of these results, the RGA matrixes of the three cases have been also
calculated for a different step (+10 kmol/h). The results obtained were similar, pointing at case 4 as the
best option for pairing.
Case 4:
𝜆
1−𝜆
1−𝜆
𝜆
=
0.65
0.35
0.35
0.65
(Eq. 4.101)
𝜆
1−𝜆
1−𝜆
𝜆
=
0.62
0.38
0.38
0.62
(Eq. 4.102)
−1.71
2.71
(Eq. 4.103)
Case 10:
Case 18:
𝜆
1−𝜆
1−𝜆
𝜆
=
2.71
−1.71
In order to provide another indicator to check the stability of the system, the Niederlinski Index (NI)
was used. This index can be calculated from the steady state gain matrix of the distillation column.
𝐾=
𝐾
𝐾
148
𝐾
𝐾
(Eq. 4.104)
∆𝑥
0.8755 − 0.9798
=
= −1.74 · 10
∆𝐷
501.9 − 441.9
(Eq. 4.105)
∆𝑥
0.9832 − 0.9798
=
= 7.08 · 10
∆𝑄𝑟
2.2 · 10 − 2.152 · 10
(Eq. 4.106)
=
=
𝐾
𝐾
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𝐾
𝐾
𝑁𝐼 =
=
∏
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∆𝑥
0.020 − 0.0198
=
= 3.33 · 10
∆𝐷
501.9 − 441.9
(Eq. 4.107)
∆𝑥
0.0155 − 0.0200
=
= −8.96 · 10
∆𝑄𝑟
2.2 · 10 − 2.152 · 10
(Eq. 4.108)
|𝐾|
1.56 · 10
=
= 0.99
(−1.74 · 10 ) · (−8.958 · 10 )
𝐾
(Eq. 4.109)
=
As NI > 0, the system will be stable [2].
Even though the RGA matrix specified that the optimal pairing is number 4, all the other pairings will
be tuned and compared in order to verify the results.
4.4.7.
Tuning the controllers of the distillation column
In order to tune the different loops of the distillation column, the independent loop method will be
used for simplicity reasons. This method obtains the open loop system identification of each process
before closing all the individual loops. Note that all the open loop responses of the different loops are
shown in Appendix B4.
Pressure loop
About the pressure controller, all the cases have the same transfer function, thus, all of them have the
same tuning parameters. From the response obtained, a first or second order model could be built.
Nevertheless, to avoid introducing a derivative action in the controller that could potentially destabilize
the distillation column, the first order transfer function has been selected (Eq. 4.110). The tuning
parameters have been obtained with a constant of 1.3:
𝑃(𝑠)
16.25
13
𝑘𝑃𝑎
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠] =
=
𝑂𝑃(𝑠)
10.72𝑠 + 1
10.72𝑠 + 1 %
(Eq. 4.110)
𝐾 = 0.51
(Eq. 4.111)
𝜏 = 10.7
(Eq. 4.112)
Column level
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In order to control the sump level, two transfer functions must be obtained, as case 4 and case 18
control it with the bottoms flow, where case 10 controls it with the reboiler duty. For case 4 and case
18, the transfer function obtained is shown in Eq. 4.113, which is a first order model. The tuning
parameters were obtained with a constant of 7.
𝐿(𝑠)
−2.3
=
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠]
𝑂𝑃(𝑠)
51.76𝑠 + 1
(Eq. 4.113)
𝐾 = −3.21
(Eq. 4.114)
𝜏 = 28
(Eq. 4.115)
When it comes to case 10, the response obtained was also a first order model, but with a much lower
time constant (Eq. 4.116), and its tuning parameters were obtained with a constant of 9.
𝐿(𝑠)
−1.59
=
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠]
𝑂𝑃(𝑠)
15.67𝑠 + 1
(Eq. 4.116)
𝐾 = −1.09
(Eq. 4.117)
𝜏 = 15.7
(Eq. 4.118)
Distillate drum
When it comes to the distillate drum, case 4 controlled the tank via the reflux flow, and the transfer
function could be fitted into a first order model (Eq. 4.119). In order to obtain the controller
parameters, the IMC method was used for a constant of 8.
𝐿(𝑠)
−13.19
=
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠]
𝑂𝑃(𝑠)
313𝑠 + 1
(Eq. 4.119)
𝐾 = −2.96
(Eq. 4.120)
𝜏 = 32
(Eq. 4.121)
For cases 10 and 18, the manipulated variable was the distillate flow, and again, the function followed
a first order model (Eq. 4.112) and the tuning was obtained for a parameter of 8.
𝐿(𝑠)
−15.19
=
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠]
𝑂𝑃(𝑠)
280𝑠 + 1
150
(Eq. 4.122)
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𝐾 = −2.24
(Eq. 4.123)
𝜏 = 32
(Eq. 4.124)
Distillate Composition
In order to control the distillate composition, case 4 uses the distillate flow, while cases 10 and 18 use
the reflux flow. The two transfer functions obtained, are the transfer functions of the valve, as flow
controllers were used. For case 4 (Eq. 4.125), the used tuning parameter was 4, obtaining Eq. 4.126
and Eq. 4.127. And for cases 10 and 18 (Eq. 4.128), the used parameter was 3, obtaining Eq. 4.129 and
Eq. 4.130.
𝑅(𝑠)
0.931
410
𝑘𝑔 1
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠] =
=
·
𝑂𝑃(𝑠)
0.2𝑠 + 1
0.2𝑠 + 1 ℎ %
(Eq. 4.125)
𝐾 = 0.05
(Eq. 4.126)
𝜏 = 0.2
(Eq. 4.127)
𝑅(𝑠)
0.934
445
𝑘𝑔 1
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠] =
=
·
𝑂𝑃(𝑠)
0.2𝑠 + 1
0.2𝑠 + 1 ℎ %
(Eq. 4.128)
𝐾 = 7.2 · 10
(Eq. 4.129)
𝜏 = 0.2
(Eq. 4.130)
Bottom composition
When it comes to controlling the bottoms composition, a temperature control will be used because
these type of controllers are affordable, reliable and fast compared to composition sensors [2]. While
cases 4 and 18 use the reboiler duty (Eq. 4.131), case 10 uses the bottoms flow (Eq. 4.134). The tuning
parameter used for cases 4 and 18 is 8 and for case 10 is 0.95.
𝑇(𝑠)
8.75
1.05
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠] =
=
[º𝐶/%]
𝑂𝑃(𝑠)
7.33𝑠 + 1
7.33𝑠 + 1
(Eq. 4.131)
𝐾 = 0.9
(Eq. 4.132)
𝜏 = 7.33
(Eq. 4.133)
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Master thesis
4.4.8.
𝑇(𝑠)
−29.08
−3.49
[𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠] =
=
[º𝐶/%]
𝑂𝑃(𝑠)
64𝑠 + 1
64𝑠 + 1
(Eq. 4.134)
𝐾 = −0.42
(Eq. 4.135)
𝜏 = 20
(Eq. 4.136)
Testing the system
In order to compare the three systems, feed flow and temperature disturbances have been introduced.
Figure 4.130 is an example of the oscillatory responses provided by case 10, which makes its
implementation unviable. This is the reason why, in the following graphics, its response has been
omitted.
84.5
Column temperature response to temperature disturbances
Case 4
Case10
Case 18
84
83.5
83
82.5
1300
1400
1500
1600
1700
1800
1900
2000
2100
2200
Time (min)
Figure 4.130. Temperature in stage 17 response to temperature disturbances (case 10 included).
For the comparison, 6 different graphics have been obtained. These graphics provide helpful insight in
the different process variables of the systems as well as the composition obtained in both bottoms and
distillate.
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About the flow disturbances introduced, in order to make it more real, they have a short duration.
Normally, if there is a controller in the previous unit, the disturbance will be attenuated and the process
is more likely to experience oscillating flow disturbances.
1. Feed flow disturbance from 800 kmol/h to 700 kmol/h at minute 1300 with a duration of 5 minutes.
2. Feed flow disturbance from 800 kmol/h to 780 kmol/h at minute 1600 with a duration of 5 minutes.
3. Feed flow disturbance from 800 kmol/h to 870 kmol/h at minute 1900 with a duration of 5 minutes.
The responses obtained for the column pressure, distillate and bottoms composition, column
temperature and the distillation drum and column liquid levels are shown in the following graphics:
Figure 4.131. Column pressure response to the flow disturbances tested.
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Figure 4.132. Distillate composition response to the flow disturbances tested.
Figure 4.133. Bottoms composition response to the flow disturbances tested.
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Figure 4.134. Column temperature response to the flow disturbances tested.
Figure 4.135. Reflux drum response to the flow disturbances tested.
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Master thesis
Figure 4.136. Column base level response to the flow disturbances tested.
About the temperature disturbances, again, short lasting disturbances have been introduced.
1. Temperature disturbance from 66.94 ºC to 71.94 ºC in minute 1300 during 5 minutes.
2. Temperature disturbance from 66.94 ºC to 63.94 ºC in minute 1600 during 5 minutes.
3. Temperature disturbance from 66.94 ºC to 67.94 ºC in minute 1900 during 5 minutes.
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Figure 4.137. Column pressure response to the temperature disturbances tested.
Figure 4.138. Distillate composition response to the temperature disturbances tested.
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Figure 4.139. Bottoms composition response to the temperature disturbances tested.
Figure 4.140. Colum temperature response to the temperature disturbances tested.
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Figure 4.141. Reflux drum level response to the temperature disturbances tested.
Figure 4.142. Column base level response to the temperature disturbances tested.
Once all the responses have been obtained, the first thing that can be noted is that both systems
provide good control, achieving good disturbance rejection in both flow and temperature, obtaining
acceptable levels of composition in both distillate and bottoms parts. The responses of case 4 look
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Master thesis
smoother than the ones of case 18. Moreover, in Figure 4.132, the distillate purity falls down to 97%
in case of a feed flow disturbance. Keeping in mind that the objective of the control system is to
attenuate the disturbance presenting the minimum deviation from the SP and with a stabilization time
as fast as possible. In addition, taking into account that the objective of this distillation process is
obtaining products with 98% purity, the case 18 is the one that suits the best these requirements.
The conclusion disagrees with the RGA method prediction. In order to explain why the pairing obtained
with the RGA is not the optimal one, few arguments can be made. The main one is that the RGA method
is based on the steady-state simulation, where the system dynamics are not accounted. So, it is possible
that the dynamic system introduces some changes that the RGA does not consider.
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5. Economic analysis
In order to state the viability of the project, an economic analysis has been carried out. It is divided in
five parts: the investment, a fixed cost; the variable cost, associated to the teaching of the course; the
market study, where an offer analysis has been done to give a competitive price to the course; the
project viability, evaluated through a VAN analysis; and finally, the pilot test, analysing the results
obtained by surveys done to UPC students, which attended the Process Control subject where some
cases of this project have been implemented.
It has been considered that the project is financed by a fictitious consultancy company named
“CHEMICON”. The name is totally invented and there is no relation with other possible homonymous
companies.
5.1. Investment
The investment is the cost associated to the realization of the project. So, it can be defined as the cost
of designing and preparing the course material. To determine the cost, the investment has been
divided in three categories: the human resources, the cost of the equipment and other expenses.
Moreover, the human resources subdivision has been broken down into three main activities:
Table 5.1. Hours destined by the designers of the course.
Task
Design of the course
Simulation
Documentation
TOTAL
Hours
200
900
200
1300
The amount of hours of work corresponds to the dedication time of both engineers (650 hours each).
To determine the cost of each employee for the company, the gross salary plus the social welfare tax
(30% of total salary) was contemplated. Considering that most sources agree that the mean gross
salary for the junior engineer is around 25000 €/year, the final cost per hour and designer is show in
Table 5.2.
Table 5.2. Cost/hour per designer.
Salary
Net salary (€/h)
Gross salary (€/h)
Total cost for the company (€/h)
Cost/hour
10,35
13,02
18,60
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In terms of calculating the cost of the equipment used, only the price of the licences has been
considered. The software used are Aspen HYSYS, MATLAB-SIMULINK and Microsoft Office. As the
company it is supposed to use those software for other projects, an amortization calculation was done
using a ratio of the hours spent for each software to the total workable hours of the year.
𝐶𝑜𝑠𝑡
= 𝐶𝑜𝑠𝑡
·
(Eq. 5.1)
𝐻𝑜𝑢𝑟𝑠 𝑢𝑠𝑒𝑑
𝑇𝑜𝑡𝑎𝑙 ℎ𝑜𝑢𝑟𝑠
About the licences, they are all professional licences with the accessories needed for the course:

Aspen HYSYS: Professional license.

MATLAB: Professional license, plus SIMULINK.

Microsoft Office: Business standard license.
Table 5.3. Licenses used, with its percentages and the final cost.
License
Aspen HYSYS
MATLAB
Office
Price/year Hours used
33000
2000
144
800
200
500
Percentage
0.38
9.6·10-2
0.24
TOTAL
Cost
12692.30
192.30
34.62
12919.23 €
The other expenses subdivision takes into account multiple things, such as electricity and internet bills
or computer maintenance. In order to approximate this cost, it has been considered a 2.5% of the sum
of the other two. The final values for the investment cost can be seen in Table 5.4.
Table 5.4. Total cost and the subdivisions for the investment in the course.
Human resources
Cost of equipment
Other expenses
TOTAL
24180 €
12919.23 €
927.48 €
38026.71 €
5.2. Variable cost
In order to calculate the variable cost of the course, the same three categories in which the investment
was divided can be accounted.
About the human resources, it is needed a professor who can be a professional of the company. His/her
salary has been decided to be the same as the junior engineer one. His/her tasks, can be divided in two
categories, which are the teaching part and the preparation part.
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Alex Nogué, Pasquale Orlo
Table 5.5. Human resources number of hours for the variable cost.
Task
Course teaching
Preparing
Hours
20
10
The course will take place in rented offices. As an estimation, the cost of renting the computer
classrooms in the Barcelona East School of Engineering (EEBE-UPC) was considered. For the concession
of this classroom, the price is of 515€ per day used. This expense is taken into account in the cost of
the equipment subdivision, together with the software cost.
Figure 5.1. PC classroom in EEBE.
The software will be used by the students and the teacher (Table 5.6), and the same calculation shown
in Eq. 5.1 has been used. Finally, the last expense added in this subgroup are the computers used and
its maintenance. In order to approximate this cost, a 2.5 % of the sum of the classroom rent and the
software used has been contemplated. Considering 10 attendees and 1 teacher, the cost associated to
a 3 days course is:
Table 5.6. Cost of the software and its reduction for the variable cost.
License
Aspen HYSYS
MATLAB
Office
Price/year Hours used Percentage Total
33000
230
0,11
3649.03 €
2000
230
0,11
221.15 €
60
230
0,11
6.63 €
Table 5.7. Partial and total cost of the rented classroom.
Classroom
Price/day Days
Computer class
515 €
Total
3
1545 €
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Master thesis
Furthermore, the course includes lunch and coffee break for the attendees and the professor, yet it
will be given in the morning and in the afternoon (7h/day). This cost has been accounted in “Other
expenses”.
Table 5.8. Cost of the other expenses category for the variable cost.
Diet
Lunch
Coffee breaks
€/attendee Nº attendees Days
30
11
5
11
Total
3
990 €
3
165 €
In the end, the total value for each course is 7270.37€ (Table 5.9). It can also be seen that the major
expense in the variable cost are the simulation software used.
Table 5.9. Final table for the variable cost.
Human resources
Cost of equipment
Other expenses
Total
558.00 €
5557.37 €
1155.00 €
7270.37 €
5.3. Market study
In order to present a competitive product market study has been carried out. The offer of three other
companies has been analysed. They offer multiple courses oriented in the field of chemical process
simulation and process control. The information is summarized in Table 5.10.
Table 5.10. Market study comparison for different companies.
Inprocess (Aspen HYSYS) [42]
Chemstations (CHEMCAD) [43]
PSE (gPROMS) [44]
Days Nº attendees
Unknown
3
10
3
1
Unknown
Unknown
2
Location
Barcelona (Spain)
USA
England, Japan, Korea, USA
England, Japan, Korea, USA
Price
1650 €
1750 €
650 €
1050 €
It has been decided that the maximum number of attendees has to be 10 in order to have small classes
and allow the professor to be able to train all the attendees accordingly. Finally, the price decided for
the 3 days course is 1600 €, without VAT.
5.4. Project viability
In order to state if the project is viable or not, a VAN analysis has been carried out. Analysing the other
companies, the frequency of the course has been estimated to be 4 courses per year. The inflation task
has been considered to be 0.79%, which is the current value in Spain [45].
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Alex Nogué, Pasquale Orlo
Table 5.11. VAN formula applied to the course viability.
Investment
Variable cost
Income
Annual
VAN
Accumulated
Year 0
Year 1
Year 2
Year 3
-38026.71
0
0
0
0 -29081.49
-29081.49
-29081.49
0
64000.00
64000.00
64000.00
-38026.71
34918.50
34918.50
34918.50
-38026.71
34644.81
34373.26
34103.84
-38026.71
-3381.89
30991.37
65095.21
From Table 5.11, it can be seen that in a bit more than one year the investment will be recovered, and
by the end of the third year, the winnings of the course could potentially be of 65095.21 €.
5.5. Pilot test
The project proved economically viable. Nevertheless, to evaluate the contents quality and the interest
of recently graduated engineers, two of the course’s cases (Tank Liquid Level and Distillation Column)
were introduced into the lab sessions of the subject Process Control of the Master’s degree in Chemical
Engineering – Smart Chemical Factories, taught by the UPC in the EEBE. Two surveys have been carried
out: one at the beginning and one at the end of the course.
The objective of the initial survey is to know about the starting level of the potential attendees that
have just finished their degree or their master’s degree. Basically, they were asked about their
knowledge on both chemical and process control. This information can be useful in order to know if
the cases presented could provide them with the knowledge predicted.
This survey was made with Google Forms, a survey administration tool that is included with Google
Drive. This app allows collecting information from the users using personalized surveys anonymously.
The questions asked to the master’s degree students were:











What is your background degree?
In a scale from 1 to 5, what is your interest in the Chemical Process Control subject?
Have you ever attended a Chemical Process Simulation course?
Have you ever used a professional process simulator (Aspen HYSYS, UniSim, ChemCAD,
gPROMs, PRO/II, VMGSim or others)?
Have you ever used Aspen HYSYS in steady state mode? (If yes, to which extent?)
Have you ever used Aspen HYSYS in dynamic mode?
Have you ever used a controller in HYSYS?
Have you ever used MATLAB?
Before starting the course, did you know basic coding in MATLAB?
Have you ever plotted arrays in MATLAB?
Have you ever used SIMULINK?
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Master thesis





Before starting the course, did you know the difference between an open loop and a closed
loop system?
Before starting the course, did you know what a transfer function was?
Before starting the course, did you know block diagram algebra?
Have you ever tuned a PID?
Before starting the course, did you know about cascade control?
All the results of the surveys can be found in Appendix D. Here are some relevant ones. The results
provided helpful insight into the master’s degree students’ education. 90% of them had previously
obtained a bachelor’s degree in chemical engineering, and more than 60 % of them had great interest
in the subject.
Figure 5.2. Student’s response to the “What is your background degree” question.
As expected from chemical engineers, 95% of the tested had previously used a process simulator,
having the majority used Aspen HYSYS, even though, a vast majority of them hadn’t used Aspen HYSYS
in dynamic mode and hadn’t had experience in building a controller in any simulation software.
Figure 5.3. Student’s response to the question “Have you ever used a professional process simulator”.
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Alex Nogué, Pasquale Orlo
Furthermore, as expected, the majority of the students had previously used MATLAB and SIMULINK,
as well as they knew the basic concepts in process control, even though, 81 % had never tuned a PID
and 71 % of them had never seen beyond surface level control schemes, such as cascade control.
Figure 5.4. Student’s response to the question “Before starting the course, did you know about cascade
control?”.
From the initial survey, some conclusions can be drawn. The potential attendee of the course has
knowledge in chemical process as well as in basic use of the professional simulators. He/she also has
the very basic control theory background, even though, most of the attendees would not know the
essentials of dynamic simulation, system identification or controller tuning.
Once all the students had been presented with the cases and had time to work with them, another
survey was sent in order to obtain their final feedback.
In this second survey, the potential attendees were asked:








Your grade of interest on the cases has been (1- Not interested at all; Extremely interested).
Your grade of satisfaction with the contents and the didactic materials provided is (1- Not
satisfied at all; Extremely satisfied).
How difficult have you found the cases addressed? (1- Not difficult at all; Extremely difficult).
The increasing difficulty of the cases addressed was conveniently structured and has helped
in the learning process and assimilation of concepts (1- Strongly disagree; Extremely agree).
Your knowledge and ability on assembling and controlling a dynamic simulation increased as
the course proceeded concepts (1- Strongly disagree; Extremely agree).
Do you think that simulating an open tank is a good starting point to learn about dynamic
simulation and chemical process control? (1- Strongly disagree; Extremely agree).
Do you think that the open tank control gave you enough knowledge about selecting the
right control strategy in chemical processes? (1- Strongly disagree; Extremely agree).
Do you think that simulating the same open tank with both MATLAB and HYSYS was useful
for providing deeper understanding of the concepts behind? (1- Strongly disagree; Extremely
agree).
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Master thesis











Do you think that MATLAB, and so mathematical modelling, is a good resource/strategy for
chemical process control? (1- Strongly disagree; Extremely agree).
Simulating the distillation column in Aspen HYSYS is easier, time saving and allows a better
understanding of the process dynamic that if it was to be done in MATLAB. (1- Strongly
disagree; Extremely agree).
Through the simulation of a distillation column, you gained strong knowledge about
multivariable control. (1- Strongly disagree; Extremely agree).
The laboratory sessions helped you integrating the control and chemical engineering
concepts and vocabulary. (1- Strongly disagree; Extremely agree).
How relevant are the cases addressed for the professional career of a chemical engineer? (1Not relevant at all; Extremely relevant).
How do you feel about the amount of information presented? (1- Too little information; 5Too much information).
How likely is it that you would attend an "Advanced" part of the course, should it exist? (1Not likely at all; Extremely likely).
How likely is it that you would recommend this course to a friend or colleague? (1- Not likely
at all; Extremely likely).
What did you like the most about the course?
What did you dislike the most about the course?
If you have got any suggestion to improve the course, please, let us know about it!
The results were really helpful in order to determine their grade of interest as well as if the material
proposed was the right fit. It can be stated that the satisfaction with the didactic material and the grade
of interest in the cases has been excellent.
Figure 5.5. Student’s response to the affirmation “Your grade of satisfaction with the contents and the didactic
materials provided is”.
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Training Course in Simulation of Chemical Process Control
Alex Nogué, Pasquale Orlo
It can also be seen that most of the students appreciated the increasing difficulty of the cases, as almost
84 % of them argued that their knowledge progressively increased along with each case.
Figure 5.6. Student’s response to the affirmation “Your knowledge and ability on assembling and controlling a
dynamic simulation increased as the course proceeded”.
When it comes to the cases presented, most of them agreed that the tank is a good starting point to
learn about process control. However, when it comes to questions regarding the use of MATLAB, such
as if they thought that simulating the tank in both software was useful in order to introduce the
concepts and if they thought that MATLAB was a good strategy for chemical process control, mixed
reviews were obtained.
Figure 5.7. Student’s response to the affirmation “Do you think that MATLAB, and so mathematical modelling is
a good resource/strategy for chemical process control?”.
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Master thesis
In addition, most of the surveyed said that they would attend an Advanced part of the course as well
as recommend it to a friend or a colleague.
Figure 5.8. Student’s response to the question “How likely it is that you would attend an Advanced part of the
course, should it exist”.
When it comes to the student’s opinions, most of them pointed that they liked the new concepts, the
usefulness of it as well as the implementation in HYSYS. When it comes to what they had disliked the
most about the course, some pointed the work-load, while others didn’t point to anything in particular.
Finally, it can be concluded that the surveys returned a good review on the course content. This means
that the potential client will probably be satisfied with this product and recommend it to other
professional. This reinforces the project viability.
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Conclusions
This project allowed designing a course to train engineers in the simulation of chemical process control.
The potential attendee profile was defined and, basing on that, the educational objectives and the
course scope were determined. Moreover, the cases were selected to provide an easier approach for
those attendees that do not have a solid chemical engineering background, applying an increasing
difficulty level.
The economic analysis of this project returned positive results. A three-day course for 10 attendees
and with a frequency of 4 times per year allowed recovering the investment in a little more than one
year, still being competitive with other companies that offer similar courses. In addition, the surveys
carried out to the master’s students revealed that the potential attendee profile has been chosen
properly and has the basic knowledge to face the course. Furthermore, the surveyed students
demonstrated interest and satisfaction with the proposed contents and are very likely to continue with
an advanced part of the course. Hence, it can be stated that the course is a viable project.
The course is based on the Svrcek’s approach to process control. The use of a chemical process
simulator enhanced the control design of four different chemical processes by applying control
methods (system identification, variable pairing, IMC tuning method) to what could be real
experimental data. The dynamic simulation in Aspen HYSYS allowed familiarizing with the process
dynamics and understanding the relations between the process variables. Furthermore, it has
enhanced testing different control strategies in a relatively quick way, picking the best one for each
case. So, process simulation proved to be a very useful tool since it allows a deeper insight into the
process and can save a lot of time and money. However, experience with the simulator and a critical
analysis by the process engineer is needed in order to obtain coherent results. Special attention must
be paid when modelling the system with a good knowledge of the thermodynamics properties and
chemical interactions of the chemical species of the process. Moreover, the simulation can be more or
less detailed, so the simulator must be aware with his/her objective in order to reproduce coherently
the desired system.
This training course serves as an introduction to process control starting from the basic knowledge,
passing through the simulation of different control schemes, and ending with a multivariable process
such as the distillation column. These contents, together with the motivation provided by the positive
results of the pilot test, can be the basis for an advanced part of this course, where plant wide control,
split range control and optimal control might be addressed.
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Environmental impact analysis
The project has no direct impact on the environment as it consists on designing a course, where the
design of the different processes is tested by simulation.
However, indirectly, the course could prove beneficial for the environment. The course teaches the
attendees how to control different chemical processes, which if done right can lead to better trained
engineers and in the future more safety for chemical plants. A good control system helps avoiding
liquid spill and gas releasing to the atmosphere.
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