Instrumental variables approach to identification of polynomial wiener systems

A new approach to identification of Wiener systems by using the instrumental variables method is presented. In this approach, an inverse characteristic of the nonlinear element is represented by a polynomial of a known order. It is shown that parameters of a modified series-parallel Wiener model estimated with the least squares method are non-consistent. To obtain consistent parameter estimates, the instrumental variables method is used. The instrumental variables are generated by filtering the system input with the linear dynamic model obtained with the least squares method. In this paper, the known least squares identification method, based on the modified series-parallel model, is also extended to Wiener systems with inverse nonlinear characteristics, which polynomial representation does not contain the first order term. Two simulation examples are also included to show the effectiveness and practical feasibility of the presented approach.