Velocity observer-based robust control of piezoelectric compliant motion systems with disturbance and hysteresis estimation

Abstract

This paper proposes a velocity observer-based robust control methodology for piezoelectric compliant motion systems with both unmeasurable hysteresis states and unknown disturbances. A dynamic asymmetric Bouc–Wen model is introduced to describe hysteresis behaviors of the piezoelectric compliant motion systems, a nonlinear state estimator is constructed to compensate the hysteresis nonlinearities. With the aid of the hysteresis state estimation, a velocity and disturbance observer is designed to simultaneously achieve output feedback control and disturbance rejection. Based on the estimations of the hysteresis state, the velocity, and the disturbance, a novel gain adaptation sliding mode control (SMC) structure is developed to robustly stabilize the tracking error without the requirement of velocity measurements, where the hyperbolic tangent function is employed to avoid the chattering, and the gain of the SMC is captured by an adaptive observer. By means of Lyapunov stability theory, the convergence of the hysteresis state estimation error, the velocity observation error, and the disturbance estimation error is analyzed, and the stability of such a control system is rigorously proved. Finally, the proposed control approach is applied to a piezoelectric compliant motion system without velocity sensors. The parameters of the asymmetric Bouc–Wen model are identified by using practical experimental data from the piezoelectric compliant motion system. Simulation and experimental results based on the identified model are provided to demonstrate the proposed control approach achieves excellent tracking performance with the relative error less than 0.6%. Compared with recently reported control approaches, more than 74.42% improvement on the control accuracy is confirmed in the complicated multifrequency trajectory tracking experiments.