【正文】 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 the way, development of puters 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 , similar neighbors to the information requests, called’queries’, are selected from the stored data. Furthermore,the local model is constructed using these neighbors. Thismemorybased(MB) modeling method, is called JustInTime(JIT) method[6], [7] , Lazy Learning method[8] or ModelonDemand(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 method[10] and the MoD method[11] 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 parameters are tuned by operators’ skills, and they are stored in the database 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 online 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 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 database. 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 putational costs. Finally, the effectiveness of the newly proposed control scheme is examined on asimulation example. II. PID CONTROLLER DESIGN BASED ON MEMORYBASED MODELING METHOD A. MB modeling method First, the following discretetime nonlinear system is considered: , （ 1） where y(t) denotes the system output and f(附錄二 :翻譯 MemoryBased OnLine Tuning of PID Controllers for Nonlinear Systems Abstract— Since most processes have nonlinearities, controller design schemes to deal with such systems are 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 memorybased(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 database. The proposed scheme generates PID parameters using stored input/output data in the database. This scheme can adjust the PID parameters in an online 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 plicated control algorithms such as adaptive control theory or robust control theory have been proposed and implemented. However, in industrial processes, PID controllers[1], [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。) denotes the nonlinear function. Moreover, _(t?1) is called ’information vector’, which is defied by the following equation: )](),1(),(,),1([:)( uy ntutuntytyt ????? ??? , （ 2） 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 database, 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: )()()()( 2 tyTTkteT TktuSDcIsc ?????? （ 3） )()()( 2 tyKtyKteK DPI ????? （ 4） where e(t) denotes the control error signal defined by e(t) := r(t) ? y(t). （ 5） 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 PK =ck ，IK = ck sT / IT 和 DK = ck DT / sT 。) denotes a linear function. By substituting Eq.(7)and