EEE5218: STAC
Lesson 1: Introduction to Automation and Control
The University of Bamenda
NAHPI/EEE B.Eng Courses Year 4
EEEE5218: Special Topics in Automation and Control
I MODERN CONTROL
Lesson 1: Introduction to Automation and Control:
Overview and concepts on nonlinear control systems with a focus on modern control, digital control,
adaptive control, optimal control and artificial intelligence.
1. Introduction to Control Systems
A Control system is an interconnection of components forming a system configuration that will provide
a desired system response. The basis for analysis of a system is the foundation provided by system theory,
which assumes a cause–effect relationship for the components of a system.
Fig1.1: control system diagram
Example: A shower
Goal: desired response: Not too hot, not too cold
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•
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Adjust water temperature to within acceptable tolerance
Don't burn yourself!
Don't take forever. (This operation has an end)
Human-in-the-Loop Control: How to do it?
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•
•
•
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Too cold - rotate knob (button) clockwise
Too hot - rotate knob counterclockwise
Much too cold - rotate faster
Much too hot - rotate faster
If we go too fast, we overshoot
In this example, the human is part of the control system. When the human is replaced in the control loop by
a regulator or a controller, we have an automatic control.
Automatic control has become an important and integral part of modern manufacturing and industrial
processes. For example, automatic control is essential in the numerical control of machine tools in the
manufacturing industries, in the design of autopilot systems in the aerospace industries, and in the design
of cars and trucks in the automobile industries. It is also essential in such industrial operations as
controlling pressure, temperature, humidity, viscosity, and flow in the process industries. The majority of
those physical variables are converted into electrical variables such as current or voltage by using
appropriated sensors for measurements.
Since advances in the theory and practice of automatic control provide the means for attaining optimal
performance of dynamic systems, improving productivity, relieving the drudgery of many routine repetitive
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EEE5218: STAC
Lesson 1: Introduction to Automation and Control
manual operations, and more, most engineers and scientists must now have a good understanding of this
field.
History of automatic control:
The first significant work in automatic control was James Watt's centrifugal governor for the speed
control of a steam engine in the eighteenth century.
In 1922, Minorsky worked on automatic controllers for steering ships and showed how stability
could be determined from the differential equations describing the system.
In 1932, Nyquist developed a relatively simple procedure for determining the stability of closed-loop
systems on the basis of open-loop response to steady-state sinusoidal inputs.
In 1934, Hazen, who introduced the term servomechanisms for position control systems, discussed
the design of relay servomechanisms capable of closely following a changing input.
During the decade of the 1940s, frequency-response methods (especially the Bode diagram
methods due to Bode) made it possible for engineers to design linear closed loop control systems (classical
controllers PI, PID) that satisfied performance requirements.
From the end of the 1940s to the early 1950s, the root-locus method due to Evans was fully
developed. The frequency-response and root-locus methods, which are the core of classical control theory,
lead to systems that are stable and satisfy a set of more or less arbitrary performance requirements. Such
systems are, in general, acceptable but not optimal in any meaningful sense. Since the late 1950s, the
emphasis in control design problems has been focused the design of optimal system. This is the
beginning of modern control.
In modern plants/systems where many inputs and outputs become more and more complex, the
modelling requires a large number of mathematical equations. Therefore, classical control theory, which
deals only with single-input-single-output systems, becomes powerless for multiple-input-multiple-output
systems.
Since about 1960, because the availability of digital computers made possible time domain
analysis of complex systems, modern control theory, based on time-domain analysis and synthesis using
state variables, has been developed to cope with the increased complexity of modern plants and the
stringent (rigorous) requirements on accuracy (precision, exactness), weight (value), and cost in military,
space, and industrial applications.
From 1960 to 1980, optimal control of both deterministic1 and stochastic1 systems, as well as
adaptive and learning control of complex systems, were fully investigated.
1
In mathematics, computer science and physics, a deterministic system is a system in which no
randomness is involved in the development of future states of the system. A deterministic model will thus
always produce the same output from a given starting condition or initial state (here the mathematical
model is well known).
From 1980 to the present, developments in modern control theory centered around robust control,
and associated topics.
Now that digital computers have become cheaper and more compact, they are used as integral parts
of control systems. Recent applications of modern control theory include such non engineering systems as
biological, biomedical, economic, and socioeconomic systems.
1
For a system to be stochastic, one or more parts of the system has randomness associated with it. for example, a
stochastic system does not always produce the same output for a given input.
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Lesson 1: Introduction to Automation and Control
2. Definitions
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Controlled Variable: quantity or condition that is measured and controlled.
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Manipulated Variable: quantity or condition that is varied by the controller so as to affect the value
of the controlled variable. Normally, the controlled variable is the output of the system.
Control means measuring the value of the controlled variable of the system and applying the
manipulated variable to the system to correct or limit deviation of the measured value from a
desired value.
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Plants: the system to be controlled is called the plant. a plant may be a piece of equipment, perhaps
just a set of machine parts functioning together in order to perform a particular operation. Any
physical object to be controlled (such as a mechanical device, a heating furnace 2 , a chemical
reactor, a hydroelectric power system, a wind farm, a solar energy system…) a plant.
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Process: a process is a natural, progressively continuing operation or development marked by a
series of gradual changes that succeed one another in a relatively fixed way and lead toward a
particular result or end. Any operation to be controlled is a process. Examples are chemical,
economic, and biological processes. A process, to be controlled can be represented graphically, as
shown in Figure 1.1
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Systems: A system is a combination of components that act together and perform a certain
objective. A system is not limited to physical ones. The concept of system can be applied to abstract,
dynamic phenomena such as those encountered in economics, in politics...The word system should,
therefore, be interpreted to imply physical, biological, economic, politic and the like, systems.
Disturbances: A disturbance is a signal that tends to adversely affect the value of the output of a
system. If a disturbance is generated within the system, it is called internal disturbance, while an
external disturbance is generated outside the system and is an input. Examples: wind gusts;
earthquakes (seismic wave); external shaking and vibration; road surface variations; variation in
feed material
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Feedback Control. Feedback control refers to an operation that, in the presence of disturbances,
tends to reduce the difference between the output of a system and some reference input and does
so on the basis of this difference.
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Control System: a system which modifies the inputs to the plant to produce a desired output. The
controller or control processor processes the sensors signals to drive the actuator. Examples: human
operator; mechanical; electro-mechanical; analog electrical; general purpose digital processor;
special purpose digital processor.
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Lesson 1: Introduction to Automation and Control
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Sensor: a sensor measures the quantity to be controlled. It is the mechanism by which the controller
detects the outputs of the plant Examples: radar altimeter; GPS; shaft encoder; LVDT; strain gauge;
accelerometer; tachometer; microphone; pressure and temperature transducers; chemical sensors;
microswitch.
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Actuator: An actuator is a component of the system that is responsible for moving and controlling
a mechanism for example by opening a valve. In simple terms ...an actuator affects the plant
(Pneumatic actuator · Rotary actuator · Linear actuator · Rigid chain actuator). Examples:
hydraulic, pneumatic, electric motors; pumps; heaters; aircraft control surfaces; voice coil;
solenoid; piezo-electric transducer.
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Open-loop control system: An open-loop control system utilizes an actuating device to to obtain
the desired response of the process directly without using feedback, as shown in Figure 1.2
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Closed loop control system: A closed-loop control system uses a measurement of the output and
feedback of this signal to compare it with the desired output (reference or command).
Fig1.2: a) Open-loop control system with external disturbances; b) Closed-loop feedback system with
external disturbances
3. Examples of control systems
3.1. Temperature Control System.
Figure 1-3 shows a schematic diagram of temperature control of an electric furnace. The temperature in the
electric furnace is measured by a thermometer, which is an analog device. The analog temperature is
converted to a digital temperature by an A/D converter. The digital temperature is fed to a controller through
an interface. This digital temperature is compared with the programmed input temperature, and if there is
any discrepancy (error), the controller sends out a signal to the heater, through an interface, an amplifier,
and a relay, to bring the furnace temperature to a desired value.
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Lesson 1: Introduction to Automation and Control
Fig1.3: Temperature control system.
3.2. Temperature control of the passenger compartment of a vehicle
The temperature of the passenger compartment differs considerably depending on the place where it is
measured. Instead of using multiple sensors for temperature measurement and averaging the measured
values, it is economical to install a small suction (pressure) blower at the place where passengers normally
sense the temperature. The temperature of the air from the suction blower is an indication of the passenger
compartment temperature and is considered the output of the system. The controller receives the input
signal, output signal, and signals from sensors from disturbance sources. The controller sends out an optimal
control signal to the air conditioner or heater to control the amount of cooling air or warm air so that the
passenger compartment temperature is about the desired temperature.
Fig1.4: Temperature control of passenger compartment of a vehicle
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Lesson 1: Introduction to Automation and Control
3.3. Speed Control System.
The basic principle of a Watt's speed governor for an engine is illustrated in the schematic diagram of Figure
l.5.
Fig 1.5: speed control system
The amount of fuel admitted to the engine is adjusted according to the difference between the desired and
the actual engine speeds. The speed governor is adjusted such that, at the desired speed, no pressured oil
will flow into either side of the power cylinder. If the actual speed drops below the desired value due to
disturbance, then the decrease in the centrifugal force of the speed governor causes the control valve to
move downward, supplying more fuel, and the speed of the engine increases until the desired value is
reached. On the other hand, if the speed of the engine increases above the desired value, then the increase
in the centrifugal force of the governor causes the control valve to move upward. This decreases the supply
of fuel, and the speed of the engine decreases until the desired value is reached.
In this speed control system, the plant (controlled system) is the engine and the controlled variable is the
speed of the engine. The difference between the desired speed and the actual speed is the error signal. The
control signal (the amount of fuel) to be applied to the plant (engine) is the actuating signal. The external
input to disturb the controlled variable is the disturbance. An unexpected change in the load is a disturbance.
4. Modeling
Engineers and scientists are frequently confronted with the task of analyzing in the real system, synthesizing
solutions to these problems, or developing theories to explain them.
One of the first steps in any such task is the development of a mathematical model of the phenomenon being
studied. The model should not be oversimplified, if not, conclusions drawn from it will not be valid in the
real system. The model should not be so complex as to complicate unnecessary the analysis.
System models can be developed by two distinct methods: analytical modelling and experimental
modelling.
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Lesson 1: Introduction to Automation and Control
Analytical modelling consists of a systematic application of basic physical laws to systems components
and their interconnexion. The intended purposes of the model must be clearly specified. The system
boundary must enclose all components or subsystems of primary interest, such as subsystems A, B, C in
figure 1.6. The environment can affect the system and this is represented by S1. the system output,
represented by the signal S6 should not affect the environment, at least not to the extend that it would modify
S1.
Experimental modelling or modelling by synthesis is the selection of mathematical relationship with
seems to fit observed input-output data
Fig 1.6: Steps of the modeling
5. Modern control
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Lesson 1: Introduction to Automation and Control
Modern control includes generally control Systems Design in State Space: pole placement, Design of
Regulator Systems with Observers, Quadratic Optimal Regulator Systems. We shall focus more on
State-Space Methods in time domain and we will use small, medium and large state-space matrices.
MATLAB is quite useful to transform the system model from transfer function to state space, and vice
versa. We shall begin our discussion with transformation from transfer function to state space. Let us write
the closed-loop transfer function as:
()
numerator polynomial in s
=
=
()
denominator polynomial in s
Once we have this transfer-function expression, the MATLAB command
[A, B, C, D] = tf2ss (Num, Den)
Consider the transfer function system
There are many (infinitely many) possible state-space representations for this system. One possible statespace representation is
6. Digital control
The current evolution of automatic systems places more emphasis on discrete systems. Digital controllers
offer many advantages in terms of both performance and flexibility. We shall provide a reminder of the
tools for modeling sampled systems; prerequisite for the synthesis of digital correctors.
During the course on linear feedback systems, we discussed the analysis and regulation of an analog process.
The correctors associated with such systems are generally analog. A logical development in automation is
to integrate a digital computer in the loop. This interaction is not without consequences on the theoretical
approach because it is then necessary to use specific tools for discrete signals.
6.1. Structures of digital feedback control
There are two types of digital feedback control structure that are similar to that of analog feedback control:
6.1.1. The computer/microcontroller is used to replace the analog controller and the comparator
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Lesson 1: Introduction to Automation and Control
In Figs 1.7 and 1.8. the computer is used to replace the analog controller and comparator. We are talking
about an all-digital loop. The computer manages all the signals (comparator, feedback loop, etc.). The PC
calculates the process control law. Like any computer, it has an operating system and numerical control
software.
Computer or Microcontroller
Control signal
Reference Error
Digital
controller
D/A
A/D
Sensor
System
/Process
Output
Figs 1.7 and 1.8. Digital feedback control structures type I
6.1.2.
The computer/microcontroller is used to replace only the analog controller
Calculator or
Digital filter
Reference
Control signal
Error
Output
ADC
Digital
controller
DAC
System
/Process
measurement
Sensor
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Lesson 1: Introduction to Automation and Control
Fig 1.9. Digital feedback control structures type II
7. Optimal control theory (OCT)
The objective of OCT is to determine the control signals that will cause a process (dynamical system) to
satisfy the physical constraints and at the same time minimize (or maximize) some performance criterion.
Minimize cost and maximize payoff (final outcome or result), utility.
Consider a dynamical system:
(1) The
cost function is defined by:
L is the Lagrangian or running cost; Kf is the potential energy.
Optimization problem is the minimization of the cost function
To have a precise definition of the Optimal Control Problem one should specify further: the time tf fixed or
free, the set of admissible controls (u) and admissible trajectories, etc. Moreover, one can fix an initial
(and/or a final) set, instead than the point x0 (and xf). Fixing the initial point x0 and letting the final condition
xf vary in some domain of Rn, we get a family of Optimal Control Problems. Similarly, we can fix xf and let
x0 vary. One main issue is to introduce a concept of solution for this family of problems and we choose that
of Optimal Synthesis. Roughly speaking, an Optimal Synthesis is a collection of optimal trajectories starting
from x0, one for each final condition xf.
The payoff function is defined by:
8. Adaptive control
An adaptive controller differs from an ordinary controller in that the controller parameters are variable, and
there is a mechanism for adjusting these parameters on-line based on signals in the system.
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Lesson 1: Introduction to Automation and Control
There are two main approaches for constructing adaptive controllers:
-so-called model-reference adaptive control method, and -so-called selftuning method.
8.1.
Model-Reference Adaptive Control (MRAC)
Fig 1.10: Model reference adaptive Control
A MRAC can be schematically represented by Fig. 1.10. It is composed of four parts:
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a plant containing unknown parameters,
a reference model for compactly specifying the desired output of the control system,
a feedback control law containing adjustable parameters, and
an adaptation mechanism for updating the adjustable parameters.
The plant is assumed to have a known structure, although the parameters are unknown.
For linear plants, the numbers of poles and zeros are assumed to be known, but their locations are
not.
For nonlinear plants, this implies that the structure of the dynamic equations is known, but that
some parameters are not.
A reference model is used to specify the ideal response of the adaptive control system to external command.
The choice of the reference model has to satisfy two requirements:
It should reflect the performance specification in the control tasks such as rise time, settling time,
overshoot or frequency domain characteristics.
This ideal behavior should be achievable for the adaptive control system (i.e., there are some
inherence constrains on the structure of reference model given the assumed structure of the plant model).
The controller is usually parameterized by a number of adjustable parameters. The controller should have
perfect tracking capacity in order to allow the possibility f tracking convergence. Existing adaptive control
designs normally required linear parametrization of the controller in order to obtain adaptation mechanisms
with guaranteed stability and tracking convergence.
8.2. Self-tuning controller
A self-tuning controller is a controller which performs simultaneous identification of the unknown plant.
This means that the unknown parameters or variables of the plant are estimated in order to be used by the
controller.
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Lesson 1: Introduction to Automation and Control
Fig 1.11: Self-tuning Control
9. Artificial Intelligence
Artificial Intelligence or sometimes called machine intelligence, is intelligence demonstrated by machines,
in contrast to the natural intelligence displayed by humans and other animals. Some of the activities that it
is designed to do is speech recognition, learning, planning and problem solving.
In the real world, the knowledge has some unwelcomed properties: Its volume is huge, next to unimaginable.
It is not well-organized or well-formatted. It keeps changing constantly.
AI Technique is a manner to organize and use the knowledge efficiently in such a way that:
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It should be perceivable by the people who provide it.
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It should be easily modifiable to correct errors.
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It should be useful in many situations though it is incomplete or inaccurate.
AI techniques elevate the speed of execution of the complex program it is equipped with.
9.1. Characteristics of an AI
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Capable of predicting and adapting, AI uses algorithms that discover patterns (outlines) from
huge amounts of information.
Makes decisions on its own, AI is capable to augment human intelligence, deliver insights and
improve productivity.
Continuous learning, AI uses algorithms to construct analytical models. From those algorithms,
AI technology will find out how to perform tasks through innumerable rounds of trial and error.
AI is forward-looking, AI is a tool that allows people to reconsider how we analyze data and
integrate information, and then use these insights to make better decisions.
AI is capable of motion and perception.
9.2. Some definitions
An Expert System is an intelligent computer program that uses knowledge and inference procedures to
solve problem that are difficult enough to require human expertise for their solutions. The term
“knowledge-based systems” is often used synonym for “expert systems”. It makes clear that the system
has an explicit knowledge base. (Examples: Flight-tracking systems, Clinical systems)
Natural language processing helps computers communicate with people in their very own language
and scales other language-related tasks. For example, NLP makes it possible for computers to read
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EEE5218: STAC
Lesson 1: Introduction to Automation and Control
text, hear speech, interpret it, measure thoughts and emotions, and determine which parts are
important. Today's machines can analyze more language-based information than humans without
exhaustion and in a continuous, unbiased way. (Examples: Google Now feature, speech recognition,
Automatic voice output)
Machine Learning (ML) is an algorithm category that enables software applications to predict responses
more accurately and specifically without explicitly programming them. Machine learning is primarily
focused on the development of algorithms which are capable of receiving input data as well as using
statistical analysis to predict an output while updating outputs with new data.
Artificial Neural Networks (ANNs): The inventor of the first neurocomputer, Dr. Robert Hecht-Nielsen,
defines a neural network as:
"...a computing system made up of a number of simple, highly interconnected processing elements, which
process information by their dynamic state response to external inputs.” The idea of ANNs is based on the
belief that working of human brain by making the right connections, can be imitated using silicon and wires
as living neurons and dendrites.
The human brain is composed of 100 billion nerve cells called neurons. They are connected to other
thousand cells by Axons. Stimuli from external environment or inputs from sensory organs are accepted by
dendrites. These inputs create electric impulses, which quickly travel through the neural network. A
neuron can then send the message to other neuron to handle the issue or does not send it forward.
Fig 1.12: biological neurons of human brain.
ANNs are composed of multiple nodes, which imitate biological neurons of human brain. The neurons are
connected by links and they interact with each other. The nodes can take input data and perform simple
operations on the data. The result of these operations is passed to other neurons. The output at each node is
called its activation or node value. Each link is associated with weight. ANNs are capable of learning,
which takes place by altering weight values. The following illustration shows a simple ANN:
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Lesson 1: Introduction to Automation and Control
Fig 1.13: Artificial Neural Network
9.2.
Artificial Intelligence Branches
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