Iterative Identification of Continuous-Time Hammerstein and Wiener Systems Using a Two-Stage Estimation Algorithm

Abstract

This article presents an iterative method to deal with the identification of continuous-time single-input/single-output Hammerstein and Wiener systems, characterized by a series connection of a nonlinear static element and a linear dynamic element. The internal variable between the nonlinear and linear elements is inaccessible to measurements so that simultaneous parameter estimation of the two elements cannot be easily achieved in a least-squares fashion. This difficulty could be circumvented by updating the internal variable at each iteration step. A two-stage estimation algorithm, in conjunction with moving-horizon smoothing and a solution-guiding mechanism, is established to ensure the convergence and accuracy of the iterative method in the face of linear structure mismatch, high static nonlinearity with an unknown characteristic, and severe noise. At the first stage, a good description of the static nonlinearity is given by a multisegment function or a polynomial in an iterative manner. Linear structure mismatch is allowed for this stage of estimation. At the second stage, the identification problem is reduced to a simple linear one with the internal variable gained at the first stage. A noniterative procedure can then be applied to determine accurately the structure and parameters of the linear dynamic element. Studies with simulated and experimental examples demonstrate that the proposed identification method is valid for a wide variety of nonlinear system dynamics and test conditions.