Adaptive control of a class of uncertain nonlinear systems with unknown input hysteresis

Abstract

Based on backstepping technique, an adaptive inverse control scheme is proposed for a class of uncertain nonlinear systems preceded by unknown hysteretic nonlinearities which are described by Krasnosel'skii-Pokrovkii (KP) model. The pseudo-inversion is introduced to compensate the hysteresis nonlinearities and the error caused by the hysteresis model and pseudo-inversion is estimated online by the adaptive controller. To avoid the possible chattering caused by the sign function, a smooth adaptive controller is designed. The proposed controller ensures the uniformly ultimate boundedness of the closed-loop system. Simulation results show the effectiveness of the proposed scheme.

Compound Control of Trajectory Errors in a Non-Resonant Piezo-Actuated Elliptical Vibration Cutting Device

“…From the figure, it can be seen that there is a nonlinear relationship between the output displacement and the input voltage of the PSA in each direction under different frequencies. This nonlinear relationship between voltage and displacement can be described by the piezoelectric hysteresis models [29,30]. Many kinds of hysteresis models have been built and used for designing controllers of PSAs.…”