Identification of Hammerstein models with hysteresis nonlinearity

Abstract

This paper deals with the identification of Hammerstein nonlinear models. The system nonlinearity is not necessarily static and can be of hysteresis type. The latter nonlinearity can be backlash, switch or any other memory operator having several transient cycles, but one permanent (major) cycle. The LTI (Linear Time-Invariant) block is nonparametric and is described by its impulse response. The considered system’s nonlinearity is any memory operator having one major cycle (periodic closed loop), which is bordered by any two arbitrary functions. The nonlinearity borders are not assumed to be invertible. The proposed identification algorithm can be used in static nonlinearity, e.g. polynomial nonlinearity, dead zone function or any piecewise affine functions. Unlike several previous studies, the proposed identification method is carried out using only one stage. In this approach, an input signal of piecewise constant (staircase) is used. It is shown that the estimated parameters converge to their true values.