Using of the Hammerstein and Wiener models in adaptive control of the nonlinear processes

Abstract

The using of the Hammerstein and Wiener models in the linear adaptive control of the nonlinear processes is described in this paper. The main aim of this research study is an increasing of the adaptive control quality by using of the factorable methods which are based on the fact that many nonlinear systems can be factorized into the linear and the nonlinear parts. The factorization of the nonlinear system into the nonlinear static part and the linear dynamic part is assumed in this paper. The transfer function of the linear dynamic part of the nonlinear system is assumed in the time-discrete second-order Z-model form. Its parameters are estimated by the using of the time-discrete leastsquares method with the directive forgetting. The estimated parameters of the linear dynamic part are used for the design of the linear time-discrete control system, which is represented by the two-degree of freedom control system configuration (2DOF). The resulting controller is derived by the using of the polynomial approach and the characteristic polynomial of the closed control loop is chosen by the using of the optimal LQ approach and Pole Placemen Method (PPM). The described method is tested on the nonlinear system which is represented by the servo-speed mechanism AMIRA DR300.