Inversion-free stabilization and regulation of systems with hysteresis using integral action

Abstract

In this paper, we present analysis on the stabilization and regulation of the tracking error for an n-dimensional dynamic system with zero dynamics, which is preceded by a Prandtl-Ishlinskii hysteresis operator. A general controller structure is considered; however, we assume that an integral action is present. We treat this problem from the perspective of switched systems, where the state of the hysteresis operator defines the switching surfaces. The common Lyapunov function theorem is utilized together with an LMI condition to show that, under suitable conditions, the tracking error of the system goes to zero exponentially fast when a constant reference is considered. A key feature of this LMI condition is that it does not require the hysteresis effect to be small, meaning that hysteresis inversion is not required. We use this condition together with a periodicity assumption to prove that a servocompensator-based controller can stabilize a system with hysteresis without using hysteresis inversion. Finally, we conduct experiments using a servocompensator-based controller, where we verify the stability of the system and achieve a mean tracking error of 0.5% at 200 Hz using a sinusoidal reference.