International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 11, November 2013
ISSN 2319 - 4847
Evaluating the Performance of Fuzzy Logic and
Classic(PID) Active Controllers in Control of
Surge Phenomenon in Centrifugal Compressors
Qasem Abdollah Nezhad1, Jafar Ghafouri2 and Mohammad Fathi3
1
Department of Mechatronics Engineering, Science and Research Branch, Islamic Azad University, Kurdistan, Iran
2
Department of Mechanical Engineering, Islamic Azad University, Tabriz, Iran
3
Department of Electrical Engineering, University of Kurdistan, Sanandaj, Iran
ABSTRACT
Compressors are essentially designed and used for the purpose of increasing the total pressure of operative fluid through axial
working. In such application safe performance and at the same time, maximum efficiency of compressing system is necessary.
Thus, occurrence of flow instabilities in system must be avoided to install compressor appropriately and prevent potential
damages. Instabilities are considered as destructive factors for compressors. Moreover, reaching the instability area will be
resulted in drastic reduction in efficiency. Surge is generally defined as a form of flow instability which essentially occurs in
dynamic compressors. Surge control system is an indispensable system, particularly for centrifugal compressors and acts as a
protective factor preventing compressor from reaching surge conditions.
In the present study we try firstly to design both fuzzy logic and classic (PID) active controllers for centrifugal compressor system
and then, to compare the obtained results from simulation of these two controllers. Finally, an appropriate and practical
controller for avoiding this unfavorable incident will be determined based on the observed results.
Keywords: centrifugal compressor, surge, active control, classic controller (PID), fuzzy logic active controller.
1. INTRODUCTION
The surge phenomenon occurs when output pressure generated by a compressor is lower than its downstream pressure.
Under such conditions a reciprocating movement will be created in gas flow[1, 2]. The risk of surge incident may be
present in all three operational phases including start-up stage, normal working, and emergency stop. Therefore, control
system is required to meet specific conditions to be effective in all the three modes. The major factors involved in causing
surge phenomenon may be listed as follow:
 High pressure at output header as the compressor is putting into operation.
 Decrease in compressor flow rate for any reason (reduction in downstream consumption, clogging of valves on the
path of transmission line, or slip in succeeding stations).
 Increase in the pressure at output header because of path blockage.
 Reduction in the pressure of gas in compressor inlet for any reason.
 Variation in fluid molecular mass because of changes in gas contents.
 Sudden reduction in rotation turns for any reason (for example emergency stop).
Since the centrifugal compressors contribute as major and expensive components in most processes of amplifying the
pressure of gaseous fluids, it seems essential then to protect these valuable assets against potential damages due to the
surge phenomenon. Surge control system (anti-surge) is responsible for meeting this requirement.
Operational point of compressor must be taken carefully into account by any operator not allowing of this point
approximates surge line and ensuring immediate intervention of control system when such situation takes place. Surge
control system is considered as one of the most critical systems for centrifugal compressors preventing them from going
into surge condition. Many different surge controllers have been developed so far, however they share a common objective
that is predicting and preventing incident of surge.
Control systems must measure flowing current and compressor head and also estimate compressor operational point based
on the measurement. Then, in the case that a flow which is passing through the compressor at a certain head is lower
than minimum value, anti-surge valve must be excited to open at a definite time and a set point (predefined point) which
is determined by surge control system. By opening this valve the compressor will be provided with more flow and
consequently compressor head will be decreased[3 – 6].
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In the present study we try firstly to design both classic(PID) and fuzzy logic active controllers for centrifugal compressor
system and then, to determine an appropriate controller for avoiding surge incident based on a comparative simulation of
both cases. It should be noted that the simulation process was carried out for four sample turns
(18000, 21000,
23000, and 25000 Rounds Per Minute(RPM)) each lasted for a five seconds duration. The proposed turns have been
selected randomly.
2. SURGE CYCLE
Surge is defined as a form of instability in flow which essentially occurs in dynamic compressors. This phenomenon
occurs when compressor is no longer able to generate enough head to overcome its downstream resistance or simply the
air pressure after the compressor is actually higher than what the compressor itself can physically maintain. Under such
conditions a reciprocating (cyclical) motion will be created in the gas flow.
Figure 1 shows surge cycle sketched on compressor characteristic curve (also known as compressor map). Let's assume
that compressor operates at stable point D. As demand for gas decreases the operating point will move towards the point
A (surge limit) and by extending beyond A boundary compressor will no longer capable of increasing the pressure. As a
consequence output pressure will be lower than that of downstream, hence flow direction will be reversed and operating
point will mutate to B. Point B is not considered a stable position in the range of compressor performance. As inversion
of flow happens downstream pressure decreases and simultaneously flow tends towards becoming positive until the
operating point reaches C. at point C the amount of flow is far too low to provide required pressure for returning to point
A. Consequently, the operating point will be altered to point D where flow rate too higher than that is demanded.
Therefore, a pressure is generated again at output leading to meet point A. This process will be repeated cyclically if no
changes are made in compressor conditions.
Figure 1 Surge cycle on characteristic curve of centrifugal compressor
Surge phenomenon may be occurred also due to lack of enough input flow since it can reduce output flow. Considering
the fact that the cycle may be repeated several times per second, it can impose severe damages on the system. Thus,
protection of centrifugal compressors against potential damages because of surge incident is highly needed[7 – 10].
3. MODELING AND DIMENSIONLESS EQUATIONS FOR CENTRIFUGAL COMPRESSOR SYSTEM
Dynamic models for compression systems were firstly developed by Emmons (1955). Practical efforts to expand this field
was not made until 1976 when a non-linear dynamic model for axial compression system was proposed by Greitzer
followed by more complete model by Moore (1986), then Graydahl (1999) attuned Moore model for variable-turn mode.
In the present study Greitzer model developed in 1976 has been adopted for describing compressor dynamic behavior.
Greitzer model is illustrated schematically in Figure 2.
Figure 2 Greitzer system model
Since the emergence of fluctuations in pressure and inversion of flow are dominant features indicating surge occurrence,
the required equations will take the form of a set of dimensionless equations based on dimensionless pressure (Ø) and
dimensionless flow (ψ). These equations are expressed by relations (1) and (2).
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
 
m
 a AcU t
P
(1)
(2)
1
 aU t2
2

where m represents mass flow (kilogram per second),  a represents air density (kilogram per cubic meter), Ac
represents surface area of compressor duct (square meter), P represents pressure difference (pascal), and
U t represents
rotor speed (meter per second)[2, 11].
4. ACTIVE CONTROL OF SURGE
Active surge control system is composed of one sensor which measures disturbances resulted from surge and one
controller which compare the amount of disturbances with critical point and in the case of violation of normal range
activate the required commands to enable controller to suppress or reduce surge. A typical example of such system circuit
is illustrated in Figure 3.
Figure 3 The circuit of active surge control system
Depending on different types and different locations of surge incident, different sensors can be selected for detection and
measurement of surge. One of the most useful options is using pressure sensor which can be employed for measuring total
disturbance in pressure, static pressure in input, or disturbances in compressor output
pressure[9, 12 – 14].
Typical layout of different sensors mounted for detecting surge in centrifugal compressors and also operators which are
activated upon receiving control signal is illustrated in Figure 4.
Figure 4 Layout of sensors and operators involved in surge control
In the present study pressure sensor mounted on compressor output or plenum space was employed for measuring
disturbances resulted from surge occurrence. The utilized operator for the purpose of reducing disturbances and
stabilizing system was anti-surge valve which opens proportional to signal received from controller and discharge a
certain portion of the outgoing flow.
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5. DESIGN OF FUZZY LOGIC ACTIVE CONTROLLER FOR CENTRIFUGAL COMPRESSOR
Introducing fuzzy sets and concept of membership degree in 1965, Dr. Lotfali Asgarzadeh founded fuzzy logic[15].
In this section centrifugal compressor system is equipped with fuzzy logic active controller. The fuzzy controller has been
designed using graphical relation of fuzzy logic toolbox. The method adopted for this purpose is of Mamdani type. Figure
5, illustrates block diagram of Fuzzy Inference System (FIS).
Figure 5 Fuzzy Inference System block diagram
The designed fuzzy logic active controller system has one input and output, i.e. the error is considered as input parameter
and the response to throttle excitation signal acts as output parameter. The membership functions of input and output are
defined as of triangular type as can be seen in Figure 6. These functions are defined by verbal variables: (MF1), (MF2),
(MF3), (MF4), (MF5), (MF6), (MF7), (MF8), (MF9), (MF10).
Figure 6 Type of input and output membership functions
Totally 10 membership functions have been defined for input and output, thus 10 inference rules are required. Figure 7
illustrates these rules.
Demux
Rul e
Rule1
Demux
Input MF
1
Demux
Rul e
max
COA
In1
Defuzzifi cati on1
Rule2
surge
Demux
Rul e
AggMethod1
Rule3
Demux
Rul e
Output MF
Rule4
Demux
Rul e
>
1
Zero Fi ri ng Strength?
Out1
0
khoroji
Rule5
Demux
Total Fi ri ng
Strength
-C-
Switch
MidRange
Rul e
Rule6
Demux
Rul e
Rule7
Demux
Rul e
Rule8
Demux
Rul e
Rule9
Demux
Rul e
Rul e10
Figure 7 Fuzzy inference rules
As shown in Figure 7, the number of blocks equal to fuzzy inference rules and the lines from and to these blocks represent
relations associated with fuzzy logic rules. Input and output variables are depicted on left side and right side of the figure
respectively. Trial and error method has been used for obtaining both input extent and applied fuzzy rules. The level of
control for this system is illustrated in Figure 8.
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Figure 8 System control level
Also, the simulated model for centrifugal compressor system equipped with fuzzy logic active controller is illustrated in
Figure 9.
Figure 9 Simulated system model
6. DESIGN OF CLASSIC ACTIVE CONTROLLER(PID) FOR CENTRIFUGAL COMPRESSOR
Figure 10 is an illustration of a PID controller.
Figure 10 PID controller
As can be seen from Figure 10, transformation function in this controller is derived from relation (3) in which U
represents output signal, E represents error signal, K p represents proportional gain, Td represents derivative element,
and
Ts represents integrator element.

U s 
1 

 K p 1  Td s 
E s 
Ti s 

(3)
PID controller advantage over most control systems lies in their general applicability. Practically, when the mathematical
model of a system is unknown and hence applying analytical approaches in designing are impossible, PID controller
would be very useful. Merits of PID controllers and their modified forms have been demonstrated in the field of process
control systems. Since these controllers are often adjusted locally different tuning rules have been proposed for them.
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Applying these rules it would be possible to provide an accurate and fine adjustment. Invention of automatic adjusting
methods has paved the way for integrating PID controllers with this function. Ziegler and Nichols have proposed a set of
rules for adjusting controllers based on step response obtained from examination or value of K p which leads to boundary
stability when proportional control is used. Ziegler-Nichols rules are employed when mathematical model of system in
not known, however they can also be used in the design of systems mathematical model of which are known. These rules
result in a set of values for K p , Ti , and Td coefficients and consequently system stability. Ziegler-Nichols rules are
vastly used for industrial control systems the dynamic behaviors of which are not known clearly. Usability of these rules
has been validated for a long time. However, these rules can also be used for systems with known dynamic behavior[16,
17].
Figure 11 Designed model for PID controller
7. THE OBTAINED RESULTS FROM SIMULATION OF CENTRIFUGAL COMPRESSOR SYSTEM
INTEGRATED WITH ACTIVE SURGE FUZZY LOGIC CONTROL SYSTEM
The provided diagrams in this section include fluctuations of dimensionless pressure in terms of time, dimensionless flow
in terms of time, and dimensionless pressure in terms of dimensionless flow. The observed results from simulation of
centrifugal compressor system equipped with active surge fuzzy logic control system will be indicated for four sample
turns: 18000, 21000, 23000, and 25000 Rounds Per Minute (RPM). Simulation time was defined as a five-second
duration. Figures 12(a),(b), 13, and 14 show the results observed in simulation for sample turn 18000 Rounds Per
Minute(RPM).
Figure12(a) Dimensionless pressure diagram in terms of time(left side), (b) zoomed view of part a (right side)
Figure 13 Dimensionless flow diagram in terms of time
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Figure 14 Dimensionless pressure diagram in terms of
dimensionless flow
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Figures 15(a),(b), 16, and 17 show the results observed in simulation for sample turn 21000 Rounds Per Minute(RPM).
Figure15(a) Dimensionless pressure diagram in terms of time(left side), (b) zoomed view of part a (right side)
Figure 16 Dimensionless flow diagram in terms of time
Figure 17 Dimensionless pressure diagram in terms of dimensionless flow
Figures 18(a),(b), 19, and 20 show the results observed for sample turn 23000 Rounds Per Minute(RPM).
Figure18(a) Dimensionless pressure diagram in terms of time(left side), (b) zoomed view of part a (right side)
Figure 19 Dimensionless flow diagram in terms of time
Figure 20 Dimensionless pressure diagram in terms of dimensionless flow
Figures 21(a),(b), 22, and 23 show the results observed for sample turn 25000 Rounds Per Minute(RPM).
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Figure21(a) Dimensionless pressure diagram in terms of time(left side), (b) zoomed view of part a (right side)
Figure 22 Dimensionless flow diagram in terms of time
Figure 23 Dimensionless pressure diagram in terms of dimensionless flow
It can be observed that dimensionless flow diagrams in terms of time are stabilized following formation of an Over Shoot
in all four suggested turns, while dimensionless pressure diagrams in terms of time are stabilized without any Over Shoot
in all suggested turns except for the turn 18000(RPM).
8. THE OBTAINED RESULTS FROM SIMULATION OF CENTRIFUGAL COMPRESSOR SYSTEM
INTEGRATED WITH ACTIVE SURGE CLASSIC(PID) CONTROLLER SYSTEM
Similar to previous section, the obtained results from simulation of centrifugal compressor system integrated with active
surge classic control system (PID) will be shown for four sample turns: 18000, 21000, 23000, and 25000 Rounds Per
Minute(RPM). Simulation time was defined as a five-second duration.
Figures 24(a),(b), 25, and 26 show the results observed for sample turn 18000 Rounds Per Minute(RPM).
Figure24(a) Dimensionless pressure diagram in terms of time(left side), (b) zoomed view of part a (right side)
Figure 25 Dimensionless flow diagram in terms of time
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Figure 26 Dimensionless pressure diagram in terms of dimensionless flow
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Figures 27(a),(b), 28, and 29 show the results observed for sample turn 21000 Rounds Per Minute(RPM).
Figure27(a) Dimensionless pressure diagram in terms of time(left side), (b) zoomed view of part a (right side)
Figure 28 Dimensionless flow diagram in terms of time
Figure 29 Dimensionless pressure diagram in terms of dimensionless flow
Figures 30(a),(b), 31, and 32 show the results observed for sample turn 23000 Rounds Per Minute(RPM).
Figure30(a) Dimensionless pressure diagram in terms of time(left side), (b) zoomed view of part a (right side)
Figure 31 Dimensionless flow diagram in terms of time
Figure 32 Dimensionless pressure diagram in terms of dimensionless flow
Figures 33(a),(b) 34, and 35 show the results observed for sample turn 25000 Rounds Per Minute(RPM).
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Figure33(a) Dimensionless pressure diagram in terms of time(left side), (b) zoomed view of part a (right side)
Figure 34 Dimensionless flow diagram in terms of time
Figure 35 Dimensionless pressure diagram in terms of dimensionless flow
As can be seen, the diagrams associated with both dimensionless flow and dimensionless pressure in terms of time for
four proposed turns are stabilized after Over Shoot.
9. CONCLUSION
The occurrence of surge phenomenon is not certainly predictable and controllable, however it can be avoided. Surge
control system is considered as one of the essential components for centrifugal compressors accounting for prevention of
compressor from reaching surge region.
Most of the surge control systems have been designed to restrict compressor performance range to a flow rate level higher
than a certain area known as surge line. The distance between control line and surge line is called surge margin. The
smaller this distance the higher yields will be gained from compressor and on the other hand the larger this distance the
lesser risk of surge will be[18].
Surge margin is taken into account as constant but optimized (usually ranges from 6 to 10 percent of real surge margin
flow) in most algorithms. Optimal surge margin is selected based on certain factors including response time of valve,
measurement system and control system in relation to surge time and the amount of uncertainty in measurement of
pressure, flow, etc.
In the present study following to determining Greitzer model as an appropriate one and obtaining dimensionless
equations for centrifugal compressor system, the simulation of this system in two modes (with active fuzzy logic
controller and with active classic (PID) controller) has been investigated the results of which have been presented in
sections 6 and 7 and for four sample turns: 18000, 21000, 23000, and 25000 RPM. The performances of these controllers
are compared in Tables 1 and 2 for dimensionless flow diagram in terms of time and dimensionless pressure in terms of
time respectively. It should be noted that the percentage of reduction in system Over Shoot was considered as an
examination criterion for comparing the performances of active control systems dealt with in this study.
Table 1: Evaluation of dimensionless flow diagrams in terms of time
Active surge classic (PID) control system
Active surge fuzzy logic control
Turns (rounds per minute)
system
47.393%
37.015%
18000
47.720%
35.190%
21000
47.720%
35.190%
23000
51.146%
33.440%
25000
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Table 2: Evaluation of dimensionless pressure diagrams in terms of time
Active surge classic (PID) control
Active surge fuzzy logic control
Turns (rounds per minute)
system
system
0.0531%
0.0250%
18000
0.0220%
Without Over Shoot
21000
0.0220%
Without Over Shoot
23000
0.0627%
Without Over Shoot
25000
As can be inferred from the data provided by Table 1 for dimensionless flow diagram in terms of time, in the case of
sample turn 18000 the system Over Shoot has been reduced by 10.378% through active surge fuzzy logic control system
by comparison with classic control system (PID) and similarly by 12.530%, 12.530%, and 17.706% for turns 21000,
23000, and 25000 respectively, hence it is easily stabilized.
Moreover, considering Table 2 for dimensionless pressure diagram in terms of time, a reduction by 0.0281% is obvious in
the system Over Shoot incorporating active fuzzy logic control system comparing with classic control system(PID).
Besides, active surge fuzzy logic control system is stabilized without Over Shoot considering 21000, 23000, and 25000
turns, whereas active surge classic control system(PID) is stabilized with an Over Shoot of 0.0220%, 0.0220%, and
0.0627% for 21000, 23000, and 25000 turns respectively.
Finally, we can conclude that surge active fuzzy logic control system is able to stabilize centrifugal compressor system
with a minimum Over Shoot (in dimensionless flow and pressure diagrams in terms of time) or even without Over Shoot
(in dimensionless pressure diagrams in terms of time).
Therefore, capability and accuracy of active fuzzy logic control system in control of surge phenomenon in centrifugal
compressors is far higher than that of active classic control systems (PID). Consequently, by applying active surge fuzzy
logic control system the following destructive outcomes will be avoided:
 Disturbances in the process.
 Decrease in efficiency.
 Short life span due to mechanical damages imposed on constituent components.
 Loss of critical and sensitive internal degrees of freedom for mechanical parts.
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Volume 2, Issue 11, November 2013
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AUTHOR
Qasem Abdollah Nezhad was born in 1984, He received bachelor of Science in Mechanical Engineering from the
Department of Mechanical Engineering, Islamic Azad University, Tabriz branch, Iran, in 2011, and Master of Science
Mechatronics Engineering from the Department of Mechatronics Engineering, Science and Research Islamic Azad
University, Kurdistan branch, Iran, in 2013. Currently he is a lecturer, He is the author of several papers in National
Conference, His research interests includes robotics, mechatronics, image processing, control systems, fuzzy control
application.
Jafar Ghafouri He received a BSs degree in Mechanical Engineering filed of Solids Design from Tabriz University,
Iran, in 1999, and received MSs degree in Mechanical Engineering major field of Transformation of Energy from
University of Science & Technology, Tehran, Iran, in 2001. In 2008, he got a PhD in the same major from Science and
Research Islamic Azad University,Tehran Branch, Iran. He's now a member of Academic Board of Tabriz Azad
University, iran, and assistant professor at the same place. The specific fields of research in which he's interested and has
presented several articles include: internal combustion engines, combustion, heat transfer, CFD, smart systems and heat
exchangers.
Mohammad Fathi He received a BSs degree in Biomedical Engineering from University of Shahid Beheshti, Tehran,
Iran, in 2000, and received MSs degree in Electrical Engineering major field of Communications from Amirkabir
University of Technology, Tehran, Iran, in 2002. Seven years later he got a PhD in the same major and from the same
university. He's now a member of Academic Board of Kurdistan University, Iran, and at the same time assistant professor
and registrar of Electrical Engineering major. His teaching career has been dealt with signal & system, communications,
engineering mathematics, communicational networks, and random processes. The special fields on which he has studied
and presented several articles include: wireless communications, optimizing communicational networks, smart systems
and smart electrical networks.
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