【正文】 initial database. Note that all PID parametersincluded in the initial information vectors are equal, that is, K(1) = K(2) = and (3) the operators’ knowhow 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 works(NN)[4] and geic 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 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() 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） where ny _ 3, nu _ 2, and h( = K(N(0)) in the initial stage. [STEP 2] Calculate distance and select neighbors Distances between the query )(tl? and the informationvectors ))(( kii ?? are calculated using the following L1norm with some weights: ? ?? ? ??? 11 )(m i n)(m a x )()()))((),(( uy nn l ll mm jtjtd ?? ???? （ 16） where N(t) denotes the number of information vectors storedin the database when the query )(t? is given. Furthermore, )(jl? denotes the lth element of the jth information , )(tl? denotes the lth element of the query at t. Moreover, )(max ml? denotes the maximum element among the lth element of all information vectors ))(,2,1),(( tNjj ??? stored in the database. Similarly, )(min ml? 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]: ??? ki id iKwtK 1 )()(? （ 17） where wi denotes the weight corresponding to the ith information vector )(i? in the selected neighbors, and is calculated by: ? ??? ???? 11 22 ))](m i n)([m a x )]()([1(nynu l ll ll mm itwi ?? ?? （ 18） [STEP 4] Data adjustment In the case where information corresponding to the current state of the controlled object is not effectively saved in the database, 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 database. The following steepest descent method is utilized in order to modify PID parameters: )( )1()()( tKtJtKtK dne w ?