Inversion-Free Hysteresis Compensation via Adaptive Conditional Servomechanism With Application to Nanopositioning Control

In this article, an adaptive conditional servocompensator is proposed to achieve precise tracking control of systems with hysteresis without requiring explicit inversion of the hysteresis. Motivated by a range of applications, such as the piezoelectric-actuated nanopositioning, the system considered in this work consists of a chain of integrators preceded by a hysteresis nonlinearity modeled by a modified Prandtl-Ishlinskii (MPI) operator with uncertainty. To facilitate the proposed control design, the MPI operator is rearranged into a form comprised of three parts: a linear term, a nominal hysteretic term represented by a classical Prandtl-Ishlinskii (PI) operator, and a hysteretic perturbation. The bound on the hysteretic perturbation is further derived based on the parameter uncertainty of the MPI operator. The controller consists of two major elements. The first is a continuously implemented sliding mode controller (SMC), which exploits the bound on hysteretic perturbation and drives the system states to a bounded set in finite time. To properly "cancel" the nominal hysteresis effect without inversion, a technique involving a low-pass filter is introduced. The second element of the proposed controller is an adaptive conditional servocompensator that aims to eliminate periodic components in the tracking error. We show that, with persistent excitation, the closed-loop variables are ultimately bounded and the tracking error approaches a neighborhood of zero, where the neighborhood can be made arbitrarily small via the choice of the SMC boundary-layer width parameter and the servocompensator order. The proposed approach is implemented experimentally on a commercial nanopositioner under different types of periodic references, and it shows superior tracking performance over the traditional proportional-integral control, as well as several hysteresis inversion-based approaches reported in the literature.