【正文】 圖 8 使用固定的設(shè)計方法情況下改變系統(tǒng)參 數(shù)的控制結(jié)果 圖 9 與圖 8的 PID控制參數(shù)想一致的軌跡 Ⅳ 結(jié)論 在本文中提出了一種應(yīng)用 MB模型方法的新型 PID控制器設(shè)計方案。首先，固定PID控制器的控制結(jié)果如圖 7所示。因為在這個過程中 PID參數(shù)得到了充分的調(diào)整。 [系統(tǒng) 1] ?????????????????)()()()()()2()1()2()1()(32 tutututxttxtxtytyty? （ 31） [系統(tǒng) 2] ?????????????????)()()()()()2()1()2()1()(32 tutututxttxtxtytyty? （ 32） 其中， )(t? 表示具有零定義且變量為 的高斯白噪聲信號。因而在本文中我們假設(shè)系統(tǒng)雅可比行列式的標(biāo)記是已知的。因此在步驟 3中所得出來的 PID 參數(shù)將作和控制誤差一致的更新。 注 意 它 在 初 始 信 息 矢 量 中 的 PID 參 數(shù) 是 相 等 的 ， 即 ：))0(()2()1( NKKK ??? ?。為了使控制系統(tǒng)能夠識別本文中所定義的 )1( ?ty — )1( ?tr ，等式（ 13）中的 )(t? 可以被重新寫成如下形式： )]1(,),1(),1(,),(),(),1([:)( ??????? uy ntutuntytytrtrt ??? （ 14） 經(jīng)過以上的準(zhǔn)備工作以后，一種基于 MB模型方法的 PID 控制被設(shè)計出來了。在估計輸出 )1( ?ty 時，需要 )(t? ，因此被叫做詢問。通過這種新方法，有 MB模型方法得到的 PID 參數(shù)在比例環(huán)節(jié)中得到了充分的整定，這主要 是為了控制誤差。懶散學(xué)習(xí)方法或 MOD方法。但是由于大部分控制系統(tǒng)具有非線性，簡單地應(yīng)用固定 PID參數(shù)很難得到交好的控制效果。通過 MB方法，可以自動產(chǎn)生基于存儲在數(shù)據(jù)中的控制對象的輸入 /輸出數(shù)據(jù)對的本地模型。 Nichols method[2] or Chien, Hrones amp。 (2) the physical meaning of control parameters is clear。) denotes a nonlinear , K(t) is given by the following equations: ))(()( tFtK ?? （ 12） )]1(,),1(),(),1(,),(),1([:)( ??????? uy ntututrntytytyt ??? （ 13） where F(_ is defined as follows: )]1(),2(),1(),(),(),1([:)( ????? tutytytytrtrt? （ 34） The desired characteristic polynomial )( 1?zT included in the reference model was designed as follows: 211 0 1 8 )( ??? ??? zzzT （ 35） where T (z?1) was designed based on the reference literature[13]. Furthermore, the userspecified parameters included in the proposed method are determined as shown inTable I. TABLE I USERSPECIFIED PARAMETERS INCLUDED IN THE PROPOSED METHOD (HAMMERSTEIN MODEL). Orders of the information vector 23??uynn Number of neighbors 6?k Learning rate ???DIP??? Coefficients to inhibit the data ???? Initial number of data 6)0( ?N For the purpose of parison, the fixed PID control scheme which has widely used in industrial processes was first employed, whose PID parameters were tuned by CHR method[3]. Then, PID parameters were calculated as , ??? DIP KKK （ 36） Moreover, the PID controller using the NN, called NNPID controller, was applied for the purpose of the parison, where the NN was utilized in order to supplement the fixed PID controller. The control results for System 1 are summarized in , where the solid line and dashed line denote the control results of the proposed method and the fixed PID controller, respectively. Furthermore, trajectories 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 rea