LPV Gain Scheduling Control of Hysteresis on an SMA Wire System

Abstract

In this work, a Linear Parameter-Varying (LPV) control method is used to compensate the hysteretic behavior of a Shape Memory Alloy (SMA) wire. Controller is implemented on an experimental system which consists of a pre-tension spring and a mass actuated with a thin SMA wire. The hysteretic characteristic of the SMA wire is modeled using the Preisach model and the model is verified both for the major and minor hysteresis loops. The small signal linear gain of the Preisach model is used as a scheduling stiffness variable. The parameter-dependent controller is scheduled based on the real time measurement of the stiffness variable. An H∞ controller is also synthesized by representing the hysteresis as a parametric uncertainty and comparisons are made with LPV gain scheduling controllers using similar weights for both controllers. Experimental trajectory tracking results show that the LPV Gain Scheduling controller has a better response and the hysteresis uncertainty is compensated for the full range of stiffness variability.