[ieee 2006 international conference on computational inteligence for modelling control and...

Fuzzy immune Self-regulating PID Control of Networked Control System

Laihua Fang1,2, Zongzhi Wu1

1. China Academy of Safety Science and Technology, Beijing, 100029, China

[email protected]

Aiguo Wu2, Aihong Zheng2

2. School of Electrical and Automation Engineering, Tianjin University, Tianjin,

300072, China

Abstract

Network-induced time delay is the main factor that deteriorates the performance of networked control system (NCS). In order to effectively restrain the impact of network delay on NCS, a fuzzy immune self-regulating PID control scheme is proposed. With ideas from the biological immune system, fuzzy immune PID control strategy is applied to NCS, in which parameter P is adaptively modulated by means of fuzzy immune algorithm, parameters I and D are dynamically regulated by fuzzy logic scheme. Simulation on network-based controlled DC motor is carried out so as to evaluate application of the presented control scheme in NCS. The result of simulation experiment shows validity of the control scheme and improvement in dynamic performance and robustness of NCS. 1. Introduction

The rapid development and wide use of computer and network technologies have made it possible for researchers to investigate network-based architectures for complex control systems and try new ideas in implementing autonomous and intelligent system.

Networked control system (NCS) is a feedback control system wherein the control loops are closed through real-time communication network. Two types of setup of NCS are presented in figure 1and 2. NCS has many advantages over traditional point-to-point control system. Some obvious ones are the reduced cabling cost, modularity, flexibility in system design, ease of installation and diagnosis. A more subtle advantage is the ability of separated systems to interact and communicate with each other. But the insertion of communication network in the feedback control loops makes the analysis and design of networked control system much more complex [1,2]. One of its fundamental issues in NCS is network-induced delay which occurs when sensors, actuators, and controllers exchange data across the network. The delay, either

constant or time varying, can degrade the performance of control system and can even destabilize the system without considering the effect of delay. Other problems such as single-packet or multiple-packet transmission of plant inputs and outputs [2], and dropping of network packets also have a great impact on the performance of the system.

Several approaches have been investigated in the

analysis, modeling and control of NCS. Deterministic control scheme is firstly proposed, in which variable network-induced delays are considered as constant by introducing buffers in data receiving and sending ends [1]. In optimal stochastic control methodology, controller is designed to guarantee the stability and performance criterion of NCS in a statistical sense, assuming the probability distributions of delay is known [3]. In robust control method, the network delays are modeled as simultaneous multiplicative perturbation, and controller is given in frequency domain [4]. Intelligent control techniques such as fuzzy logic modulation and genetic algorithm are also presented in some literatures [5, 6, 7].

In this paper, a fuzzy immune adaptive PID control strategy is proposed and applied in NCS, in

Figure 1. Hierarchical structure of NCS

+

Actuator Plant Sensor

Network (Industrial Ethernet/Fieldbus /Internet/ wireless network)

Primary Controller (Computer)

-

Time delay

Other network users

Other network users

Packet loss

Time delay

Packet loss

Remote controller

International Conference on Computational Intelligence for ModellingControl and Automation,and International Conference onIntelligent Agents,Web Technologies and Internet Commerce (CIMCA-IAWTIC'06)0-7695-2731-0/06 $20.00 © 2006

which parameter P is adaptively modified in means of fuzzy immune algorithm, parameters I and D are regulated by fuzzy logic scheme. A networked control system for DC motor control is implemented on industrial Ethernet in order to validate the feasibility of fuzzy immune PID control in NCS. Simulation result shows good performance of the control scheme, compared with other method.

2. Immune mechanism

As is known, immune is a special physiological reaction in biosome, corresponding antibody is produced to resist attacking antigen, which is destroyed by phagocytosis or particular enzyme generated by antibody. Immune system is composed of antibody and lymphocyte, which is made up of T cells (auxiliary cell hT and suppressor cell sT ) produced by thymocyte and B cells created by marrow [8]. When antigen invades organism and is digested by surrounding cells, messages are sent to hT and sT cells, and B cell is stimulated to create more antibody so as to eliminate antigen. If quantity of antigen is large, much more auxiliary cells hT yield, but number of suppressor

cell sT reduces, which results in more B cell production; if antigen becomes less, number of

sT increases and that of hT decreases, which results in the decrease of B cell. Synergism between suppressor mechanism and main feedback mechanism is realized through quick response of immune system to antigen and stabilizing immune system. Figure 3 shows the regulatory principle of immune system in body fluid.

3. Immune PID control

Discrete form of regular incremental PID control is described as follows：

( )( ))2()1(2)(

)()1()()1()(−+−−+

+−−+−=

kekekekkekkekekkuku

d

ip(1

) where dip kkk ,, is proportional, integral and differential coefficient respectively. Due to its simplicity and ease in adjustment, traditional PID control is widely used in industrial control; however, this traditional PID control algorithm is not ideal in networked control system, in which network-induced delay is random.

Though it is complex, immune system’s ability to adaptively resisting antigen is obvious. Intelligent behavior in creature information system provides various theory reference and technical methods for science and engineering field. Based on the immune feedback theory, immune PID controller is proposed as following [9]:

Assuming the number of kth generation of antigen is )(kε , the output of auxiliary cell hT is )(kTh ,

impact of sT on B is )(kTs , and all impetus that B cell received is

)()()( kTkTkS sh −= (2) where

)()( 1 kkkTh ε= , ( ) )()(),()( 2 kksksfkkTs ε∆= .

If number of antigen )(kε is supposed to be equivalent to the error )(ke , and overall impetus )(kS that B received is equivalent to )(ku , then following control scheme is gained:

－+

Foreign antigen

Stem cell

T cell

B cell

Auxiliary Th

Suppressor Ts

Macrophage Plasma cell

antibody

Integrated

Free antibody

Figure 3. Mechanism of immune regulatory system

Figure 2. General Structure of NCS

Time delay Network (Industrial Ethernet/Fieldbus /Internet/ wireless network)

Actuator Plant Sensor

Primary Controller

(Computer)

Time delay

Other network users

Other network users

Packet loss Packet loss


)())(),(()()( 21 kekukufkkekku ∆−=

( )( ) )()(),(1 kekukufK ∆−= η

)(1 kek p= (3)

where 1kK = is control of response speed，

1

2

kk=η is used to control stability ，

)))(),((1(1 kukufkk p ∆−= η (4)

where ))(),(( kukuf ∆ is a selected nonlinear function. In order to determine ))(),(( kukuf ∆ , fuzzy control theory is utilized to acquire an approximate function. Input )(ku , )(ku∆ and output

))(),(( kukuf ∆ is fuzzified with two fuzzy sets for simplicity, which is positive （ P ） ,the other is negative (N). Output is fuzzified with three fuzzy sets, which are positive, zero and negative receptively. Combination of Z-shape, S-shape and delta shape membership function is used to describe fuzzy sets of input and output variables. Following control rules are defined to determine ))(),(( kukuf ∆ : （1） PisuandPisuIf ∆ , Nisuufthen ),( ∆ . (2) NisuandPisuIf ∆ ,

Zisuufthen ),( ∆ . （3） PisuandNisuIf ∆ ,

Zisuufthen ),( ∆ . (4) NisuandNisuIf ∆ ,

Pisuufthen ),( ∆ . In each rule, fuzzy logic AND operation is used. Controller’s output ( ))(),( kukuf ∆ is obtained by Mom (Maximum of means) defuzzification method. It can be seen from equation (3) that immune controller based on immune feedback mechanism is a nonlinear proportion controller, and proportion factor described as equation (5) varies as controller output changes.

)))(),((1(1 kukufKk p ∆−= η (5) where K is gain. So output of immune PID controller is

)())1()((()1()( 1 kekkekekkuku ip +−−+−=

))2()1(2)(( −+−−+ kekekekd (6)

4. Fuzzy immune PID control

While proportion 1pk is regulated by fuzzy immune

scheme mentioned above, proportion ik and dk is modified online using fuzzy control scheme so as to adapt well to different error E and error change rate Ec. Fuzzy immune self-tuning PID control is shown in figure 4.

Seven language fuzzy sets, which are NB(Negative

Big), NM(Negative Middle), NS(Negative Small),ZO(Zero),PS(Positive Small),PM(Positive Middle),PB(Positive Big), are used to describe input

),( ece and output di kk ∆∆ , .Membership function is determined by the combination of delta function and S-shape function, control rules are defined as table 1.

Table 1. Fuzzy control rules of ik∆ 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 BM 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 PB PB PB

Table 2. Fuzzy control rules of dk∆

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 NS PS PS PS PS PB PB PB PM PM PM PS PS PB

Mamdani fuzzy reasoning and normal MOM defuzzification method are utilized to obtain adaptively

kp1

r y

ki kd

PID regulator

Fuzzy reasoning

Fuzzy immune

regulating d/dt

Plant

d/dt

Figure 4. Structure of Fuzzy immune self-adjusting PID controller

－

u

Netw

ork


correcting value ik∆ and dk∆ . Regulating formula of integral coefficient and differential coefficient in PID controller are given as following:

iii kkk ∆+= )0( (7)

ddd kkk ∆+= )0( (8)

where )0(),0( di kk are initial values.

5. Case study

In order to demonstrate and measure the effectiveness of the presented controller using fuzzy immune PID algorithm mentioned above, a DC motor is used to work as network-based controlled plant. It is a common device for actuation and propulsion systems and a good example for time-delay sensitive application. In practical application, there are many other control loops, which compete for network bandwidth and cause network time delay. Ethernet is used as transmitting media in the simulation. Transfer function of controlled plant can be described as following:

)12.0(20)(

+=

sssG

Simulink model utilized in modeling and simulating network-based DC is shown in figure 5.

Network channel between server and client are shown in fig 6.

Fig 7 depicts membership functions of controller

input )(ku , )(ku∆ and output ))(),(( kukuf ∆ . Using control scheme above and traditional PID, we get the step response of networked controlled DC motor, which is shown in Fig 8. It can be seen that the system under the control of fuzzy immune PID quick comes to stability again when disturbance occurs at 3.5seconds.

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

u

Deg

ree

of m

embe

rshi

p

NB PB

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

du

Deg

ree

of m

embe

rshi

p

NB PB

Figure 6. Network channel

(a). from server to client

(b). from client to server

Controller

n3 n4

Client to server network

TI

i

V - +

w

Te

th

y

n1 n2 U E

1

1

0

R

To Workspace1

To Workspace

Server to client network

DC motor

Figure 5. Simulink blocks for network-based DC modeling


-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

f

Deg

ree

of m

embe

rshi

p

NB Z PB

Figure7. Membership of system input and output

6. Conclusions

It can be concluded from simulation and experiment that fuzzy immune PID control scheme decreases the rise time, settling time and maximum overshoot of system response. Simulation results clearly indicate the effectiveness of fuzzy immune self-tuning PID control scheme and improvement in the step response performance compared with traditional PID control. Application of fuzzy immune PID control makes networked control system acquire a fast dynamical response and strong robustness of performance. References [1] Wei Zhang, M.S. Branicky, and Stephen M.Phillips,

Stability analysis of networked control systems, PhD Dissertation: 2-6, Case Western Reserve University, 2001.

[2] J.Nilsson, Real-time controls systems with delays, PhD Dissertation:10-25,Lund, Sweden, 1998.

[3] Yang Y.Q., Xu D., Tan M., Hybrid and stochastic stabilization analysis and ∞H control for networked control systems, Robotics, Automation

and Mechatronics, IEEE Conference on Volume 1:502-506,Dec,2004.

[4] Goktas F., Distributed control of systems over communication networks. PhD Dissertation. University of Pennsylvania, 2000.

[5] Lee K C, Lee S. Remote fuzzy logic control of networked control system via Profibus-DP. IEEE Transaction on Industrial Electronics: 50(4), 784-792, 2003.

[6] Alumtairi B N, Chow M Y． Stabilization of networked PI control system using fuzzy logic modulation．Proceedings of the American Control Conference: 975-980, Denver, Colorado, USA, 2003.

[7] Lee K.C., Lee S., Remote controller design of networked control system using genetic algorithm, IEEE International Symposium on Industrial Electronics, Vol.3, 1845-1850, June, 2001.

[8] Castro L N. et. Artificial Immune System: Part I- Basic Theory and Applications, TR-DCA, 8-l2, 1999.

[9] Yongsheng Y, Lihong R., A novel fuzzy self-tuning immune feedback control system, Control and decision, 15(4), 443-446, 2000.

Fig 8. Step response of system under fuzzy immune PID control and traditional PID


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