An Iterative Algorithm for the Subspace Identification of SISO Hammerstein Systems

Abstract

AbstractThis paper describes an algorithm to identify state-space models for single input single output (SISO) Hammerstein structures based on input-output measurements. The algorithm consists of two main steps. First, a subspace algorithm is used to determine the system order and estimate the A and C system matrices. Estimation of the other state space matrices as well as the nonlinearity is then formulated as nonlinear optimization problem in which the state space model of the linear component and the coefficients of the basis function expansion of the nonlinear component are distinct. This formulation minimizes the number of parameters to estimate; moreover any one parameter is related to either the linear dynamics or the static nonlinearity. The unknown parameters are then estimated using an iterative procedure that solves a least square problem at each step. Simulation studies using a well known model of ankle joint reflex stiffness demonstrate that the algorithm is accurate and performs well in the non-ideal conditions that prevail during practical experiments.