Parametric Identification of Parallel Hammerstein Systems

Abstract

This paper proposes a parametric identification method for parallel Hammerstein systems. The linear dynamic parts of the system are modeled by a parametric rational function in the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> - or <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> -domain, while the static nonlinearities are represented by a linear combination of nonlinear basis functions. The identification method uses a three-step procedure to obtain initial estimates. In the first step, the frequency response function of the best linear approximation is estimated for different input excitation levels. In the second step, the power-dependent dynamics are decomposed over a number of parallel orthogonal branches. In the last step, the static nonlinearities are estimated using a linear least squares estimation. Furthermore, an iterative identification scheme is introduced to refine the estimates. This iterative scheme alternately estimates updated parameters for the linear dynamic systems and for the static nonlinearities. The method is illustrated on a simulation and a validation measurement example.