L1 Adaptive Control of Hysteresis in Smart Materials

Smart materials display coupling between electrical, magnetic, thermal and elastic behavior. Hence these materials have inherent sensing and actuation capacities. However, the hysteresis inherent to smart materials presents a challenge in control of these actuators/sensors. Inverse compensation is a fundamental approach to cope with hysteresis, where one aims to cancel out the hysteresis effect by constructing a right inverse of the hysteresis. The performance of the inverse compensation is susceptible to model uncertainties and to error introduced by inexact inverse algorithms. We employ a mathematical model for describing hysteresis. On the basis of the hysteresis model, a robust adaptive inverse control approach is presented, for reducing hysteresis. The asymptotic tracking property of the adaptive inverse control algorithm is proved and the issue of parameters convergence is discussed in terms of the reference trajectory. Moreover, sufficient conditions under which parameter estimates converge to their true values are derived. Simulations are used to examine the effectiveness of the proposed approach.