State estimation of dynamic systems with sandwich structure and hysteresis

Abstract

In this paper, a non-smooth observer is proposed to estimate the states of a sandwich system with hysteresis. Based on the analysis of observability of this system, a non-smooth observer is constructed. The non-smooth observer has a switchable transition matrix and contains an additional item which can switch according to the working zone of the system. By considering the suppression of model uncertainty and disturbance, the robust design of the non-smooth observer for the sandwich system with hysteresis is proposed. In the robust observer, the estimation error caused by the switched error is included as an extended disturbance and the selection of the feedback matrices of the robust observer has been converted into an optimal problem. Finally, the proposed methods are implemented to estimate the states of a micro-positioning stage with piezoelectric actuator which can be described as a non-smooth sandwich system with hysteresis. The estimations results by the non-smooth and the robust observer are superior to the conventional and the non-robust observer in the experimental case, respectively.