1、附录二 :翻译 Memory-Based On-Line Tuning of PID Controllers for Nonlinear Systems Abstract Since most processes have nonlinearities, controllerdesign schemes to deal with such systems are required.On the other hand, PID controllers have been widely used forprocess systems. Therefore, in this paper, a new
2、 design schemeof PID controllers based on a memory-based(MB) modeling isproposed for nonlinear systems. According to the MB modelingmethod, some local models are automatically generated basedon input/output data pairs of the controlled object stored inthe data-base. The proposed scheme generates PID
3、 parametersusing stored input/output data in the data-base. This schemecan adjust the PID parameters in an on-line manner even ifthe system has nonlinear properties. Finally, the effectivenessof the newly proposed control scheme is numerically evaluatedon a simulation example. I. INTRODUCTION In rec
4、ent years, many complicated control algorithms suchas adaptive control theory or robust control theory have beenproposed and implemented. However, in industrial processes,PID controllers1, 2, 3 have been widely employedfor about 80% or more of control loops. The reasons aresummarized as follows. (1)
5、 the control structure is quitsimple； (2) the physical meaning of control parameters isclear； and (3) the operators know-how can be easily utilizedin designing controllers. Therefore, it is still attractive todesign PID controllers. However, since most process systemshave nonlinearities, it is diffi
6、cult to obtain good controlperformances for such systems simply using the fixed PIDparameters. Therefore, PID parameters tuning methods usingneural networks(NN)4 and genetic algorithms(GA)5 havebeen proposed until now. According to these methods, thelearning cost is considerably large, and these PID
7、 parameterscannot be adequately adjusted due to the nonlinear properties.Therefore, it is quite difficult to obtain good controlperformances using these conventional schemes.By the way, development of computers enables us tomemorize, fast retrieve and read out a large number ofdata. By these advanta
8、ges, the following method has beenproposed: Whenever new data is obtained, the data is stored.Next, similar neighbors to the information requests, calledqueries, are selected from the stored data. Furthermore,the local model is constructed using these neighbors. Thismemory-based(MB) modeling method,
9、 is called Just-In-Time(JIT) method6, 7 , Lazy Learning method8 or Model-on-Demand(MoD)9, and these scheme have lots of attentionin last decade. In this paper, a design scheme of PID controllers based onthe MB modeling method is discussed. A few PID controllershave been already proposed based on the
10、 JIT method10and the MoD method11 which belong to the MB modelingmethods. According to the former method, the JIT method isused as the purpose of supplementing the feedback controllerwith a PID structure. However, the tracking property is notguaranteed enough due to the nonlinearities in the case wh
11、erereference signals are changed, because the controller does notincludes any integral action in the whole control system. Onthe other hand, the latter method has a PID control structure.PID parameters are tuned by operators skills, and they arestored in the data-base in advance. And also, a suitabl
12、e set ofPID parameters is generated using the stored data. However,the good controlperformance cannot be necessarily obtainedin the case where nonlinearities are included in the controlledobject and/or system parameters are changed, because PIDparameters are not tuned in an on-line manner correspond
13、ingto characteristics of the controlled object.Therefore, in this paper, a design scheme of PID controllersbased on the MB modeling method is newly proposed.According to the proposed method, PID parameterswhich are obtained using the MB modeling method areadequately tuned in proportion to control er
14、rors, and modifiedPID parameters are stored in the data-base. Therefore, moresuitable PID parameters corresponding to characteristics ofthe controlled object are newly stored. Moreover, an algorithmto avoid the excessive increase of the stored data,is further discussed. This algorithm yields the red
15、uction ofmemories and computational costs. Finally, the effectivenessof the newly proposed control scheme is examined on asimulation example. II. PID CONTROLLER DESIGN BASED ON MEMORY-BASEDMODELING METHOD A.MB modeling method First, the following discrete-time nonlinear system is considered: , （ 1）
16、where y(t) denotes the system output and f() denotes thenonlinear function. Moreover, _(t1) is called informationvector, which is defied by the following equation: )(),1(),(,),1(:)( uy ntutuntytyt ,（ 2） where u(t) denotes the system input. Also, ny and nurespectively denote the orders of the system
17、output and thesystem input, respectively. According to the MB modelingmethod, the data is stored in the form of the informationvector _ expressed in Eq.(2). Moreover, _(t) is required incalculating the estimate of the output y(t+1) called query.That is, after some similar neighbors to the query are
18、selectedfrom the data-base, the predictive value of the system can beobtained using these neighbors. B. Controller design based on MB modeling method In this paper, the following control law with a PIDstructure is considered: )()()()( 2 tyTTkteT TktuSDcIsc （ 3） )()()( 2 tyKtyKteK DPI （ 4） where e(t)
19、 denotes the control error signal defined by e(t) := r(t) y(t). （ 5） r(t) denotes the reference signal. Also, kc, TI and TDrespectively denote the proportional gain, the reset time andthe derivative time, and Ts denotes the sampling interval.Here, KP , KI and KD included in Eq.(4) are derived by the
20、relations PK =ck ，IK = ck sT / IT 和 DK = ck DT / sT 。 denotes the differencing operator defined by.11: z . Here, it is quite difficult to obtain a good control performancedue to nonlinearities, if PID parameters(KP, KI , KD) inEq.(4) are fixed. Therefore, a new control scheme is proposed,which can a
21、djust PID parameters in an on-line mannercorresponding to characteristics of the system. Thus, insteadof Eq.(4), the following PID control law with variable PIDparameters is employed: ).()()()()()()( 2 tytKtytKtetKtu DPI （ 6） Now, Eq.(6) can be rewritten as the following relations: )()( tgtu （ 7） )1
22、(),2(),1(),(),(),(:)( tutytytytrtKt （ 8） ) ,(),(),(:)( tKtKtKtK DIP （ 9） where g() denotes a linear function. By substituting Eq.(7)and Eq.(8) into Eq.(1) and Eq.(2), the following equation canbe derived: )()1( thty （ 10） )1(,),1(),(),(),1(,),(:)( uy ntututrtKntytyt （ 11） whereny _ 3, nu _ 2, and h(
23、) denotes a nonlinear function.Therefore, K(t) is given by the following equations: )()( tFtK （ 12） )1(,),1(),(),1(,),(),1(:)( uy ntututrntytytyt （ 13） where F() denotes a nonlinear function. Since the futureoutput y(t + 1) included in Eq.(13) cannot be obtained at t,y(t+1) is replaced by r(t+1). Because the control system so that can realize y(t + 1) ! r(t + 1), is designed in thispaper. Therefore, _(t) included in Eq.(13) is newly rewrittenas follows:
