The Smith-PID Control of Three-Tank-System Based on Fuzzy Theory

Transcription

1 54 JOURNAL OF COMPUTERS, VOL. 6, NO., MARCH The Smth-PID Control of Three-Tank-Sytem Baed on Fuzzy Theory Janqu Deng Tnghua Unverty/ School of Automaton, Bejng, Chna Naval Aeronautcal Engneerng Inttue,Shandong, Chna Emal: Cu Hao Bejng Informaton Scence & Technology Unverty / School of Automaton, Bejng, Chna E-mal:haocu44@6.com Abtract Accordng to the character of the volume-lag of the controlled proce of three-tank-ytem, Smth predctor wa adopted to compenate three-tank-ytem fuzzy adaptve control ytem. Fuzzy adaptve Smth predctve control ytem compoed wth Smth predctor and fuzzy adaptve controller. The PID parameter were ettng on lne. Th algorthm ue fuzzy adaptve PID control to mprove the retance ablty to random urbance and Smth predctve control to overcome the tme-delay character of controlled object. Smulaton reult howed that th control algorthm ha the advantage of trong adaptve ablty and noe mmunty. Index Term -fuzzy control, adaptve, Smth-PID, threetank-ytem I. INTRODUCTION A hown n [], the controlled proce of three-tankytem ha obvouly character of volume-lag. Due to the complexty of the controlled object, traonal PID control can t atfy the control requrement of the ytem. Smth PI controller wa ued n []. Becaue the parameter K p and K were man-et, the control effect wa not atfactory. Fuzzy adaptve controller wa ued n []. The random urbance wa nhbted effectvely, but the control effect hould be mproved becaue of the delay of the ytem. The cheme of the control of the three-tankytem are manly the two above by now. In recent year, the reearch of advanced control wa ncreae day by day, and fuzzy adaptve control one of them. Fuzzy adaptve control whch often compoed nto ynthetc controller wth other control cheme ha great potental for the control of nonlnear and uncertan ytem. A fuzzy adaptve controller wa degned n [] baed on the dynamc model and the knematc controller of the moble robot of non-holonomc contrant. The controller can overcome the nfluence of the urbance and the unknown of the parameter of the robot model[]. Fuzzy adaptve controller wa appled to the reconfgurable manpulator n [4]. The fuzzy adaptve Natonal Natural Scence Foundaton Project (65745). Natonal Natural Scence Foundaton Project (66745). ytem can approxmate the dynamc model of the ubytem well. Fuzzy adaptve ldng mode control cheme and t trengthen cheme were ued n uncertan ytem and nonlnear uncertan ytem n [5] and [6]. Fuzzy adaptve control wa appled to the control ytem of DC motor n [7], whch can overcome urbance effectvely. The tablty of the cloed-loop ytem wa proved wth the ue of Lyapunov analy. A fuzzy adaptve controller wa propoed n the control of wheeled nverted pendulum n [8]. Baed on Lyapunov ynthe, the fuzzy control enure that the ytem output track the gven bounded reference gnal to wthn a mall neghborhood of zero, and overcome urbance effectvely. In adon, fuzzy adaptve control wa ued n nonlnear SISO ytem[9,,] and MIMO ytem[,], and obtaned deal control effect. The traonal Smth controller can control the delay ytem effectvely. The fuzzy control changng the human fuzzy language to the machne language that computer can nguh and controllng the complex object through proceng the fuzzy nformaton accordng to the human experence. So, the fuzzy controller ha good control effect to the ytem wth random urbance. The fuzzy adaptve control and Smth predctve control are combned together n th paper, whch mprove the robutne of Smth control greatly. II. PROBLEM DESCRIPTION A. Controlled Object Decrpton Shangha new Aotuo three-tank-ytem a nonlnear couplng controlled model wth mult-nput and multoutput. The ubject of the expermental devce compoed by the three ame columnform tank whch are made by tranparent organc gla, a reervor, and correpondng actuator and enor. Such a Fgure, T, T and T are three water contaner. V, V and V are juncton valve between any two of them. V7 and V8 are two adjutable proportonal valve. The water njected nto T and T through pump P and P. V4, V5 and V6 are three manual regulatng valve, whch can dcharge ACADEMY PUBLISHER do:.44/jcp

2 JOURNAL OF COMPUTERS, VOL. 6, NO., MARCH 55 the water of the three contaner nto tank. Through ettng the open or cloe tate of the x manual valve, dfferent object model can be combned. In th ytem, the manual valve V4, V5 and V6 are cloed, pump P are cloed, and the manual valve V, V and V are adjuted to the approprate openng (demandng that: V>V>V). The lqud n the reervor extracted by pump P, njected nto the contaner T through the proportonal valve V7, and then the lqud njected nto the contaner T through the manual valve V, reached contaner T through manual valve V, and njected nto the reervor through the manual valve V. In the object model, the nput varable the flow Q whch njected nto contaner T, the controlled varable the lqud level h of the contaner T. That compoe the three-tank-control-ytem. The ytem ngle-nput ngle-output thrd-order object model wth volume tmedelay. The control chematc dagram of three-tank-ytem hown n Fgure. Fgure. The chematc dagram of the control devce of threetank-ytem B. Mathematcal Modelng Varable and parameter are defned a below: hlqud level, Q j -flow, Q -nflow, A-cro ectonal area of the contaner, R-lqud retance of the manual valve V, =,,; (,j) {(,);(,);(,)}. Q repreent the flow from T to T, Q repreent the flow from T to T, and Q repreent the flow from T. The total delay tme of the three-tank-ytem τ, and the volume tme-delay of each contaner τ/. Suppoe that the flow njected nto T Q (t). Becaue the volume tme-delay of the contaner T τ/, t lqud level can be expreed a h (t-τ/). The flow from T to T expreed a Q (t-τ/). Becaue the volume tme-delay of the contaner T τ/, t lqud level of T can be expreed a h (t-τ/). The flow from T to T expreed a Q (t-τ/). The output lqud level of T h (t-τ). The flow of T Q (t-τ). In th ytem, the nflow Q nput of the controlled proce, The lqud level h of T the output, and the mathematcal model the mathematcal expreon between h and Q. Three balance equaton of T, T and T are etablhed: τ dh ( t ) τ A = Q() t Q( t ) () τ dh ( t ) τ τ A = Q( t ) Q( t ) () dh ( t τ ) τ A = Q( t ) Q ( t τ ) () Expreng (), () and () n ncremental form: τ dh ( t ) τ A = Q() t Q( t ) (4) τ dh ( t ) τ τ A = Q( t ) Q( t ) (5) dh ( t τ ) τ = ( ) ( τ ) (6) A Q t Q t Accordng to flud dynamc, there lnear relatonhp between the lqud level and flow n the turbulence tuaton. Through lnear proceng: τ h ( t ) τ Q ( t ) = (7) R τ h ( t ) τ Q ( t ) = (8) R Q( t τ ) = (9) R h ( t τ ) After Laplace tranformaton, the mathematcal model of the three-tank-ytem : H() W() = () Q () K W() = e ( T+ )( T+ )( T+ ) τ () Therento, T the tme contant of the frt contaner, T =R A; T the tme contant of the econd contaner, T =R A; T the tme contant of the thrd contaner, T =R A; K the magnfcaton factor, K=R ; τ the lag tme. Suppoe that: the tranfer functon of the ytem n th paper can be repreented by thrd-order nertal lag lnk: e W() = () III. FUZZY CONTROLLER Fuzzy control a computer ntellgent control baed on fuzzy et theory, fuzzy language varable and fuzzy logc nference. The bac concepton of fuzzy control propoed by the famou profeor of Calforna Unverty of Amerca L.A.Zadeh at the frt tme. Pae more than twenty year development, gnfcant ucce ha been obtaned n the apect of fuzzy control theory and applcaton reearch. The bac prncple block of the fuzzy control hown n Fgure. The core part fuzzy controller. The control law of the fuzzy controller realzed by the computer program. The proce of realzaton of the fuzzy control algorthm decrbed a follow: The accurate quantty of ACADEMY PUBLISHER

3 56 JOURNAL OF COMPUTERS, VOL. 6, NO., MARCH Fgure. The bac prncple block dagram of the fuzzy control the controlled varable ample obtaned by computer, and then compare the value wth the gven value to obtan the error gnal E whch uually elected a one of the nput value of the fuzzy controller. The accuracy value of the error gnal E fuzzed to the fuzzy value. The fuzzy value of the error gnal E can be expreed by the correpondng fuzzy language to obtan a ubet of the fuzzy language et e (e a fuzzy vector), and then e and the fuzzy control rule R (fuzzy operator) are ued to obtan the fuzzy control value u baed on the combnaton rule of the nference: u = e R () The man dfference between the fuzzy control ytem and the uual computer dgtal control ytem that the fuzzy control ytem adopt fuzzy controller. Fuzzy controller the core of the fuzzy control ytem. The performance of the fuzzy control ytem manly depend on the tructure of the fuzzy controller, the fuzzy rule, the compotonal nference algorthm and the fuzzy decon method, ect. Fuzzy controller alo called fuzzy logc controller. Becaue the fuzzy control rule are decrbed by the fuzzy conon entence of the fuzzy theory, the fuzzy controller a language controller. It alo called fuzzy language controller. The compoton block dagram of the fuzzy controller hown n Fgure. Fgure. The compoton block dagram of the fuzzy controller Fuzzy nterface: The nput of the fuzzy controller mut be fuzzed to olve the output of the control. So, t the nput nterface of the fuzzy controller. It man role changng the real nput value to a fuzzy vector. For the fuzzy nput varable e, t fuzzy ubet uually dvded a follow: e={negatve Bg, Negatve Small, Zero, Potve Small, Potve Bg}={NB, NS, ZO, PS, PB} e={negatve Bg, Negatve Mddle, Negatve Small, Zero, Potve Small, Potve Mddle, Potve Bg}={NB, NM, NS, ZO, PS, PM, PB} e={negatve Bg, Negatve Mddle, Negatve Small, Negatve Zero, Potve Zero, Potve Small, Potve Mddle, Potve Bg}={NB, NM, NS, NZ, PZ, PS, PM, PB} The memberhp functon are uually expreed ung trangle. Fgure 4. The memberhp functon of varable Knowledge Bae: The knowledge bae compoed by databae and rule bae. Databae: The databae tore the memberhp functon vector of the fuzzy ubet of all the nput varable and output varable. If the unvere the contnuou doman, the databae tore memberhp functon. It upple data for the nference engne n the olvng proce of fuzzy relatonhp equaton of the rule nference. Rule bae: The rule of the fuzzy controller are baed on the experence of the manual operator or the knowledge of expert. It a language expreon form baed on people ntuton. Fuzzy rule are uually connected by a ere of relatonal word, uch a f_then, ele, alo, end and or, ect. The relatonal word mut through tranlatng to make the fuzzy rule numercal. The commonly ued relatonal word are f_then and alo. For the mult varable fuzzy control ytem, the commonly ued relatonal word are and, ect. For example, the nput ACADEMY PUBLISHER

4 JOURNAL OF COMPUTERS, VOL. 6, NO., MARCH 57 varable of the fuzzy control ytem are e(error) and e c (error change). Ther correpondng language varable are E and EC. A group of fuzzy rule are: R: IF E NB and EC NB then U PB R: IF E NB and EC NS then U PM The f part uually called preme part, and the then part uually called concluon part. It bac tructure can be concluded to: If A and B then C. Therento, A a fuzzy ubet of unvere U, and B a fuzzy ubet of unvere V. Accordng to the manual control experence, the control decon table R can be organzed off-lne. R a fuzzy ubet of the Cartean product et U V. The control value can be expreed a: C = ( A B) R (4) Therento, the fuzzy drect product operaton. the fuzzy compoe operaton. The rule bae ued to tore the fuzzy control rule. It upple control rule for the nference engne. The number of the rule related to the fuzzy ubet dvon of the fuzzy varable. The accuracy of the rule bae connected wth the accuracy of the knowledge of expert. Inference and Defuzzy-nterface: Inference the functon part of obtanng the fuzzy control value through fuzzy control rule baed on the nput fuzzy value and the fuzzy control rule. In the fuzzy control, the nference method wth mple operaton wll be adopted conderng the nference tme. The mot bac nference Zadeh approxmate nference. It nclude forward nference and backward nference. The forward nference uually ued n the fuzzy control, and the backward nference uually ued n the expert ytem of the engneerng feld. The acqurement of the nference concluon expree that the rule nference functon of the fuzzy control ha been completed. But the reult a fuzzy vector. The accuracy output control value ha been obtaned through defuzzy. The output termnal wth convertng functon called Defuzzy-nterface. IV. FUZZY ADAPTIVE PID CONTROLLER Wth the development of computer technology, artfcal ntellgence method ued to tore the adjutng experence of operator to the computer. Accordng to the te actual tuaton, computer can adjut PID parameter automatcally. That the expert PID controller. The controller combned the clacal PID control wth the advanced expert ytem, and realzed the optmal control of the ytem. Th control method determne the object model accurately, model the experence of operator, and adjut PID parameter by nferrng. Becaue the experence of operator can t be decrbed accurately, and the varou emaphore and the evaluaton ndex can t be expreed quantfcatonally, the expert PID method lmted. Fuzzy theory the effcent path to olve the problem. The bac theory and method of fuzzy mathematc are ued to contruct fuzzy et to expre the conon of rule and operaton. Then, the computer control the ytem baed on the actual repone conon. Fuzzy adaptve PID control ha many knd of tructure form rght now, but ther workng prncple are bacally dentcal. Fuzzy adaptve PID control on the ba of PID algorthm, through calculatng the error e and the error rate e c of the current ytem, reaonng ung fuzzy nference rule and adjutng parameter by earchng fuzzy matrx tale. In the degn of fuzzy adaptve controller, the error e and the error rate e c of the current ytem are nput, whch can meet the demand of elftunnng of the PID parameter baed on dfferent e and e c n dfferent tme. The fuzzy adaptve controller modfe PID parameter on lne baed on fuzzy control rule. It tructure hown n Fgure 5. R () de k p k G () c kd U() Y() Fgure 5.The tructure of the fuzzy adaptve controller The fuzzy adaptve controller fndng the relatonhp between PID parameter and dfferent e, dfferent rate e c, detectng e and e c contantly durng the operaton, and modfyng the three parameter on lne baed on fuzzy control theory to meet dfferent demand of control parameter for dfferent e and dfferent rate ec. In that way, the controlled object ha good dynamc and tatc performance[4]. A. Fuzzy Inputtng Method Fuzzy controller wa adopted n adjutng the proporton parameter k p, ntegral parameter k and dfferental parameter k d on lne. The dfferent e and dfferent rate ec of nput are fuzzed by 7 fuzzy et. They are PB, PM, PS, Z, NS, NM, NB. The output proporton parameter k p, ntegral parameter k and dfferental parameter k d are fuzzed by 7 fuzzy et. They are PB, PM, PS, Z, NS, NM, NB. The dcrete unvere of e and ec {-, -, -,,,, }. The dcrete unvere of output are: k p {-., -., -.,,.,.,.}, k {-.6, -.4, -.,,.,.4,.6}, and k d {-, -, -,,,, }. There are 49 fuzzy control rule whch are hown n table [4]. The fuzzy varable of the fuzzy adaptve controller adopt form of trangle functon, S mode functon and Z mode functon. B. Fuzzy Rule Conder from the tablty, repone velocty, overhoot and teady tate accuracy, the rule of K p, K and K d are: The role of proportonal coeffcent K p peedng up the repone velocty of ytem and mprovng the adjutng accuracy of the ytem. The bgger the K p, the qucker the repone velocty of the ytem, the hgher the ACADEMY PUBLISHER

5 58 JOURNAL OF COMPUTERS, VOL. 6, NO., MARCH TABLE I. THE FUZZY INFERENCE RULES TABLE OF THE KP, KI,KD e c e k p /k /k d NB NM NS Z PS PM PB NB PB/NB/PS PB/NB/NS PM/NM/NB PM/NM/NB PS/NS/NB Z/Z/NM Z/Z/PS NM PB/NB/PS PB/NB/NS PM/NM/NB PS/NS/NM PS/NS/NM Z/Z/NS NS/Z/Z NS PM/NB/Z PM/NM/NS PM/NS/NM PS/NS/NM Z/Z/NS NS/PS/NS NS/PS/Z Z PM/NM/Z PM/NM/NS PS/NS/NS Z/Z/NS NS/PS/NS NM/PM/NS NM/PM/Z PS PS/NM/Z PS/NS/Z Z/Z/Z NS/PS/Z NS/PS/Z NM/PM/Z NM/PB/Z PM PS/Z/PB Z/Z/NS NS/PS/PS NM/PM/PS NM/PM/PS NM/PB/PS NB/PB/PB PB Z/Z/PB Z/Z/PM NM/PS/PM NM/PM/PM NM/PM/PS NB/PB/PS NB/PB/PB adjutng accuracy of the ytem, the eaer the producton of overhoot, and what more lead to the untable of the ytem. If the value of K p too mall, the adjutng accuracy wll be reduced, the repone velocty wll be low, the adjutng tme of the ytem wll be prolonged, and the tatc and dynamc charactertc wll become wore. The role of ntegral coeffcent K elmnatng the teady-tate error of the ytem. The bgger the K, the elmnatng of the teady-tate error of the ytem more quckly. If K too bg, ntegral aturaton phenomenon wll appear n the early tage of the repone proce and the overhoot of the repone proce wll be bg. If K too mall, the teady-tate error of the ytem wll be hard to elmnate, the adjutng accuracy of the ytem wll be affected. The role of dfferental coeffcent K d mprovng the dynamc charactertc of the ytem. The role manly nhbtng the devaton changng toward any drecton. It can forecat the changng of the devaton. If K d too bg, the repone proce wll brake n advance, the adjutng tme wll be prolonged, and the noe mmunty of the ytem wll be decreaed. The effect of the three parameter and the relatonhp between them have to be condered when ettng the PID parameter. The relatonhp among e, e c and K p, K, K d ha been concluded a follow: When e(t) bg, K p hould be bg too, o that the tme contant and the dampng coeffcent of the ytem wll decreae. The value hould be not too bg, otherwe, the ytem wll be untable. To avod the out of range control of the ytem n the begnnng, K d hould be mall. To avod the bg overhoot, K can be et to zero. When e(t) medum zed, K p hould be relatvely mall. So, the overhoot of the ytem wll be mall. The value of K d mportant to the ytem th tme. The value of K d hould be proper to guarantee the repone peed of the ytem. The value of K can be ncreaed properly, but not too bg. When e(t) mall, the value of K p and K hould be bgger to guarantee the good teady performance of the ytem. The value of K d hould be proper to avod concuon of the ytem n the equlbrum. Baed on the relatonhp among e, e c and K p, K, K d whch were ummarzed above, combned wth the analy and the actual operaton experence of the engneer and techncan and conderng the effect of the dfferent rate e c (t), table wa obtaned whch are the fuzzy rule of regulatng the three parameter of the PID controller[5]. C. Fuzzy Inference Inference the proce of accomplhng fuzzy nference and obtanng the fuzzy control varable baed on the fuzzy nput and fuzzy control rule whch are ued to olve the fuzzy relaton equaton. Mamdan organum adopted n th paper. Mamdan organum a common organum n fuzzy control. It a compotonal rule of nference whch take dfferent form n fuzzy mplcaton relaton. Suppoe that the fuzzy conon entence are: R : f x A and y B then z C (=,, n) The nference proce : Calculatng the fuzzy mplcaton relaton: R (=,, n) Suppoe that: A = ( a a a ), whch m m dmenon row vector. B = ( b b bn), whch n dmenon row vector. C = ( c c ct), whch t dmenon row vector. Calculatng the fuzzy relaton of the fuzzy et n the antecedent of R : T P = A B = A B. Therento, A B the cartean product of fuzzy vector, and the reult m n fuzzy matrx. Calculatng the fuzzy mplcaton relaton P C whch between the antecedent and conequent of R. For eay, the fuzzy matrx P traghtened to m n T dmenon fuzzy row vector. R = P C = P C. Calculatng the total fuzzy mplcaton relaton R R = R R R (5) Calculatng the fuzzy relaton between the new nput A and B. P = A B (6) Calculatng the fuzzy et of the output value C = ( A B ) R = P R (7) D. Ambguty Reoluton of the Output The nference reult repreent the achevement of the rule nference of the fuzzy control. But the reult tll a fuzzy vector. In the actual fuzzy control, there mut be a certan value to control or drve the actuator. So, the fuzzy vector obtaned through fuzzy nference mut be ACADEMY PUBLISHER

6 JOURNAL OF COMPUTERS, VOL. 6, NO., MARCH 59 converted to obtan the clear control output. Th proce called ambguty reoluton. The electon of ambguty reoluton method related wth the electon of the hape of memberhp functon and the nference method. Matlab provde fve knd of ambguty reoluton method: () centrod (area centrod method), () bector (area-equal-dvdng method), () mom (average maxmum memberhp degree method), (4) om (mall maxmum memberhp degree method), (5) lom (bg maxmum memberhp degree method). Centrod ant-fuzzy method adopted n th paper. To obtan accuracy control varable, the fuzzy method aked to expre the calculaton reult of the memberhp degree functon of the output. The area centrod method takng the centrod of the area whch encloed by the memberhp degree functon curve and the abca a the fnally output. vµ v() v dv (8) V v = µ () vdv For the dcrete flter tuaton: v = V m k = v v µ ( v ) k v k k = m µ ( v ) v k (9) Compared wth the maxmum memberhp degree method, the area centrod method ha more mooth output nference control. The output of the ytem wll change even f the nput gnal ha lttle change. The ngle loop control ytem wth pure delay hown n Fgure 6, whoe cloed-loop tranfer functon hown a follow: φ() Y() It charactertc equaton : Gc () G () G () e τ = c R () = + τ Gc () G () e () + G ( ) G ( ) e τ = c G () e τ Fgure 6. The ngle loop control ytem wth pure delay () Obvouly, there pure delay n the charactertc equaton. If τ bg enough, the ytem wll be untable. That the eence that the long tme delay proce hard to control[9]. e τ appear n the charactertc equaton, becaue the feedback gnal cted from pont a of the ytem. If the feedback gnal cted from pont b, the pure delay part removed outde of the control crcut. A hown n Fgure 7. After tme delay τ, the controlled varable Y wll repeat change of X. Gc () G () e τ Fgure 7. Improved ngle loop control ytem wth pure delay Becaue the feedback gnal X ha no delay, the repone of the ytem greatly mproved. Pont b not ext or lmted by the phycal conon n the practcal ytem. So, the feedback gnal can t be cted from pont b. Accordng to th problem, Smth propoed artfcal model method. The tructure hown n Fgure 8. E E Gc U () G () G () m X m Fgure 8. Smth predct control ytem If the model accurate, uch a G () = Gm (), τ=τ m, and there no load urbance(d=). Y=Y m, E m =Y- Y m =, X=X m. So, X m can change X a the frt feedback loop and the pure delay part moved outde of the control loop. If the model naccurate or there load urbance n the control proce, X not equal to X m, E m =Y-Y m, and the control precon not a great atfacton. So, E m ued to realze the econd feedback loop. Th the control trategy of Smth predctor controller[5]. e τ e τ V. FUZZY ADAPTIVE SMITH CONTROLLER The pute Smth predctve controller compenate the delay part of the tme-delay ytem. It PID control demand that the ytem mut have accuracy tranfer functon. For the plant model wth tme-varyng tranfer functon or tme-varyng parameter, Smth predctve controller can t acheve the deal control effect. What more, the Smth predctve controller entve to the error. If the error too bg, the control effect wll be decreaed. Becaue the fuzzy adaptve controller adopt fuzzy et theory, t ha ome tolerance degree to the nterference factor of telf and external. It allow the tranfer functon of the controlled object varyng wth tme. The fuzzy adaptve control can work effectvely whether the controlled object lnear or nonlnear. The combnaton of Smth predctve controller and fuzzy adaptve controller can control the overhoot of the ytem effectvely and acheve a good control effect. If the pute fuzzy adaptve controller ued to control the large tme-delay ytem, the concuon of the ytem wll be exacerbated, the adjutng tme wll be prolonged, and the control performance wll become wore, becaue the control varable wll have effect on the controlled object after a long tme. The control varable mut be reponded n advance. If the Smth predctve controller added, the delay tme of the ytem compenated; the E m ACADEMY PUBLISHER

7 5 JOURNAL OF COMPUTERS, VOL. 6, NO., MARCH control varable can control the controlled object n real tme, and the deal control effect wll be obtaned. The control problem of the pure delay tme-varyng ytem can be olved effectvely when fuzzy adaptve PID controller combned wth Smth predct controller. The adjutng tme of the ytem wll be hortened, the concuon and the overhoot of the ytem wll be elmnated, the ant-nterference ablty wll be enhanced, and the robutne and adaptve ablty wll be mproved. The tructure of the control ytem hown n Fgure 9. de E E k p k Gc () kd U G ( ) e τ G () m X m e τ E m Fgure 9. Fuzzy adaptve Smth-PID control ytem The bac prncple of the method that: fuzzy control ued to adjut the parameter k p k k d of the PID controller G c (). The output of the PID controller G c () hown a follow: method of fuzzy adaptve Smth PID wa hown n Fgure. uk ( ) = uk ( ) + kp[ e'( k) e'( k )] + ke'( k) + k [ e'( k) e'( k) + e'( k )] d () In the equaton (), k p proporton parameter, k ntegral parameter, and k d dfferental parameter. u(k) the output of the controller n the k th amplng tme, and u(k-) the output of the controller n the (k-) th amplng tme. e (7) fuzzpd (mamdan) 49 rule kp (7) k (7) e'( k) = E ( k) () m If the model of the controlled object accurate, and there no load urbance, the frt feedback loop hould be ued, m=. Otherwe, the econd feedback loop hould be ued, m=. ec (7) Sytem fuzzpd: nput, output, 49 rule kd (7) VI. FUZZY ADAPTIVE SMITH CONTROL SIMULATION The mathematcal model of one three-tank-ytem e W() = The mulaton proce wa performed a follow: Smth PI method, fuzzy adaptve PID method, and fuzzy adaptve Smth PID method were ued n th paper. One unt pule nterference gnal wa added n the mddle of the mulaton proce. The mulaton wa carred wth MATLAB7.4.. The graph of the fuzzy nference ytem hown n Fgure. The graph of the memberhp functon of the fuzzy adaptve PID controller hown n Fgure ~5. The curve of the output of the fuzzy adaptve PID controller are hown n Fgure 6~8. The value of K p and K were taken a.5 and.5 when takng the method of Smth PI. The value of K p, K and K d were taken a.5,.4 and.4 when takng the method of fuzzy adaptve Smth PID. The tep repone curve of the ytem wth the method of Smth PI and fuzzy adaptve PID were hown n Fgure 9 and Fgure. The tep repone curve of the ytem wth the Degree of memberhp Fgure. Fuzzy nference ytem NB NM NS Z PS PM PB e Fgure. The memberhp functon of nput e ACADEMY PUBLISHER

8 JOURNAL OF COMPUTERS, VOL. 6, NO., MARCH 5 NB NM NS Z PS PM PB NB NM NS Z PS PM PB.8.8 Degree of memberhp.6.4 Degree of memberhp ec kd Fgure. The memberhp functon of nput ec Fgure 5. The memberhp functon of output K d Degree of memberhp NB NM NS Z PS PM PB kp Fgure. The memberhp functon of output K p kp tme() Fgure 6. The curve of the output K p of the fuzzy adaptve PID controller NB NM NS Z PS PM PB Degree of memberhp k Fgure 4. The memberhp functon of output K k tme() Fgure 7. The curve of the output K of the fuzzy adaptve PID controller ACADEMY PUBLISHER

9 5 JOURNAL OF COMPUTERS, VOL. 6, NO., MARCH.4 kd rn,yout..8.6 X: 4 Y:. X: Y: X: Y:.8 X: 6 Y: tme() Fgure 8. The curve of the output K d of the fuzzy adaptve PID controller tme() Fgure. The output curve of the ytem wth fuzzy adaptve Smth PID method rn,yout.5.5 X:.8 Y:.77 X: 8.5 Y: X: 6.8 Y: X: 9.7 Y: The fgure how that: the repone proce of the ytem ha no overhoot when ung the method of fuzzy adaptve Smth PID, and can reach table n 4. The repone proce of the ytem ha bg overhoot when ung the method of Smth PI, and can reach table n 8. The repone proce of the ytem ha no overhoot when ung the method of fuzzy adaptve PID, and can reach table n 54. For ant-nterference, the ytem ha better reacton effect when ung the method of fuzzy adaptve Smth PID. The mulaton how that the method of fuzzy adaptve Smth PID can olve the contradcton of the rapy and the tablty tme() Fgure 9. The output curve of the ytem wth Smth PI method rn,yout X: 54 Y:.996 X: 4 Y:.8 VII. CONCLUSIONS Fuzzy adaptve Smth predctor wa ued to control three-tank-ytem wth delay n th paper. The fuzzy adaptve PID part can mprove the retng ablty and adaptve ablty of the ytem to random urbance, and the Smth predct control part can overcome the delay charactertc of the controlled object. MATLAB7.4. ued a development platform and three-tank-ytem a reearch object n th paper. Smth PI method, fuzzy adaptve PID method, and fuzzy adaptve Smth PID method were ued n the mulaton. The mulaton reult how that fuzzy adaptve Smth PID method can make the ytem ha better adaptve ablty, horter ettlng tme, better tablty, and tronger ant-nterference ablty tme() Fgure. The output curve of the ytem wth fuzzy adaptve PID method ACKNOWLEDGMENT The author would lke to thank the fnancal upport by the Natonal Natural Scence Foundaton Project (65745) and Natonal Natural Scence Foundaton Project (66745). REFERENCES [] WA NG Qng-lan, Xe Xue-jun, Smth Control of Three Tank Water Sytem Baed on C++ Bulder, Journal of Qufu Normal Unverty(n Chnee), vol..8, pp ACADEMY PUBLISHER

10 JOURNAL OF COMPUTERS, VOL. 6, NO., MARCH 5 [] SUN Hong-yng, YAN De-wen, LI Bn, The Level Control of Three Water Tank Baed on Self-Tunnng Fuzzy-PID Controller, Electrc Applcaton(n Chnee), vol.5.6, pp [] WANG Yu-hua, YU Shuang-he, DU Ja-lu, TIAN Yuan, HU Yng, Adaptve Fuzzy Control of Uncertan Nonholonomc Moble Robot, Journal of Sytem Smulaton(n Chnee), vol..9, pp [4] ZHU Mng-chao, LI Yng, LI Yuan-chun, JIANG R-hua, Oberver-baed decentralzed adaptve fuzzy control for reconfgurable manpulator, Control and Decon(n Chnee), vol.4.9, pp [5] Navd Norooz, Mehd Roopae and M. Zolghadr Jahrom, Adaptve fuzzy ldng mode control cheme for uncertan ytem, Communcaton n Nonlnear Scence and Numercal Smulaton, vol.4. 9, pp [6] Mehd Roopae, Manoor Zolghadr,Sna Mehkar, Enhanced adaptve fuzzy ldng mode control for uncertan nonlnear ytem, Communcaton n Nonlnear Scence and Numercal Smulaton, vol.4. 9, pp [7] Geramo G. Rgato, Adaptve fuzzy control of DC motor ung tate and output feedback, Electrc Power Sytem Reearch, vol.79.9, pp [8] Zhjun L, Chunquan Xu, Adaptve fuzzy logc control of dynamc balance and moton for wheeled nverted pendulum, Fuzzy Set and Sytem, vol. 6.9, pp [9] Salm Labod, Therry Mare Guerra, Adaptve fuzzy control of a cla of SISO nonaffne nonlnear ytem, Fuzzy Set and Sytem, vol.58.7, pp [] Shaocheng Tong, Yongmng L, Peng Sh, Fuzzy adaptve backteppng robut control for SISO nonlnear ytem wth dynamc uncertante, Informaton Scence, vol.79.9, pp. 9-. [] H.F. Ho, Y.K. Wong, A.B. Rad, Adaptve fuzzy ldng mode control wth chatterng elmnaton for nonlnear SISO ytem, Smulaton Modellng Practce and Theory, vol.7.9, pp [] Tong Shaocheng, L Changyng, L Yongmng, Fuzzy adaptve oberver backteppng control for MIMO nonlnear ytem, Fuzzy Set and Sytem, vol.6.9, pp [] Chao-Shung Chen, Dynamc tructure adaptve neural fuzzy control for MIMO uncertan nonlnear ytem, Informaton Scence, vol.79.9, pp [4] LIU Jn-kun, Advanced PID control and MATLAB mulaton (n Chnee), The econd eon. Publhng Houe of Electronc Indutry, May,7, pp. 6. [5] SHI Xn-mn, HAO Zheng-qng, Fuzzzy control and MATLAB mulaton (n Chnee), Publhng Houe of QngHua Unverty, Mar,8, pp. 4 Janqu Deng (Changde cty, Hunan provnce, Chna, Augut 4 974) Mater degree, Navgaton, Gudance and Control, Naval Aeronautcal Engneerng Inttute, Shandong, Chna,. Doctoral tudent, Tnghua Unverty, Bejng, Chna. The major feld of tudy: cybernaton. He teache at Naval Aeronautcal Engneerng Inttue now. The poton teacher. The nttue located n Shandong provnce of Chna. The artcle he ha publhed : The NCS controller baed on GA optmze (Journal of Central South Unverty, 9). The current and prevou reearch nteret are: oftware engneerng and oftware archtecture. Cu Hao (Qnhuangdao cty, Hebe provnce, Chna, Mar. 986) Bachelor degree, Automaton, Bejng Informaton Scence and Technology Unverty, Bejng, Chna, 8. Potgraduate, Detecton Technology and Automatc Equpment, Bejng Informaton Scence and Technology Unverty, Bejng, Chna. The major feld of tudy: ntellgent control and t applcaton. She dong part-tme job n the Zhong Neng Qng Yuan Company now. The poton Software Engneer. The company located n Souhu Manon, Bejng, Chna. The artcle he ha publhed are: Reearch on Degnng of Soccer Robot Color Tag and Identfyng Algorthm (Hangzhou, Chna, Proceedng of 9 Internatonal Conference on Intellgent Human Machne Sytem and Cybernetc, 9); Fuzzy Immune Adaptve Smth-PID Control for Water Qualty Adjutng Sytem of Thermal Power Plant (Wuhan, Chna, The nd Internatonal Workhop on Intellgent Sytem and Applcaton (ISA), ); The current and prevou reearch nteret are: the ntellgent adaptve control baed on the feature model; the analy and degn of the network control ytem. M. Hao awarded the thrd prze n the 6 th Electronc Degn Contet n Bejng. ACADEMY PUBLISHER