The application of immune genetic algorithm in main steam temperature of PID control of BP network

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2012 International Conference on Applied Physics and Industrial Engineering

The application of immune genetic algorithm in main steam

temperature of PID control of BP network

Han Li

1

,Zhang Zhen-yu

2

1_{School of Automation Engineering}

Northeast Dianli University Jilin,p.r.China

2_{School of Automation Engineering}

Northeast Dianli University Jilin,p.r.China

Abstract

In order to overcome the uncertainties, large delay, large inertia and nonlinear property of the main steam temperature controlled object in the power plant, a neural network intelligent PID control system based on immune genetic algorithm and BP neural network is designed. Using the immune genetic algorithm global search optimization ability and good convergence, optimize the weights of the neural network, meanwhile adjusting PID parameters using BP network. The simulation result shows that the system is superior to conventional PID control system in the control of quality and robustness.

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1. Introduction

The control of boiler over-heated steam temperature in the power plant has great effect on economic benefits and safe operation. To boiler over-heated steam temperature, there are many interference factors that interfere frequently and greatly, by the action of all kinds of interferences, the dynamic characteristics of over-heated steam temperature features in uncertainties, large delay, large inertia and nonlinear. These characteristics are very obvious in supercritical units. As a result, the effect of conventional PID cascade control which is based on fixed model is dissatisfactory [1]. Even though one unit of more ideal parameter is set, when the objects are interfered and models change, the characteristic of the control is still hard to achieve an ideal effect [2]. In order to overcome faults of conventional PID, change its function, many kinds of intelligent control strategies and hybrid algorithm emerge.

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This paper putsforward one kind of intelligent control system which is connected by immune genetic algorithm, BP Neural Network and classical PID controller, adjusts PID control parameter on line and realizes the intelligent PID control of over-heated steam temperature. The control system adjusts PID control parameter on line by application of self-learning, self-adapting and capability of approaching to arbitrary function of BP Neural Network, and optimizes the initial weight value by application of global optimum capability of immune genetic algorithm [3], avoids the impossible problems of slow convergence, local minimum points and so on. The simulation experiment proves the effect of the system.

2. PID controller set by BP Neural Network

2.1 Structure of Control

The PID controller based on the BP Neural Network as seen in figure 1 [4], the structure of BP Network as seen in figure 2. The controller is made up of two parts, the classical PID controller carries on a closed loop control of the objects, and parameters kp,ki,kd are on-line adjustments; on-line adjustments

are completed by BP Network, according to the real time data of system operation,

) (k

rin ,yout(k),error(k), adjusts parameters of PID controller k_p,k_i,k_d according to BP arithmetic, to achieve the optimization of one kind of performance index. BP Network set up three-layer, network structure is [4,5,3].

p K Ki Kd

Figure 1. PID controller based on the BP Neural Network

Figure 2. BP network structure

Input layer is equivalent model, output=input: (1) (1) 1 2 (1) (1) 3 4 ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 O k rin k O k yout k O k error k O k (1) Activation function of output layer uses nonnegative sigmoid function:

5 (3) (3) (2) 1 1 0 5 (3) (3) (2) 2 2 0 5 (3) (3) (2) 3 3 0 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) p i i i i i i i d i i i O k K k g O k O k K k g O k O k K k g O k Z Z Z ½ ® ¾ ¯ ¿ ½ ® ¾ ¯ ¿ ½ ® ¾ ¯ ¿

¦

(2)

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Activation function of hidden layer uses plus-minus symmetrical sigmoid function: 4 (2) (2) (1) 0 ( ) ( ) 1, 2,3, 4,5 i ij j j O k f ® Z O k ½¾ i ¯

¦

¿ (3) Performance index function of optimization:

2

1 _{( )} _{( )}

2

J rin k yout k (4) Adjust weight coefficient of Network layers according to gradient descent algorithm, and a momentum term is annexed:

( ) ( ) ( ) ( 1) ( ) J k k k k k Z K D Z Z w ' ' w (5) ( )k

K is learning rate; D( )k is inertia coefficient.

Auto-modulation learning rate is used, because biggish learning rate may cause some errors skip set minimum and never be convergence, while smaller learning rate may slow the learning process.

( ) ( 1) 0.99, 1.04 ( 1) ( ) ( 1) 1.003, ( 1) ( ) ( 1), ( ) 1.04 ( 1) k k J J k k k J J k k k J J k J k K K K K K K u t u u d d d u (6) 2.2 Control Algorithm

x Determine the structure of BP network. That is to determine the nodes number M of input layer and the nodes number Q of hidden layer, the initial weighting value Z_ij(1)(0) and Z_li(2)(0) of each layer, the initial value K(0) of learning rate, and inertia factorD, now k 1.

x Get rin(k) and yout(k) by sampling, and calculate the error(k):error(k) rin(k)yout(k). x Calculate the input and output of all layer's nerve cell of BP Neural Network according to formula

(1), (2), (3).

x Calculate the output u(k) of PID controller according to PID parameters kp,ki,kd.

x Adjust the weighting coefficient Z_ij(1)(k) and Z_li(2)(k) on line according to formula (4), (5), (6). x Set k k1, and return to the second step.

3. Immune genetic algorithm and the combinatorial optimization problems

3.1 Immune Genetic Algorithm

Immune genetic algorithm (IGA) is one kind of improved genetic algorithm based on biology immune mechanism [5], it is one kind of bionic simulated evolutionary algorithm that imitates and reflects biological immune system, and combined with engineering optimal problems [6], [7]. Based on the genetic algorithm, immune genetic algorithm overcomes the low searching efficiency, poor individuals variety and premature of genetic algorithm effectively [8], and ensure that algorithm convergence rapidly in globally optimal solution by application of the mechanism of biodiversity maintenance and the mechanism of consistency adjustment of biological immune system [9]. The flow chart of immune genetic algorithm is as seen in figure 3.

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Figure 3. The flow chart of immune genetic algorithm

3.2 The Design of BP Neural Network Based on Immune Genetic Algorithm

In view of limitation of BP net work, the effect of control relies on the choice of initial value greatly, the global search capability of immune genetic algorithm combined with the local accurate searching of BP network, then study offline the initial weights of BP Neural Network realized, set PID on-line [10], [11]. The process consists of four steps:

a) Antibody code. Real coding is used here, initial antibody product random among real interval [-0.5, 0.5].

b) Function design of Fitness. The definition of fitness function F(x_i) is set function of indicator function

E

_i of neural network property.

A E x F i i 1 ) ( (7)

¦

L k k k i d O E 1 2 ) ( 2

1 _,_L_{is the number of nodes of BP network output layer,}

k

d is the expected output, O_k is the real output,

A

is the constant that is greater than 0, the aim of use of A is to avoid arithmetic overflow because the denominator is close to 0.

c) Genetic manipulation.

1) Crossover: two point crossing method is used.

2) Gauss alternative method. Change the weight of network with the formula: ) 1 , 0 ( ) ( P M _i i m i x F x x ( 8 ) m i

x is the post-variation antibody, x_i is the antibody before it mutate; P(0,1) is the gauss operator; ) 1 , 1 (

M is the mutation rate of individuals.

d) Diversity to maintain and population update based on concentration. The strategy of population update of IGA combined with the interaction inhibition among antibodies of immunity based on concentration, choice probability P(x_i) of factor concentration adjust individual is used. The main aim is to suppress high concentration antibody, to ensure the individual of high fitness is selected. If the concentration of antibody is too high, it is easy sink into immature convergence. concrete method is:

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F x F F x F C x P _i _i i i max ) ( max ) ( 1 ) ( D ¸E ¹ · ¨ © § (9) E

D, are the adjustable parameter of (0,1); maxF is the maximum fitness of all antibodies; Ci is the

concentration of antibody

x

_i, definition is the ratio of antibodies with close fitness and the sum of antibody of population.

From the above formula, we can conclude: when the concentration of antibody is high, the antibody with high fitness is hard to be selected; when the concentration of antibody is low, the antibody with high fitness is easy to be selected. By this way, good individual is withheld, the choice of close antibody is reduced, and the variation of individual is ensured.

4. Simulated research of temperature control based on IGA-BP Neural Network

This paper use table 1 simulates the designed control system by the application of dynamic characteristic of supercritical units.

TABLE I. THE DYNAMIC CHARACTERISTICS OF THE OVER-HEATED STEAM TEMPERATURE SYSTEM OF A 600WM BOILER

Load Anterior guidanceć/(kg s/ )Inert zoneć/ć

37ˁ˄D˙179.2kg s/ ˅ _{5.027 /(1 28 )} _s2 _{1.048 /(1 56.6 )} _s8

50ˁ˄D˙242.2kg s/ ˅ _{3.076 /(1 25 )} _s2 _{1.119 /(1 42.1 )} _s7

75ˁ˄D˙347.9kg s/ ˅ _{1.657 /(1 20 )} _s2 _{1.202 /(1 27.1 )} _s7

100ˁ˄D˙527.8kg s/ ˅ _{0.815 /(1 18 )} _s2 _{1.276 /(1 18.4 )} _s6

In emulation, BP neural network use 4-5-3 structure with three layers, inputs are ( ), ( ), ( ),1e k r k y k , parameters are K(0) 0.4,D 0.05. IGA use real number coding, every real number express a connection weight or threshold, initial antibody is produced random among [-0.5, 0.5], in formula (7),A 0.001; in formula (8), M 0.1; in formula (9), D E 0.5, select with roulette, crossover rate is 0.6ˈinitial population is 50, aim error is set as 0.002ˈthe condition of end of arithmetic is that the best individual hold the line during ten iterations, then the searching end.

1) This paper use two kinds of concatenate main steam temperature control system consist of IGA-BP and conventional PID controller, the step response curve of control system is seen in figure 4.

0 500 1000 1500 2000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 time(s) ri n, yo ut Curve 1 Curve 2

Curve 1—Response curve of conventional PID control Curve 2—Response curve of PID control based on IGA-BP

0 500 1000 1500 2000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 time(s) in t,y o u t Curve 1 Curve 2

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(c) Step response curve under load of 50% (d) Step response curve under load of 37% Figure 4. The control system step response curve under different load

From the above figure, we can conclude: under different load, the control effect of Neural Network system with IGA-BP is better than that of conventional PID controller, obviously, its overshoot is little, transit time is short, regulation quality is excellent, rapid and veracity are also very good.

2) The anti-jamming capability of control system.

When the system is steady under load of 100%, and t=1000s, input water supply perturbation, doing 0.1step disturbance, the response carve of system output is as shown figure 5(a). At the same time, burn rate disturbance is added, and t=1000s, doing 0.1step disturbance, the response carve of system output is as shown figure 5(b). 0 500 1000 1500 2000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 time(s) ri n, yo u t Curve 1 Curve 2

0 500 1000 1500 2000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 time(s) ri n. yo u t Curve 1 Curve 2

(a) Step response curve when pulsing water disturbance (b) Step response curve when pulsing water andburning rate disturbance Figure 5. Step response curve under load 100% when pulsing disturbance

As seen in simulation diagram, when bound is added to the system, carve 2’ overshoot is less than carve 1’, especially the disturbances of water flow and burn rate, carve 2’ overshoot is less than carve 1’ obviously. Compare to conventional PID, the compound controller's transit time is short, overshoot is little, anti-jamming capability is excellent and robustness is good.

5. Conclusion

By comparison of simulation study of two kinds of control system's large delay objects with uncertainty model, the control system based on the IGA-BP neural network the paper puts forward can fit changes of the parameters of controlled objects, have strong anti-jamming capability, good robustness and excellent regulation quality, is better than conventional PID controller.

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