PID控制器中英文对照外文翻译文献.docx

PID控制器中英文对照外文翻译文献中英文对照外文翻译文献 (文档含英文原文和中文翻译) 外文: Memory-Based On-Line Tuning of PID Controllers for Nonlinear Systems AbstractSince most processes have nonlinearities, controller design schemes to deal with such systems are required.On the other hand, PID controllers have been widely used for process systems. Therefore, in this paper, a new design scheme of PID controllers based on a memory-based(MB) modeling is proposed for nonlinear systems. According to the MB modeling method, some local models are automatically generated based on input/output data pairs of the controlled object stored in the data-base. The proposed scheme generates PID parameters using stored input/output data in the data-base. This scheme can adjust the PID parameters in an on-line manner even if the system has nonlinear properties. Finally, the effectiveness of the newly proposed control scheme is numerically evaluated on a simulation example. I. INTRODUCTION In recent years, many complicated control algorithms such as adaptive control theory or robust control theory have been proposed and implemented. However, in industrial processes, PID controllers1, 2, 3 have been widely employed for about 80% or more of control loops. The reasons are summarized as follows. (1) the control structure is quitsimple; (2) the physical meaning of control parameters is clear; and (3) the operators know-how can be easily utilized in designing controllers. Therefore, it is still attractive todesign PID controllers. However, since most process systems have nonlinearities, it is difficult to obtain good control performances for such systems simply using the fixed PIDparameters. Therefore, PID parameters tuning methods using neural networks(NN)4 and genetic algorithms(GA)5 have been proposed until now. According to these methods, the learning cost is considerably large, and these PID parameters cannot be adequately adjusted due to the nonlinear properties. Therefore, it is quite difficult to obtain good control performances using these conventional schemes.By the way, development of computers enables us to memorize, fast retrieve and read out a large number of data. By these advantages, the following method has been proposed: 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, is called Just-In-Time(JIT) method6, 7 , Lazy Learning method8 or Model-on-Demand(MoD)9, and these scheme have lots of attention in last decade. In this paper, a design scheme of PID controllers based onthe MB modeling method is discussed. A few PID controllers have been already proposed based on the JIT method10 and the MoD method11 which belong to the MB modeling methods. According to the former method, the JIT method is used as the purpose of supplementing the feedback controller with a PID structure. However, the tracking property is not guaranteed enough due to the nonlinearities in the case where reference signals are changed, because the controller does not includes any integral action in the whole control system. On the other hand, the latter method has a PID control structure.PID parameters are tuned by operators skills, and they are stored in the data-base in advance. And also, a suitable set of PID parameters is generated using the stored data. However,the good control performance cannot be necessarily obtained in the case where nonlinearities are included in the controlled object and/or system parameters are changed, because PID parameters are not tuned in an on-line manner corresponding to characteristics of the controlled object. Therefore, in this paper, a design scheme of PID controllers based 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 errors, 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 reduction of memories and computational costs. Finally, the effectiveness of the newly proposed control scheme is examined on asimulation example. II. PID CONTROLLER DESIGN BASED ON MEMORY-BASED MODELING METHOD A. MB modeling method First, the following discrete-time nonlinear system is considered: , where y(t) denotes the system output and f(·) denotes the nonlinear function. Moreover, _(t1) is called information vector, which is defied by the following equation: f(t):=y(t-1),L,y(t-ny),u(t-1),Lu(t-nu), where u(t) denotes the system input. Also, ny and nure spectively denote the orders of the system output and the system input, respectively. According to the MB modeling method, the data is stored in the form of the information vector _ expressed in Eq.(2). Moreover, _(t) is required in calculating the estimate of the output y(t+1) called query.That is, after some similar neighbors to the query are selected from 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 PID structure is considered: Du(t)=kcTsTe(t)-kc(D+DD2)y(t)TITS =KIe(t)-KPDy(t)-KDD2y(t) where e(t) denotes the control error signal defined by e(t) := r(t) y(t). r(t) denotes the reference signal. Also, kc, TI and TD respectively denote the proportional gain, the reset time and the derivative time, and Ts denotes the sampling interval. Here, KP , KI and KD included in Eq.(4) are derived by therelations KP=kc，KI=kcTs/TI和KD=kcTD/Ts。Ddenotes the differencing operator defined by. D:=1-z-1. Here, it is quite difficult to obtain a good control performance due to nonlinearities, if PID parameters(KP, KI , KD) in Eq.(4) are fixed. Therefore, a new control scheme is proposed, which can adjust PID parameters in an on-line manner corresponding to characteristics of the system. Thus, instead of Eq.(4), the following PID control law with variable PID parameters is employed: Du(t)=KI(t)e(t)-KP(t)Dy(t)-KD(t)D2y(t). Now, Eq.(6) can be rewritten as the following relations: u(t)=g(f¢(t) f¢(t):=K(t),r(t),y(t),y(t-1),y(t-2),u(t-1) K(t):=KP(t),KI(t),KD(t), where g(·) denotes a linear function. By substituting Eq.(7)and Eq.(8) into Eq.(1) and Eq.(2), the following equation canbe derived: y(t+1)=hf(t) f(t):=y(t),L,y(t-ny+1),K(t),r(t),u(t-1),L,u(t-nu+1) where ny _ 3, nu _ 2, and h(·) denotes a nonlinear function.Therefore, K(t) is given by the following equations: K(t)=F(f(t) f(t):=y(t+1),y(t),L,y(t-ny+1),r(t),u(t-1),L,u(t-nu+1)where F(·) denotes a nonlinear function. Since the future output 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 this paper. Therefore, ¯_(t) included in Eq.(13) is newly rewritten as follows: f(t):=r(t+1),r(t),y(t),L,y(t-ny+1),u(t-1),L,u(t-nu+1) After the above preparation, a new PID control scheme is designed based on the MB modeling method. The controller design algorithm is summarized as follows.STEP 1 Generate initial data-base The MB modeling method cannot work if the past data is not saved at all. Therefore, PID parameters are firstly calculated using Zieglar & Nichols method2 or Chien, Hrones & Reswick(CHR) method3 based on historical data of the controlled object in order to generate the initial database. That is, _(j) indicated in the following equation isgenerated as the initial data-base: F(j):=f(j),K(j),j=1,2,LN(0) where f¢(j) andK(j) are given by Eq.(14) and Eq.(9). Moreover, N(0) denotes the number of information vectorsstored in the initial data-base. Note that all PID parametersincluded in the initial information vectors are equal, that is, K(1) = K(2) = · · · = K(N(0) in the initial stage. STEP 2 Calculate distance and select neighbors Distances between the query fl(t) and the informationvectors f(i)(i¹k) are calculated using the following L1-norm with some weights: ny+nu+1d(f(t),(f(j)=ål=1fl(t)-fl(j)maxf(m)-minf(m)where N(t) denotes the number of information vectors storedin the data-base when the query f(t) is given. Furthermore, fl(j) denotes the l-th element of the j-th information vector.Similarly, fl(t)denotes the l-th element of the query at t. Moreover, maxfl(m) denotes the maximum element among the l-th element of all information vectors(f(j),j=1,2L,N(t) stored in the data-base. Similarly, minfl(m)denotes the minimum element. Here, k pieces with the smallest distances are chosen from all information vectors. STEP 3 Construct local model Next, using k neighbors selected in STEP 2, the localmodel is constructed based on the following LinearlyWeighted Average(LWA)12: Kad(t)=åwK(i)ii=1kwhere wi denotes the weight corresponding to the i-th information vector f(i) in the selected neighbors, and is calculated by: nu+ny+1wi=ål=1fl(t)-fl(i)2(1-)2maxfl(m)-minfl(m) STEP 4 Data adjustment In the case where information corresponding to the current state of the controlled object is not effectively saved in the data-base, a suitable set of PID parameters cannot be effectively calculated. That is, it is necessary to adjust PID parameters so that the control error decreases. Therefore, PID parameters obtained in STEP 3 are updated corresponding to the control error, and these new PID parameters are stored in the data-base. The following steepest descent method is utilized in order to modify PID parameters: Knew(t)=Kad(t)-h¶J(t+1)¶K(t) h:=hP,hI,hD where _ denotes the learning rate, and 饎he following J(t+1)denotes the error criterion: J(t+1):=1e(t+1)22 e(t):=yr(t)-y(t). yr(t) denotes the output of the reference model which isgiven by: z-1T(1)yr(t)=r(t)-1T(z) (23) T(z-1):=1+t1z-1+t2z-2. (24) Here, T (z1) is designed based on the reference literature13. Moreover, each partial differential of Eq.(19) is developed as follows: ¶J(t+1)¶J(t+1)¶e(t+1)¶y(t+1)¶u(t)ü=¶KP(t)¶e(t+1)¶y(t+1)¶u(t)¶KP(t)ïï¶y(t+1)ï=e(t+1)(y(t)-y(t-1)ï¶u(t)ï¶J(t+1)¶J(t+1)¶e(t+1)¶y(t+1)¶u(t)ï=¶KI(t)¶e(t+1)¶y(t+1)¶u(t)¶KI(t)ïïý¶y(t+1)ï=-e(t+1)e(t)ï¶u(t)ï¶J(t+1)¶J(t+1)¶e(t+1)¶y(t+1)¶u(t)ï=¶KD(t)¶e(t+1)¶y(t+1)¶u(t)¶KD(t)ïï¶y(t+1)ï=e(t+1)(y(t)-2y(t-1)+y(t-2)¶u(t)ïþ . Note that a priori information with respect to the systemJacobian ¶y(t+1) is ¶u(t)required in order to calculateEq.(25). Here, using the relation x = |x|sign(x), the systemJacobian can be obtained by the following equation: ¶y(t+1)¶y(t+1)¶y(t+1)=sign,¶u(t)¶u(t)¶u(t) where sign(x) = 1(x > 0), 1(x < 0). Now, if the sign of the system Jacobian is known in advance, by including ¶y(t+1)¶u(t) in h, the usage of the system Jacobian can make easy14. Therefore, it is assumed that the sign of the system Jacobian is known in this paper. STEP 5 Remove redundant data In implementing to real systems, the newly proposed scheme has a constraint that the calculation from STEP 2 to STEP 4 must be finished within the sampling time. Here,storing the redundant data in the data-base needs excessive computational time. Therefore, an algorithm to avoid the excessive increase of the stored data, is further discussed. The procedure is carried out in the following two steps. First, the information vectorsF(i) which satisfy the following first condition, are extracted from the data-base: First condition d(f(t),f(i)£a1,i=1,2,L,N(t)-k whereiF(i)s defined by F(i):=f(i)K(i),i=1,2,L Moreover, the information vectors F(i) which satisfy the following second ): condition, are further chosen from the extractedF(inewìïKl(i)-Kl(t)üïíý£a2ånewïïKl(t)þ l=1î 32) is defined by where F(i):=f(i),K(i).i=1,2,LF(i ), the information vector with the smallest value in the second If there exist pluralF(i) is only removed. By the above procedure, the redundant condition among all, F(idatacan be removed from the data-base. Here, a block diagram summarized mentioned above algorithms are shown in Fig. yry Model PID y Kold Knew Databas Memory-B ased Kold y u r + e ModPID _ rIII. SIMULATION EXAMPLE In order to evaluate the effectiveness of the newly proposed scheme, a simulation example for a nonlinear system is considered. As the nonlinear system, the following Hammerstein model15 is discussed: System 1 üy(t)=0.6y(t-1)-0.1y(t-2)ï+1.2x(t-1)-0.1x(t-2)+x(t)ýx(t)=1.5u(t)-1.5u2(t)+0.5u3(t)ïþ System 2 üy(t)=0.6y(t-1)-0.1y(t-2)ï+1.2x(t-1)-0.1x(t-2)+x(t)ýx(t)=1.0u(t)-1.0u2(t)+1.0u3(t)ïþ where x(t) denotes the white Gaussian noise with zero mean and variance0.012. Static properties of System 1 and System 2 are shown in Fig.2. Fig.2 From Fig.2, it is clear that gains of System 2 are larger than ones of System 1 at. y³1.0Here, the reference signal r(t) is given by: ì0.5(0£t<50)ï1.0(50£t<100)ï r(t)=íï2.0(100£t<150)ïî1.5(150£t£200)The information vector ¯_ is defined as follows: f(t):=r(t+1),r(t),y(t),y(t-1),y(t-2),u(t-1) The desired characteristic polynomial T(z-1)included in the reference model was designed as follows: T(z-1)=1-0.271z-1+0.0183z-2 where T (z1) was designed based on the reference literature13. Furthermore, the user-specified parameters included in the proposed method are determined as shown inTable I. TABLE I USER-SPECIFIED PARAMETERS INCLUDED IN THE PROPOSED METHOD (HAMMERSTEIN MODEL). Orders of the information n=3yvector nu=2 k=6 Number of neighbors Learning rate h=0.8PhI=0.8hD=0.2 Coefficients to inhibit the a=0.51data a2=0.1 Initial number of data N(0)=6 For the purpose of comparison, the fixed PID control scheme which has widely used in industrial processes was first e