A Neuron Model-free Controller with immune Tuning gain for Hydroelectric Generating Units

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1 A Neuro Model-free Cotroller with immue Tuig gai for Hydroelectric Geeratig Uits Jiamig Zhag, Nig Wag ad Shuqig Wag Abstract A euro model-free cotrol method with immue scheme tuig gai for hydroelectric geeratig uits is preseted i this paper. Uder the operatig coditios of various guide vae opeig, the characteristics of a hydroelectric geeratig uit show much differece i parameters. The iflueces of the time-varyig parameters ad the disturbaces o the cotrol system ca be reduced by usig the euro model-free cotrol method with immue scheme turig gai. With a example, the simulatio results show that the euro model-free cotroller has good cotrol performace, fast trasiet respose ad strog robustess. A I. INTRODUCTION hydroelectric geeratig uit is a complex cotrolled plat with o-miimum phase, oliear ad time-varyig parameters. Obviously, to desig a cotroller for such a system is a difficult issue. The traditioal cotrol methods are usig a PID cotroller uder assumig that the plat is a time-ivariat liear system with kow structure ad parameters []. However, the parameters of the plat usually could ot be obtaied i practice, ad they will chage i a large scale with the differet operatig coditios. I this case, it is impossible for the PID cotroller with fixed parameters to solve the problems caused by ucertai factors. With the developmet of artificial itelligece ad process cotrol theory, itelliget cotrol methodology has bee advaced greatly ad widely applied i the various process fields, which provides a ew possibility to solve the cotrol problems of hydroelectric geeratig uits. The applicatio of fuzzy cotrol i water turbie speed goverig was ivestigated i [], []. Due to the large variatio withi the Mauscript received September,. Jiamig Zhag is with the Natioal Key Laboratory of Idustrial Cotrol Techology, Istitute of Advaced Process Cotrol, Zhejiag Uiversity, Hagzhou, 7, P. R. of Chia. (Phoe: ; Fax: ; jmzhag@ iipc.zju.edu.c). Nig Wag is with the Natioal Key Laboratory of Idustrial Cotrol Techology, Istitute of Advaced Process Cotrol, Zhejiag Uiversity, Hagzhou, 7. ( wag@ iipc.zju.edu.c). Shuqig Wag is with the Natioal Key Laboratory of Idustrial Cotrol Techology, Istitute of Advaced Process Cotrol, Zhejiag Uiversity, Hagzhou, 7. ( sqwag@ iipc.zju.edu.c). parameters of the plat, it is ot easy for fuzzy cotrol methods to meet the requiremets of all operatig coditios. Therefore, Jig et al [4] developed the itelliget fuzzy cotroller with a eural etwork model of a hydroelectric geeratig uit. Qiao et al [5] preseted a self-adaptive goverig method with pole locatio ad o-lie idetificatio of the model parameters. However, these methods are model-based, ad there still ests the modelig problem. Oce the structure ad parameters of the plat are chaged i large scale uder the differet operatig poits, the cotroller performace will be deteriorated. Based o the euro model-free cotrol method [6], this paper tries to improve the euro model-free cotrol performace with immue mechaism tuig euro gai for cotrollig a hydroelectric geeratig uit uder differet operatig coditios. This paper is orgaized as follows. Sectio II gives a brief itroductio of euro model-free cotrol methodology ad the immue feedback law, ad proposes the euro model-free cotrol method with immue scheme tuig gai. Sectio III describes the characteristics of a hydroelectric geeratig uit ad presets the computer simulatio results. Coclusios are summarized i sectio IV. II. THE NEURON MODEL-FREE CONTROLLER WITH IMMUNE FEEDBACK LAW A. The euro model-free cotroller I [6], i order to overcome the shorts of model-based cotrol system, Wag et al developed a adaptive euro model ad its learig strategy for cotrol, ad preseted the euro model-free cotrol method. Applied i several idustrial processes ([7], [8]), the euro model-free cotrollers show their advatages i treatig with the ucertaities of the processes. The adaptive euro model-free cotrol system is described i [6] as Fig.. Where, p i ( stads for the learig strategy. The Trasfer takes the charge of covertig the output of the cotrolled plat ad the set poit ito iputs of the euro cotroller accordig to the desiger. O the base of the structure of the euro model-free cotrol system, the euro output u ( ca be formulated as

2 K w ( x ( () i i where, K > is the euro proportioal coefficiet; ( ( i,, L) deote the euro iputs; w i ( are the x i x ( x ( x ( w ( w ( w ( p i ( coectio weights of iputs x i (. Followig the associative learig strategy ( pi ( z( (, z( is the teacher sigal), the euro model-free cotrol algorithm with ormalizatio is preseted as followig i [6] [ K wi ( ( ] [ wi ( ] () wi ( t + ) wi ( + d[ r( ] ( where, u ( is the cotrol sigal came from the output of the euro cotroller; r( is the set poit; y( is the plat output. is the umber of iput variables. The iputs of the euro x i ( ca be selected as ( ) x( r(, x ( r(, () x ( x ( x ( t ) Ivestigatio has revealed that the cotrol performace will be deteriorated whe above euro model-free cotroller with a fixed gai K is used i the plats with variable ope-loop gai or severe oliearity. The cotrol practice has also proved that the bigger K would lead to a faster system respose ad a bigger overshoot. However, a smaller K may result i a slower system respose ad loger settlig time. Therefore, the value of K does sigificat ifluece o the performace of euro cotrol systems, special for the cotrolled plat with ucertaity i static gai. To the hydroelectric geeratig uit, the static gai is chaged accordig to the value of the guide vae opeig (α ), this characteristics request that the cotroller gai must be self-adjustable for differet guide vae opeig (α ). For this purpose, this paper proposed a method to tue the gai usig immue feedback mechaism, ad i order to achieve a fast respose ad small overshoot, the actio of Trasfer will be modified accordig to the system error. K Trasfer Plat Fig.. The geeral euro cotrol system B. Immue feedback law The artificial immue system is extracted from the atural immue system, ad is a curret research hot i artificial itelligece ([9], []). The immue system has the ability to idetify ad elimiate foreig materials such as atiges ad germ cells ad also has memory as well as patter recogitio ad learig abilities. Withi the immue system, there is a feedback mechaism which simultaeously performs two diverse tasks: rapidly respodig to the presece of foreig material while quickly stabilizig the immue system. Accordig to the feedback mechaism of the immue system, oe ca draw out the immue feedback law as follows []. First, we defie that ε ( is the amout of atige at the kth geeratio, T H ( is the output from the helper T-cells stimulated by the atiges, T S ( is the effect of the suppressor T-cells o the B-cells, the, the total stimulatio received by the B-cells S ( is S T T (4) H where, kε T H S, k f [ S( ] ε T S, f ( ) is a oliear fuctio itroduced to accout for the effect of the reactio betwee the killer T-cells ad the atige at the (k-d)th geeratio. Assumig that the amout of killer T-cells is give by the differetiatio of the activity of the B-cells, the amout of killer T-cells u kill ( is defied by [] u kill ε k f[ ukill ] { ηf[ u ]} ε k K where, K k, η k k kill ε (5). I this equatio, the parameter K govers the reactive speed, ad the parameter η govers the stability of the system. The immue feedback mechaism provides a possible way to improve cotrol system performace. Some research works o this topic have bee reported i recet years []-[4]. I this paper, the immue feedback law is used to tue the euro cotroller gai. C. The euro model-free cotroller with immue tuig gai This sectio presets the developed euro model-free cotrol with immue algorithm. The immue feedback law is applied to regulate the gai of the euro model-free cotroller, ad the structure of the cotrol system with immue tuig gai is set up ad show as i Fig.. Where, IMF represets the immue feedback law used to determie the gai of the euro cotroller. By cosiderig the amout of foreig materials ε ( as the error of the system output, ad treatig

3 Fig.. Neuro model-free cotrol systems with immue turig gai the euro gai as the amout of killer T-cells, oe ca obtai the followig tuig strategy K K ( k ) + α ( ηf ( y( )) e( (6) x ( x ( x ( w ( w ( w ( where, the oliear fuctio f ( ) is selected as followig format i this paper [] f ( x) γ exp( x β ) (7) where, γ ad β are two costats determied by the user. Thus, the cotrol algorithm is preseted as K( K( k ) + α( η( γ exp(( y( k )) β ))) e( (8) K( [ wi ] [ wi ] wi ( k + ) wi + di[ r( ] The actio of the Trasfer is to produce suitable iputs for the euro cotroller. I order to make the developed cotroller ru well, this paper selected the three iputs ( ) as x r( x λ r( sig( r( ) (9) x x x ( k ) where, the iput x ( ) is differet from the selectio of Eq. k K IMF Trasfer p i ( Plat (), the reasos are two. First, this type of Trasfer ca ehace the system sesitivity to a smaller system error; Secod, this Trasfer will reduce the system sesitivity to a larger system error. λ is a proportioal coefficiet. Equatio (8) ad (9) costructer the euro model-free cotroller with immue tuig gai. III. THE SIMULATION RESULTS FOR A HYDROELECTRIC GENERATING UNIT A. The dyamic characteristics of a hydroelectric geeratig uit The goverig system of a hydroelectric geeratig uit cosists of servomotor, water turbie, diversio system, electric geerator ad exteral load, show as i Fig.. Where, M t is the turbie torque, Q t is the flow, H is the r + - Speed goveror u Servo system y h turbie M t Q t + - Mg Hydraulic system Geerator & load Fig.. The cotrol system for a hydraulic turbie geerator uit water head, is the rotatioal speed. It is a complex cotrolled plat with o-miimum phase ad variable structure ad parameters uder differet operatig coditios. Usig the first priciple modelig method, local liearizatio ad simplificatio approach, this plat ca be described with liearizatio model as follows. The servomotor is represeted as a followig first order process y( Ty s + () where, T y is the buffer time costat of the servomotor. Similarly, the electric geerator is also depicted as a first order process v( [ mt ( mg ( ] () T s + e a b where, T a is the time costat of electric geerator, e b is the load regulatig coefficiet. The diversio system ca be appromately deoted as a elastic water hammer model, H ( 8T ws () Q( T s + 8 r where, T w is the iertia costat of water flow, T r is the reflectio time of pipelie. To some work coditio, the water turbie ca be described as follows with local liearizatio method, mt ehh + evv + e y yh () qt eqhh + eqvv + eqy yh mt mt mt qt where, eh, ev, e y, eqh, h v y h e qv qt qt, eqy, they are all the trasmissio v y h coefficiets. m t, q t, h, v, ad y h are the amouts of relative deviatio of turbie torque M t, water flow rate Q, water head H, rotatig speed ad guide vae opeig a. From the above, with the techology of local liearizatio, we ca obtai the appromate trasfer fuctio of the hydroelectric geeratig uit as followig, v( G( (4) e y ( e qy e h e qh e y ) T w s + Tys + eqhtws Tas + eb ev h H

4 Table Parameters of water turbie model uder three special operatig poits [5] α(mm) T y ( T w ( T r ( T a ( e v e y e h e qv e qy e qh e b The table gives the parameters of the liearizatio model uder three special operatig poits [5]. Thus, it ca be see that the goverig system is a high-order system with oliear ad time varyig parameters. Substitutig the parameter values of table i Eq. (5), we ca obtai the correspodig trasfer fuctios as follows [5] Case : for a. mm, 8s G ( (5).655s +.486s s + Case: for α 5. mm, 65s +.68 G 5 ( (6).587s +.67s s + Case : for α. mm,.496s +.84 G ( (7).597s +.s s + Obviously, the ope loop trasfer fuctio plat has a zero o the right had of s plae, therefore, it is a o-miimal phase plat; the chage of guide vae opeig causes variatios of the model parameters greatly. The uit step resposes for the plat uder the three cases are show as i Fig.4-Fig.6. It is obvious that this process is a overdamped process. Alog with the icreasig of guide vae opeig (α ), the static gai is decreasig, ad the respose time is icreasig. To this cotrolled process with such serious varyig parameters, it is testified that the covetio PID cotrol method is hardly to obtai a satisfactory result. B. Simulatio ad results To verify the effectiveess of the proposed cotrol method (equatios (8) ad (9)), the simulatio tests for a hydroelectric geeratig uit uder differet operatig coditios are performed. Durig the simulatio experimets, we assumed that the ormal operatio poit is set as 5mm of the guide vae opeig, its characteristic is described as Eq. (6) ad the cotroller parameters are selected for the previous euro model-free method [6]. The correspodig parameters are selected as followig: to the euro cotroller of [6]: K ( ). 5, d 5, d 4, d. To the proposed cotroller with the immue feedback law to tue the euro gai, the followig parameters are chose as K ( ).7, η., β, α., γ., λ., d 4, d 4, d 4. For differet operatig coditio, the parameters of the cotrollers are ot modified agai. All of the simulatio results of the previous euro cotroller ad the proposed cotroller are give i Fig. 7 Fig.. From the above simulatio results, oe ca draw the followig coclusios: whe the plat model chages from the ormal case (Eq. (6) ) to the other cases (Eqs. (5) or (7)), the robustess of the ew cotroller is verified. The smaller overshoot, shorter settlig time ad stroger disturbacerejectio are achieved for the proposed euro cotroller. From those results, we ca also coclude that the ew modified euro model-free cotrol method has satisfyig performace ot oly i ormal case but also i other cases. Comparig with other reported results ([4], [5]), this cotrol algorithm is very simple ad model-free, that is to say that this cotrol method does ot request to model the cotrolled plat durig the desig of cotroller. Normalized Frequecy Fig.4. The uit step respose of the hydroelectric geeratig uit uder a. mm Normalized Frequecy Fig.5. The uit step respose of the hydroelectric geeratig uit uder α 5. mm Normalized Frequecy Fig.6. The uit step respose of the hydroelectric geeratig uit uder α. mm

5 Normalized Frequecy Fig.7. Trackig usig the proposed cotroller whe a. mm Normalized Frequecy Fig.8. Trackig usig the proposed cotroller whe a 5. mm Normalized Frequecy Fig.9. Trackig usig the proposed cotroller whe a. mm Normalized Frequecy Fig.. Trackig usig the euro of Eqs. () ad () cotroller whe a. mm Normalized Frequecy Fig.. Trackig usig the euro of Eqs. () ad () cotroller whe a 5. mm Normalized Frequecy Fig.. Trackig usig the euro of Eqs. () ad () cotroller whe a. mm IV. CONCLUSIONS I this paper, a developed euro model-free cotrol method based o the immue feedback law is proposed, ad simulatio tests for a complex hydroelectric geeratig uit are performed. The results verified that the proposed approach is of effectiveess ad has a quick respose ad good performace. Oe of the advatages of this method is model-free, that make the cotrol system desig procedure very simple for practical. REFERENCES [] C. Guo ad N. Liag, Itelliget PID cotrol for hydro-turbie goverig system, Large Electric Machie ad Hydraulic Turbie, No. 5, pp 56-6, 997 [] Y.-S. Cao, W. Y., Cai ad G. D. Che, Applicatio of itelliget weight fuctio fuzzy cotrol i hydraulic turbie goverig system, Iteratioal Joural Hydroelectric Eergy, Vol. 9, No., pp. 69-7,84, [] L. Chag ad B. Gog, Study o turbie goveror based o fuzzy PID cotrol, Joural of Huazhog Uiversity of sciece ad techology, Vol. 9, No., pp. 9-9,97,

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