Adaptive filtering scheme for parameter identification of nonlinear Wiener–Hammerstein systems and its application

In this paper, a novel adaptive filtering scheme is first proposed to estimate the parameters of the nonlinear Wiener–Hammerstein systems with hysteresis, which is derived by exploiting the filtering technique and cost function framework. Different from the conventional cost function, the cost function of this paper involves estimation error information term and initial estimate term. In this scheme, the filtering technique is utilised to produce the estimation error information by using a group of auxiliary variables. The estimation error information term can improve the estimation accuracy. Based on developed cost function framework, the parameter update law is derived. Furthermore, the convergence of the proposed scheme is proved under the persistent excitation condition (PE). The efficiency and applicability of the proposed scheme are validated through the simulation and experiment.