Hysteresis Compensation Using Extended High-Gain Observer and Dynamic Inversion

Hysteresis is a nonlinearity exhibited by a wide class of smart materials, such as piezoelectrics and shape memory alloys, and it presents challenges in the control of smart material-actuated systems (for example, piezo-based nanopositioning systems). Existing methods for hysteresis compensation typically require an explicit model of the hysteresis, which tends to be high-dimensional operators and entails significant complexity in model identification and inversion. In this paper a novel hysteresis compensation method based on extended-high-gain observers and dynamic inversion is presented, which does not assume any specific hysteresis model. An extended high-gain observer is used to estimate the hysteresis output as well as other unknown dynamics of the system model, and then dynamic inversion is implemented to cancel the effect of hysteresis. With a mild assumption on the system and the input nonlinearity, the analysis of the closed-loop system under output feedback shows fast performance recovery to the trajectories of a target system, and that the tracking error converges exponentially to zero. Simulation results are presented to support the efficacy of the proposed approach.