tuning pid controller parameters using tabu search algorithm

8/3/2019 Tuning PID Controller Parameters Using Tabu Search Algorithm

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The cost function to be minimisedis defmed by:.n

(4)

where yd and ypare the desired and the actualoutputs of theplant, respectively, To is the total time over which cost iscomputed and T is sampling period.Performance of the PID designed by tabu search algorithm iscalculated using its cost value. For this purpose the follow-ing function isused:

W i ) =A-J(i) (5)where A is a positive constant, J(i) is the cost value com-puted when theparameter values obtained from i&move orneighbor of the presen t solution areused.Tabu search algorithm chooses the next solution among theneighbours BccoTding to the their evaluation values. Evalua-tion value of i* neighbor is calculated byeval(i)= a*improvement(i)+ rPrecency(i)) -where recency(i) and fbquency(i) are hepa ivingthe information about the past steps of the search, and a, rland fj are improvement, recency and tkquency factors, re-spectively. The improvement(i) is the difference betweenthe perfoxmance values of the present solution@) and itsneighbor(i),i e n t ( i ) =performance(i)-ptxformanw(s) (7 )For forbidding strategy of the tabu search, two conditionsare used: recency(i)S r2*N (recency umdition), Erequency(i)2 fi*avfieq (fkquency condition). Here,2 and f i are re-cency and fkquency factors used for forbidding strategy, Nis the number of element in the binary sequence and avfieqis the average change of bits.

fi*fbquency(i) (6)

3. SIMULATIONRESULTSIn this work, each parameter is represented with 8 bits.Therefore, the length of a binaty sequence s 24. Each pa-rameter is f M roduced as integer number, and then it isd e d into he predefmed ange of that parameter.The proposedmethod hasbeen estedon he following time-delayed seumd-orderprocess for the comparison 6]:

G(S) = eo.* / (s+l) (8)Table 1 shows he simulation results obtained. In the table,& represents he petcentmaximumovershoot, T5 stands orthe 5 percent settling time, and IAE, SE are the integral of

the absolute error and the integtal of the squared error, re-spectively.Time response obtained b m he process under the controlof thePID umtrollerdesigned using tabu search algorithm isplotted in Figure 1.The results obtained by usingZiegler-Nichols PID controller a n d K i f a ~ PID controller arealso presented.The parametem of Ziegler-Nichols PID con-O.125Tw The ccmtroller designed Using proposed methndyields better umtrol p e r f i m c e than the Ziegler-Nicholsand Kitas PID controllers do. This can be seen 6-omthe performance index values given in Table 1.

troller are deterrmned 89 Kp = 0.6Ku,Ti = 0.5Tu, and Td =

4. CONCLUSIONThis paper describes a new method far the design of stsn-dard PID controllers. The method is based on the tabusearch algorithm. Tabu search algorithm is empIoyed fwtuning of the control parameters of the PID controller for agiven process. The s imd tion results obtained showed thatthe proposedmethodcan be efficiently used for tuning con-trol parameters of PID controller. Although this letter de-scribes he proposed method for a standard PID controllerdesign and gives simulation results the extension of themethod to the design of adaptive PID COntrolIers are beingundertaken.

3. REFERENCES[I] J.G. Ziegler and N.B. Nichols, OptimumSettmgs for

[2] T. Kitamori, A method for Control System DesignBased upon Partial Knowledge about Controlled Proces~,Trans. ICE Japan, vol. 15,1979,pp.549-555.[3] C.C. Hang,K.J. Astrh and W.K Ho, Refinements ofthe Ziegler -Nichols Tuning Fonnula, Proc. IEE, Pt.D.,[4] F. Glover, Tabu Search-Part I, ORSA Journal onCom-[SI D.Karaboga and A. Kaplan, OptimisingMultivariableFunctions Using Tabu Search, The tenth Int. Symp. onComp. andW. ciences (ISCIS X),Kusadasi, Turkiye,Oc-[6] Z.Y.hao, T. Masayoshi and S. Isaka, Fuzzy GainScheduling of PIDControllers, IEEE Trans. on SMC, vol.

~ u t o m t i c controiiers, TW . ASME, V O ~ . 64,1942,~p.759-768.

vol. 138,1991,~.111 -118.puting, Vol. 1, N0.3, 1989,p ~ .90-206.

tober, 1995, VOL?.,~p.793-799.23 N0.5, september/october,1993, ~p.1392-1398 .

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Table 1. Results obtained by using Ziegler-Nichols, Ki-tamori and Proposed PID controllersZiegler-NicholsPID ControllerK,,= 2.808Kd = 1.151K, 1.7122IAE = 1.375ISE=0.842Y a = 3 2 %4 ~ 4 . 1 3

Kltamoris Proposed PIDPIDController ControllerKp 2.212 IG, 2.194& = 1.148 Kd = 1.465Ki = 1 OS58 Ki = 1.209IAE= 1.016 IAE =0.995ISE=0.787 ISE= 0.741Y,,,=6.7% Ya= 5.5%Tg = 2.304 Ts= 1.8

W1.21

0.80.80.40.20

Figure 1. Time responses obtained eo m the process underthe control of Ziegler-Nichols, Kitamori and Proposed PIDcontrollers

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tuning pid controller parameters using tabu search algorithm

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