Frontiers in Computing and Intelligent Systems 
ISSN: 2832-6024 | Vol. 7, No. 1, 2024 

 

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Research	and	Simulation	of	Fuzzy	Expert	Anti‐surge	
Control	System	for	Compressor	
Yanan Yi, Mingge Sun 

School of Information and Control Engineering, Jilin Institute of Chemical Technology, Jilin 132022, China 

 

Abstract: In order to solve the problem of compressor surge caused by flow fluctuations that cannot be effectively solved by 
conventional PID control, a fuzzy expert PID controller was designed based on the analysis of the working principles of fuzzy 
controllers and expert controllers. This controller has the advantages of good stability and high control accuracy of fuzzy control, 
as well as the advantage of fast response time of expert controllers. The MATLAB simulation results show that the fuzzy expert 
PID control algorithm has the characteristics of high stability, fast response speed, and small overshoot compared to conventional 
PID. 

Keywords: Compressor; Anti-surge Control; Fuzzy-Expert PID Control. 
 

1. Introduction 
Compressor as the main unit component of catalytic 

cracking unit, in its use process, surge phenomenon is very 
easy to appear, surge will not only cause instability of process 
parameters, bring great chaos to production, but also greatly 
shorten the service life of the compressor. In recent years, 
there have been many researches on compressor surge control 
methods. Qin Xiao dong [1] et al. proposed the constant 
pressure approximation control method, which effectively 
expands the compressor operating range and adopts fuzzy 
PID output control to accelerate the system response speed. 
However, this method has high requirements on the selection 
of initial conditions and the parameter setting is more 
complicated; Tian Hai and Liang Mao yu [2] adopt a method 
that combines synchronous frequency conversion of two wind 
turbines with minimum extreme flow method and fuzzy PID 
control, effectively avoiding the occurrence of surge. Due to 
the need for parameter tuning in both synchronous frequency 
conversion and fuzzy PID control, the combination of the two 
makes parameter adjustment more difficult; Fang Lin [3] uses 
an expert PID algorithm combined with a PLC controller to 
achieve blower surge prediction and anti-surge control, 
ensuring the stable operation of the unit, but has poor 
adaptability to nonlinear systems. A method combining fuzzy 
PID control with expert PID control is proposed to address 
the flexibility issue of parameter adjustment in the 
compressor control system mentioned above. 

2. Compressor Surge 

2.1. Impact on Compressor Surge 
The surge generated by compressors is mainly determined 

by two factors, internal and external. Internal cause: Under 
abnormal operating conditions, the unit causes the flow rate 
to be less than the minimum value, resulting in a decrease in 
the flow rate of the compressor, and even a state of no flow; 
External cause: The pressure of the pipeline network is higher 
than the outlet pressure provided by the compressor, causing 
gas backflow and causing significant vibration [4] 

The surge characteristic curve of the compressor is shown 

in Figure 1, where the horizontal axis represents the 
compressor flow rate Q, the vertical axis represents the 
compressor outlet pressure P, and N represents the 
compressor speed [5]. A1-A4 are the surge points at different 
speeds. When at a certain speed, the compressor enters the 
surge zone (to the left of the surge point), the outlet pressure 
gradually decreases, and the flow rate also decreases. At this 
time, the surge phenomenon will also follow. The relationship 
between compressor flow rate and speed is proportional, and 
as the compressor flow rate decreases, the speed will also 
decrease accordingly. From the graph, it can be seen that as 
the speed increases, the surge zone becomes larger. In 
addition, inlet pressure, temperature, gas molecular weight, 
and pipeline capacity are also factors that affect compressor 
surge [6]. 

 
Fig 1. Compressor characteristic curve 

2.2. Main Performance Parameters of 
Compressor in Catalytic Cracking Unit 

Taking the main fan unit of a catalytic cracking unit in a 
certain refinery as an example, the main equipment is a 
compressor. In order to prevent compressor surge, it is 
necessary to maintain the main performance indicators of the 
compressor within the fluctuation range of the values listed in 
Table 1, with a margin of 5-10%. 

 
 



 

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Table 1. Main performance parameters of the compressor 

Parameter inlet pressure Inlet flow speed 
Outlet 

pressure 
Outlet flow 

numerical value 0.098MPa 3262Nm3/min 5848r/min 0.4MPa 3200Nm3/min

3. Compressor Anti-surge Control 
The anti-surge control methods for compressors can be 

divided into active and passive anti surge control, but usually 
passive anti surge control is used for anti-surge control of 
large compressors. The control principle of the passive 
control method is to adjust the opening of the anti-surge valve 
based on the inlet flow rate of the compressor, thereby 
achieving the purpose of anti-surge [7]. 

The schematic diagram of the traditional compressor anti-
surge control system is shown in Figure 2. 

 
Fig 2. Schematic diagram of traditional compressor anti-surge 

control system 
 
The flow regulator FC is a conventional PID controller, and 

according to the compressor characteristic curve, the set value 
of FC must be greater than the surge flow value. When the 
system load decreases, the inlet air flow rate of the 
compressor decreases, the FC output decreases, and the anti-
surge valve gradually opens to ensure that the inlet flow rate 
of the compressor is not lower than the surge flow rate, thus 
achieving the purpose of anti-surge [8]. Although 
conventional PID controllers can achieve anti surge, they are 
only suitable for low load situations and not suitable for other 
load situations. Therefore, based on the conventional PID 

controller, a fuzzy expert PID controller has been proposed to 
improve the shortcomings of the conventional PID controller 
and achieve online parameter tuning. 

4. Fuzzy Expert PID Control System 

4.1. Fuzzy PID Controller 
Fuzzy PID controller is based on conventional PID 

controllers and utilizes fuzzy theory to construct a fuzzy 
relationship between error e and error change rate ec, as well 
as the three parameters kp, ki, and kd of PID, in order to 
achieve more accurate control. Its structure is shown in Figure 
3. The fuzzy controller needs to first fuzzify the input quantity, 
then go through fuzzy reasoning, and finally clarify the fuzzy 
reasoning results, outputting three parameters kp, ki, and kd to 
achieve online tuning of PID controller parameters [9]. 

 

 
Fig 3. Structure diagram of fuzzy PID controller 

4.1.1. Fuzzification and Membership Function 
Due to the fact that the fuzzy PID controller is a two input 

and three output controller, with e and ec as input variables 
and kp, ki, and kd as output variables, with compressor flow 
rate as deviation e and compressor flow rate change rate as ec. 
Using fuzzy sets {NB, NM, NS, ZO, PS, PM, PB} to fuzzify 
e and ec [10]. The domains for selecting e and ec are both [-
3,3]; According to the regulation law of the compressor flow 
PID, the domain of kp is taken as [-0.3,0.3]; The domain of ki 
is [-0.05,0.05]; The domain of kd is [-2,2], at which point the 
control performance of the system is optimal. Among them, 
the input and output variables are represented by triangular 
membership functions. 

4.1.2. Establishment of Fuzzy Rules 
 

Table 2. Fuzzy Rule Table for kp Variables 
ec 

e 
NB NM NS ZO PS PM PB 

NB PB PB PM PM PS ZO ZO
NM PB PB PM PS PS ZO NS
NS PM PM PM PS ZO NS NS
ZO PM PM PS ZO NS NM NM
PS PS PS ZO NS NS NM NM
PM PS ZO NS NM NM NM NB
PB ZO ZO NM NM NM NB NB

 
The fuzzy control rule table determines the control effect 

of the fuzzy controller and is the core of the fuzzy controller. 
When the deviation e and deviation change rate ec are large, 
in order to reduce system overshoot and oscillation, kp should 
be increased while reducing the effects of ki and kd; When the 

deviation e gradually decreases, in order to reduce steady-
state error and improve system accuracy, it is necessary to 
appropriately reduce kp while increasing the effects of ki and 
kd [11]. Determine the magnitude of the corresponding effects 
of kp, ki, and kd based on the deviation e and deviation change 



 

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rate ec at different response stages. Based on the above 
experience, the fuzzy PID control rule tables for kp, ki, and kd 

are shown in Tables 2, 3, and 4. 

 
Table 3. Fuzzy Rule Table for ki Variables 

ec 
e 

NB NM NS ZO PS PM PB 

NB NB NB NM NM NS ZO ZO
NM NB NB NM NS NS ZO ZO
NS NB NM NS NS ZO PS PS
ZO NM NM NS ZO PS PM PM
PS NM NS ZO PS PS PM PB
PM ZO ZO PS PS PM PB PB
PB ZO ZO PS PM PM PB PB

Table 4. Fuzzy Rule Table for kd Variables 
ec 

e 
NB NM NS ZO PS PM PB 

NB PS NS NB NB NB NM PS
NM PS NS NB NM NM NS ZO
NS ZO NS NM NM NS NS ZO
ZO ZO NS NS NS NS NS ZO
PS ZO ZO ZO ZO ZO ZO ZO
PM PB PS PS PS PS PS PB
PB PB PM PM PM PS PS PB

4.2. Expert PID Controller 
4.2.1. Expert PID Control Structure Diagram 

Expert PID controller is a controller that utilizes an expert 
rule library to adjust and modify PID parameters in real 
time[12]. The expert PID control structure diagram is shown 
in Figure 4. 

 
Fig 4. Expert PID control structure diagram 

4.2.2. Expert Control Rule Design 
e(k) represents the sampling error value at the current 

moment, and if e (k-1) and e (k-2) are the error values of the 
first two moments, the relationship is as shown in formulas (1) 
and (2) [13]. 

△e(k)=e(k)-e(k-1)                 (1) 

△e(k-1)=e(k-1)-e(k-2)              (2) 
Based on the error and its variation, the design rule for 

expert PID is [12]. 
1)When |e(k)|>M1, the error value at this time is very large. 

No matter how the error trend changes, the compressor will 
experience surge. The anti-surge valve should be fully opened 
and the speed should be appropriately reduced. 
2)When e(k) △ e(k)>0, it indicates that the error is 

increasing or is a constant value. The design rule in this state 
is: when |e(k)|≥M2, M2<M1 indicates that the error value is 
still too large, the compressor is in a critical state of surge, and 
the error value continues to increase. At this point, the 
controller will issue an alarm signal, and the compressor anti-
surge control needs to adopt a strong control method. The 
controller output is shown in formula (3). 

u k =u k-1 +k1{kp e k -e k-1 +kie k +kd e k -2e k-1 +e k-2 }  (3) 
When |e(k)|<M2, although the error value is increasing at 

this time, the compressor is in a safe operating state, and the 
controller output is as shown in formula (4) 

u k =u k-1 +kp e k -e k-1 +kie k +kd[e k -2e k-1 +e k-2 ] (4) 

3)When e(k) △ e(k)<0,e(k) △ e(k-1)>0,or e(k)=0, it 
indicates that the anti-surge control of the compressor is in a 
stable operating state, and the input and output of the control 
system have reached balance or there is a trend of error 
reduction. At this time, the output of the controller remains 
unchanged. 
4) When e(k)△e(k)<0 or e(k)△e(k-1)<0, the current error 

is at the extreme position, and the control action should be 
selected based on the size of the error. If |e(k)|≥M2, the control 
effect is strong, and the controller output is as shown in 
formula (5). 

u k =u k-1 +k1kpem(k)              (5) 
On the contrary, |e(k)|<M2, the control effect is weak, and 

the controller output is as shown in formula (6). 
u k =u k-1 +k2kpem(k)              (6) 

5) When |e(k)|≤ε When the error is almost zero, the 
compressor operates safely within a certain range. With the 
proportional and differential coefficients unchanged, the 
integral control is appropriately increased to further enhance 
system stability. 

Parameter in formula: M1>M2>0; K1>k2>0; Em(k) 
represent the k-th extreme value of error e;△e(k) is the rate 
of error change of the k-th value; u (k) represents the output 
of the controller for the kth time; K1<1; 0<k2<1; ε Is a smaller 
positive number. 

4.3. Design of Fuzzy Expert PID Controller 
The structure diagram of the fuzzy expert PID controller 

designed for anti-surge control of compressors is shown in 
Figure 5. Given an input signal, compare it with the set value 
to obtain the deviation e(k), and then select the appropriate 
control mode based on the absolute value of the error |e(k)| 
and the product of e(k) △e(k). At the same time, the real-
time values of e(k) and △e(k) are used to adjust the flow 



 

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control effect of the compressor, thereby making the control 
of the controlled object more flexible and accurate. The 
comprehensive use of fuzzy control and expert PID control 
ideas enables the controller to combine the advantages of both, 
ensuring high control accuracy and being able to flexibly 
respond to different control scenarios and operating 
conditions. 

The specific switching principles are as follows: 

1) When e(k)△e(k)<0 and e(k)△e(k-1)>0 or e(k)=0 (i.e. 
when the deviation is at the extreme position) and |e(k)|>M1 
Select an expert PID controller (i.e. when the deviation is 
large). 

2) In other cases, a fuzzy PID controller is used to adjust kp, 
ki, and kd, and corresponding control is implemented to 
control the flow rate of the compressor. 

 
Fig 5. Structure diagram of fuzzy expert PID controller 

 

5. Analysis of Simulation Results 

5.1. Transfer Function 
Through the analysis of the working principle of the above 

control system, the controlled object can be equivalent to two 
pure lag inertial links connected in series, and its transfer 
function is shown in formula (7). 

G s =
k

(Ts+1)2 e-τs                 (7) 

T is the time constant of the inertial link; K is the 
amplification coefficient of the inertial link; τ Is the delay 
time of the lagging link. Where K=3.85, T=16 τ= 27. 

5.2. Simulation Result 
The simulation curves of conventional PID controller and 

fuzzy expert PID controller in MATLAB for anti-surge 
control of compressors are shown in Figure 6. 

 

 
Fig 6. PID and Fuzzy - Expert PID Control Simulation Results 

 
Table 5. Comparison of conventional PID, fuzzy PID and fuzzy-expert PID control data 

Control mode PID Fuzzy PID fuzzy-expert PID
Overshoot (%) 22 3 0.8 

Adjust the time(s) 420 400 210 
Rise time(s) 75 82 70 

 
It is evident from Figure 6 that the fuzzy-expert PID controller is significantly superior to the conventional PID 



 

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controller and the fuzzy PID controller in terms of control 
time, response speed and overshoot. Comparison of specific 
control data is shown in Table 5. 

6. Conclusion 
Simulation results show that compared with conventional 

PID controller, fuzzy-expert PID controller significantly 
speeds up the response speed of the system, shortens the time 
for the system to reach stability, significantly enhances the 
control capability of the system, effectively improves the 
stability of the unit operation, and reduces the probability of 
surge. Ensure the safe operation of the entire unit. 

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