【文章內(nèi)容簡介】 ????????????????????????????????????????????????????????????????????????)()1())2()1(2)()(1()()()()1()1()1()1()1()()1()()1()()1()()()()1()1()1()1()1()()1()()1())1()()(1()()()()1()1()1()1()1()()1(tutytytytyttKtututytytttJtKtJtutytettKtututytytttJtKtJtutytytyttKtututytytttJtKtJDDIIPP????????? （ 25） Note that a priori information with respect to the systemJacobian )( )1( tuty? ?? is required in order to calculateEq.(25). Here, using the relation x = |x|sign(x), the systemJacobian can be obtained by the following equation: ),)( )1(()( )1()( )1( tutys igntutytuty ? ??? ???? ?? （ 26） where sign(x) = 1(x 0), ?1(x 0). Now, if the sign of the system Jacobian is known in advance, by including )()1( tuty ??? in ? , the usage of the system Jacobian can make easy[14]. 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 database needs excessive putational 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 vectors )(i? which satisfy the following first condition, are extracted from the database: [First condition] ktNiitd ??? )(,2,1,))(),(( 1 ???? （ 27） wherei )(i? s defined by ?,2,1)],()([:)( ??? iiKii ? （ 28） Moreover, the information vectors )(i? which satisfy the following second condition, are further chosen from the extracted )?(i? : 2231 )()()( ???????????? ???l n e wln e wlltK tKiK （ 29） where )?(i? is defined by ?,2,1?)].?(),?([:)?( ??? iiKii ? （ 30） If there exist plural )?(i? , the information vector with the smallest value in the second condition among all, )?(i? is only removed. By the above procedure, the redundant datacan be removed from the database. Here, a block diagram summarized mentioned above algorithms are shown in Fig. III. 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 model[15] is discussed: [System 1] ?????????????????)()()()()()2()1()2()1()(32 tutututxttxtxtytyty? （ 31） _ + Model PID Tuner Database Model MemoryBased PID Controller [System 2] ?????????????????)()()()()()2()1()2()1()(32 tutututxttxtxtytyty? （ 32） where )(t? denotes the white Gaussian noise with zero mean and variance . Static properties of System 1 and System 2 are shown in . From , it is clear that gains of System 2 are larger than ones of System 1 at. ?y Here, the reference signal r(t) is given by: ????????????????)202050()150100()10050()500()(tttttr （ 33） The information vector 175。_ 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 s