Self-tuning Fuzzy Control of MIMO System and its Application

Self-tuning Fuzzy Control of MIMO System and its Application

Copyright © 2001 IFAC IF AC Conference on New Technologies for Computer Control 19-22 November 2001, Hong Kong SELF-TUNING FUZZY CONTROL OF MIMO SYST...

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Copyright © 2001 IFAC IF AC Conference on New Technologies for Computer Control 19-22 November 2001, Hong Kong

SELF-TUNING FUZZY CONTROL OF MIMO SYSTEM AND ITS APPLICATION

Liu Changliang, Niu Yuguang, Liu Jizhen, Jin Xiuzhang

North China Electric Power University Baoding, HeBei , China

Abstract : Against the serious coupling among system variables , long time delay of outputs response and time changing of model of the low speed pulverizer of power plant, a kind of self-tuning fuzzy control algorithm is presented . In the algorithm, the coupling among system variables has been eliminated, the proportion of the deviation and its differential can be adjusted automatically according to the control process, and accurate object model is not needed when setting the controller parameters. The fuzzy control algorithm in this paper has been used into power plant and satisfactory control result acquired. Copyright02001IFAC Key words: Fuzzy Control , Self-tuning control, MIMO, Power station control, Simulation

I.

manual mode at present. With the development of fuzzy control theory, fuzzy control has been largely used for process of power plant and other industrial process, and satisfactory results obtained (Adel Ben-Abdennor, 1996; Bolis, V., c., 1995 ; G. V. S. Raju, 1990).

INTRODUCTION

The low speed pulverizer (LSP) of power plant is a typical MIMO system with three inputs and three outputs . It is used mainly in 125MW, 200MW and some 300MW power units in china. Due to the serious coupling among system variables, the long time delay of outputs response and model changing with time, perfect control result can't be achieve with the conventional PID control system, most LSP system of power plants in china can only run at

The inputs of the LSP system are position of cold air valve , hot air valve, recycle air valve and speed of coal feeder. The outputs are inlet pressure, outlet temperature and coal mass of the pulverizer. Generally, the control variables

458

are recycle air valve, hot air valve and coal feeder speed. The cold air is used to protect pulverizer when outlet temperature is too high and it closed normally. The coupling among process variables is very serious. For example, too much coal in the pulverizer will result in blockage. In this case, the speed of feeder should be adjusted to reduce the input coal flow. On the one hand, this will bring the increase of outlet temperature; hot air valve should be adjusted to keep the temperature. On the other hand, the regulation of hot valve will affect inlet pressure, recycle air valve should be adjusted to keep the pressure.

V. S. Raju and Jun Zhou, 1991; 1993). The number

of control rules can be decreased largely in the controller. In this paper, the control rules are substituted with fuzzy control formula. The configuration of self-tuning fuzzy controller of LSP system is shown in Fig.2.

Po To

This paper presents an approach to realize a fuzzy based coordinated control scheme for LSP of power plants. A LSP system of 200MW fossil power plant is used in this paper. The schematic is shown in Fig. l

F Ig . k

lilt:

~ulIlIgunlllUlI

Ul

:SC:U-LUlIllIg

lU.U;y

controller Where Po, To, Mo are the set points of inlet pressure, outlet temperature, coal mass; P, T, M are their measure values; VI' V z, Vj are the controller outputs; Fp, F n FM. are the feedback values, they are used into signal trace when auto/manual switched. The controller is composed of four parts: (1) the information treatment and fuzzify, it is used to acquire the position feedback and process values, calculate the errors and error rates and fuzzify them. (2) the control rules set, it provides all the control rules in various conditions. (3) knowledge base, it provides all parameters of controller and data about the LSP system at normal conditions and abnormal conditions. (4) inference engine, it matches the operation status and the control rules. The error ep and error rate ecp of inlet pressure, the error er and error rate eCr of outlet temperature, the error em and error rate eCm of coal mass in the pulverizer defined as following:

Fig. l Schematic diagram of low speed pulverizer system of 200MW power unit

2. THE SELF-TUNING FUZZY CONTROLLER FOR LSP SYSTEM Generally, the fuzzy contro Her is composed of many control rules that stipulate a certain action be initiated in a specific condition. The number of rules is a function of membership and system variables. If the membership of fuzzy set is rn, the system variable number per rule is n, then the total number of rules is m n. In the LSP system, there are six system variables, the errors and their rates of P, T, M. If the error and its rate is fuzzified as 9 levels, the total number of rules is 9 6 =531,441. That means the number of rules is too large to be used into practice. G. V. S. Raju and Jun Zhou introduced a kind of hierarchical fuzzy control algorithm (G.

ep(k)= Pork) - P(k) eCp(k)=ep(k) - ep(k-l) er(k)= To (k) - T(k) ecr(k)= er(k) - er(k-l) eM(k)= Ma(k) - M(k) ecM(k)= eM(k) - eM(k-l)

(1)

(2) (3) (4) (5) (6)

Based on the actual dynamic characteristic of

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LSP system, the fuzzified fields of system variables can be choose as follow: ep E [-200Pa, 200Pa], eCpE [-20Pa/Sec, 20Pa/Sec], erE [-IS 'C, IS'C], ecrE [-4'C/min, 4'C/min], eME [10%, 10%], eCM E [-3%/min, 3%/min] . The system variables are fuzzified as {-4, -3, -2, -1, 0, 1,2,3, 4}, where -4, -3, -2, -1, 0, 1,2,3,4 mean respectively large negative, medium negative, small negative, zero negative, zero, zero positive, small positive, medium positive, large positive sets . The errors and its rates after fuzzified denoted as E p , EC p , Er, ECr. EM' ECM. According to the habit of operators, the partnership between process variables and actual objects is: inlet pressure-recycle air valve, outlet temperature-hot air valve, coal mass in the pulverizer-coal feeder speed. Dues to the temperature of recycle air and outlet temperature is near, the regulation of recycle air valve only affects the inlet pressure. The regulation of hot air affects the output temperature and inlet pressure, its affection to coal mass can be ignored. The regulation of feeder speed affects the coal mass and outlet temperature, its affection to inlet pressure can be ignored. When some process variable deviate its set point, all the control variables should be changed at same time to ensure the stabilization of the system. For example, if the coal in pulverizer is lacking, the LSP will run at uneconomical status. If the coal in pulverizer is too much, the coal blockage will occur. The optimal coal mass changed with the kind, humidity, size of coal. The speed of feeder is adjusted to keep the optimal coal, meanwhile, the hot air value is adjusted to keep the outlet temperature and the recycle air valve is adjusted to keep the inlet pressure.

dUrKi. aEp +(1- a)ECp)-Ki,13Er+(1-f3}ECr) (!) dU2= K2i.., 13Er+ (1- 13) ECr)+ K2i., YEM+ (1- Y)EC"J (8) dU]=KJ,.. YEM+(1- Y)EC"J (9)

Where, a, 13, Yare coefficients between 0 and 1 that reflect the portion of error and its rate . For fast process, the value should be large, for slow process, the value should be small. That means the fast process should be controlled mainly by error, slow process controlled mainly by error rate. K II , K 12 , K n , K n , K]] are coefficients that reflect the coupling relation among process variables. A group of values of Q , j3, Y is shown in Table 1. Table 1

£ /£/ =1 /£/ =2 /£/ =3

[:l~

0 0

2 8s+1 O.S (80s + 1)3 0

0 -0.6Se- 40S (2Ss + 1)2 0.3e- 3OS (20s + 1)2

y

a

13

Y

O. 7 0.8 0. 9

O. 3 0.4 O. 5

0.35 0.45 O. 55

The utilization of adjustable coefficients a, j3, Y in the control rules can improve the control performance effectively. When error is large, the controller will change output fast to shorten the control period. Otherwise, the controller will change output mainly according to the error rate to reduce excess regulation. The value of Q , j3, Y is related to system dynamic characteristics, they can be got by means of simulation.

The transfer functions of the LSP system In Fig. l can be get by the identification test. The result at 100% power load is as follows:

0.4 10s+ 1

Value of a, 13,

The value of KS- iJ= 1,2,3 ):an be got according to the relationship among system variables. For example, when output temperature is high, the hot air valve should close, the inlet pressure will decrease, so the recycle valve should open. To keep inlet pressure, the effect of recycle valve should balance the effect of hot air valve. Because the gain from hot air valve to inlet pressure is 2, the gain from recycle valve to inlet pressure is 0.4, K 12IK n =2J0.4=S. For the same reason, K2/KJ]=0 .6SJO .S=1.3. They only reflect the approximate static relation. Accurate values are not needed.

[~l

Fig.3 The transfer function of LSP Where xl, x2 are the positions of recycle air valve and hot air valve, x3 is the feeder speed.

A group of values of Q , j3, Y is shown in Table 2. Table 2. The Value of Ku.

Based on the analysis above, the fuzzy control formula of recycle air valve, hot air valve, coal feeder can be calculated as:

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5

When three disturbance act on LSP system at same time, the response of p. T, M are shown in Fig.4 (d).

1.3

When outlet temperature is too high, the speed of feeder should increase to prevent coal fire. So, the formula (9) should be modified as: UJ=KJJ3£r+ (1- /3)ECJ+KJ. YEM+ (1- Y)ECM ] (9A) If IE r l=4 then KJ2=I .O else KJ2=Oo

....,.

.

'" , - - - - - - - - ,

..,. .,.. .",

.,..

In actual control, the increment control formula is used . The controller's output can be calculated as : (10) U;(k+l)=U;(k)+K;dUL (i=1,2,3)

i

.

(a) .

Inlet pressure P

".,

(b). Outlet temp. T h ·IIXI

~

~

10 ,-------~.,

"

Where, Kj is the proportion factor. It is used to de-fuzzify the controller's fuzzy logic outputs. In abnormal condition, fast regulation needed. For example, if the inlet pressure is bigger than atmospheric pressure, the coal powder will leak into air, when recycle valve has closed to minimal position, the hot air valve and feeder speed should be decreased. Too high outlet temperature will result in coal powder fire, the hot air valve should be closed fast, and the feeder speed should be increased. Too much coal in the pulverizer will result in blockage, the feeder speed should be decreased fast. In these failure cases, the fuzzy controller's output should change at maximal speed. For example, the control rules when inlet pressure is abnormal are written as follows: if P>Pm and M >Mm and U,<=U Ii then dU]= -4, dUJ = -4 (11) if P>P m and M
.... '"

ID

"

.>lO . ,

~-...."...----_<

.,..., L -_ _ _ _ _ _-! '"

'"

o

(c).

Coal mass M

4(IIUC

(d).

P, T, M

Fig.4. The responses of P, T, M to set point disturbance Because the model of LSP system is time changing, we need to check the robust performance of the controller. After the model changed to transfer function in Fig.5, the response of p. T, M to set point disturbance is shown in Fig.6. 0.6 15s+ I

[:]=

Where Pm is the high limit of inlet pressure, Mm is the high limit of coal mass, UIi is the low limit of recycle valve.

1.5

0

12s+ 1

0

0.6 (90s + 1)3

0

0

_0.5e-6OS

(15s+1)2

Fig.5. Another transfer function of LSP P. -100

..

'C

ao

00

-1>0

7J

.,

_200

70

ao

-:250

.,

-JOO

60

P

3.

SIMULATION RESARCH AND APPLICATION IN POWER PLANT

[::]

(25s + 1)2 0.4e- 5OS

To evaluate the performance of the self-tuning fuzzy control scheme, set point disturbance is simulated. The response of inlet pressure P to 100Pa set point disturbance, outlet temperature T to 10 'e set point disturbance and coal mass M to 10% set point disturbance is shown in Fig.4 (a)-(c).

" 70 100

200

JOO

400

sec

Fig.6. The responses of P, T, M to set point disturbance after parameter changed

It

461

is

shown

in

fig.4-6

that good

control

performance can be get with the self-tuning fuzzy controller and the control performance has little change when the parameters of LSP system changed. At present, the self-tuning fuzzy controller has been used into 125MW power unit of Taizhou Power plant, Zhejiang province, 200MW power unit of Jiujiang power plant, Jiangxi province, and many other power plants in china.

output can be written as :

n dUi = j~lKij(aijEj +(l-aij)EC j )

Where Cfr
Generally, the coal mass in pulverizer is reflected by pressure difference DP between inlet and outlet. When coal mass changed, DP will change after 3-5 minutes delay, so it can't be used into real time control of LSP system. It can only reflect the coal mass in pulverizer at static state . So a special instrument is made to measure the coal mass . It is installed on the seat of LSP inlet, and used to measure the amplitude and frequency of vibration, then the signal is transferred to microprocessor. The vibration component corresponding to coal mass of pulverizer is separated and transferred into 420mA signal. It can reflect the change of coal mass in pulverizer quickly. So, the vibration signal is used to reflect the dynamic coal mass in the LSP, DP signal is used to correct the static value . The real time running curve is shown in Fig.7. Po

0

'c 75

-400

30

40

15

20

-'>00

REFERENCE

"

-)00

·200

In this paper, a self-tuning fuzzy control algorithm for LSP of power plant has been studied and applied to many power plants. The simulation results and application in actual power plant indicate that the self-tuning fuzzy controller exhibits good robustness. The controller can be applied to other MIMO system without much difficulty. However, the values of controller's parameter still need further investigation.

r-----------------,120

~..,

.. ..

·100

4. CONCLUSION

Adel Ben-Abdennor (1996). An autonomous Control system for boiler-turbine units, IEEE transaction on energy conversion. Vol.ll, No .2, pp401-406. Bolis, V. C. and Maffezzoni (1995). Synthesis of the overall boiler-turbine control system by single

60

-liDO 1.00

lom

1200

I.m

I6fCl

IBm

loop auto-tuning technique, Control Engineering Practice , Vol. , 3, No ., 6, pp761-771. G. V. S. Raju and lun Zhou (1993). Adaptive hierarchical Fuzzy controller, IEEE transaction on system. man. and cybernetics. Vol. 23 , No.4, p973-980 G. V. S. Raju and lun Zhou (1991) . Hierarchical Fuzzy controller, Int. J. Contr.. vo1.54 , No.5, pp 120 1-1216, 1. G. V. S. Raju and J.Zhou (1990). Fuzzy logic control for steam generator feedwater control, proc. Amer. Contr. Coni . San Diego, CA., pp14911493.

1Il00 HHJAM

Fig. 7. Running curves in real power plant In actual control, the static errors exist because the 0 in error fuzzy set is corresponding to a region of process value . To the LSP, the small static error of P. T, M is permitted, so it doesn't matter. If one wants to eliminate the static error, the fuzzy control algorithm can be modified. One method is to increase the fuzzified grades of error, the static error will be decreased. Another method is to adopt integral algorithm (for example, PID) when fuzzified error is equal to zero, the error will be eliminated. The self-tuning fuzzy controller for LSP can be applied to other MIMO system . The controller's 462