【正文】 of PID parameters using the proposed method are shown in . From , owing to nonlinearities of the controlled object, the control result by the fixed PID controller is not good. On the other hand, from and , the good control result can be obtained using the proposed method, because PID parameters are adequately adjusted. Moreover, the number of data stored in the database was 49. Using the algorithm to remove needless data, the number of data stored in the database can be effectively 21 )()(1:)( ?? ??????? Nt trtNepo c ?? （ 37） where N denotes the number of steps per 1[epoc]. Furthermore, the number of iteration was set as 1, because PID parameters can be adjusted in an online manner by the proposed method. Moreover, the NNPID controller was applied to System 1. Error behaviors of _ expressed in Eq.(37) are shown in , and control results are shown in . From , the necessary number for learning iterations was 86[epoc] until the control result using the NNPID controller could be obtained the same control performances as the proposed method, that is, until ?? was satisfied. Therefore, the effectiveness of the proposed method is also verified in parison with the NNPID controller for nonlinear , the case where the system has timevariant parametersis considered. That is, the system changes from Eq.(31) Fig. 5. Error behaviors using the controller fused the fixed PID with the NNPID for Hammerstein . 6. Control result using the controller fused the fixed PID with the NNPID for Hammerstein model. to Eq.(32) at t = 70. First, the control result with the fixed PID controller, is shown in , where PID parameters are set as the same parameters as shown in Eq.(36). Since the gain of the controlled object bees high gain around r(t) = , the fixed PID controller does not work well. On the other hand, the proposed control scheme was employed in this case. The control result and trajectories of PID parameters are shown in and . From these figures, a good control performance can be also obtained because PID parameters are adequately adjusted using the proposed method. The usefulness for the nonlinear system with timevariant parameters is suggested in this example. IV. CONCLUSIONS In this paper, a new design scheme of PID controllers using the MB modeling method has been proposed. Many PID controller design schemes using NNs and GAs have been proposed for nonlinear systems up to now. In employing these scheme for real systems, however, it is a serious problem that the learning cost bees considerably the other hand, according to the proposed method, such putational burdens can be effectively reduced using the algorithm for removing the redundant data. In addition, theeffectiveness of the proposed method have been verified by a numerical simulation example. The application of the newly proposed scheme for real systems and the extension to multivariable cases are currently under consideration. 基于記憶的在線非線性系統(tǒng) PID 控制器整定 摘 要 由于大部分控制過程具有非線性，所以設(shè)計一種能夠處理具有非線性系統(tǒng)的控制器就顯得尤為重要。 Reswick(CHR) method[3] 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 database: )0(,2,1)],(),([:)( NjjKjj ???? ? （ 15） where )(j?? and )(jK are given by Eq.(14) and Eq.(9). Moreover, N(0) denotes the number of information vectorsstored in the initial database. Note that all PID parametersincluded in the initial information vectors are equal, that is, K(1) = K(2) = _(t) included in Eq.(13) is newly rewritten as follows: )]1(,),1(),1(,),(),(),1([:)( ??????? uy ntutuntytytrtrt ??? （ 14） 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 database The MB modeling method cannot work if the past data is not saved at all. Therefore, PID parameters are firstly calculated using Zieglar amp。) denotes a nonlinear , K(t) is given by the following equations: ))(()( tFtK ?? （ 12） )]1(,),1(),(),1(,),(),1([:)( ??????? uy ntututrntytytyt ??? （ 13） where F( ? denotes the differencing operator defined by. 11: ???? z . 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 online manner corresponding to characteristics of the system. Thus, instead of Eq.(4), the following PID control law with variable PID parameters is employed: ).()()()()()()( 2 tytKtytKtetKtu DPI ?????? （ 6） Now, Eq.(6) can be rewritten as the following relations: ))(()( tgtu ??? （ 7） )]1(),2(),1(),(),(),([:)( ????? tutytytytrtKt? （ 8） ) ] ,(),(),([:)( tKtKtKtK DIP? （ 9） where g( 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,