Implementable Adaptive Inverse Control of Hysteretic Systems via Output Feedback With Application to Piezoelectric Positioning Stages

This paper aims to develop a neural-network-based robust adaptive output-feedback motion controller for a class of hysteretic nonlinear systems, where the inverse hysteresis approach is adopted. The developed scheme is applied to the piezoelectric positioning stage, showing the advantages of the proposed approach by the experimental results. The main contributions are: 1) by using the neural networks as an approximator, the nonlinear function in the systems can be completely unknown; 2) by designing a high-gain observer to estimate the states of the system and cope with the uncertainties of the system, only the output of the control system is required measurable; 3) experiments on the piezoelectric positioning stage were conducted where the piezoelectric positioning stage is considered as a third-order system under the condition only the output of the system is available; 4) by adjusting the initial conditions of the states observer and adaptive laws of unknown parameters, the arbitrarily small L∞norm of the tracking error is deviated. It is proved that all the signals in the closed-loop systems are semiglobally ultimately uniformly bounded.