Design of Implementable Adaptive Control for Micro/Nano Positioning System Driven by Piezoelectric Actuator

The micro/nano positioning system discussed in this paper includes a piezoelectric actuator (PEA) and flexure-hinge-based positioning mechanism. Due to the existence of the hysteretic nonlinearity in the PEA and the friction in the system, the accurate positioning of the piezo-actuated positioning system calls applicable control schemes for practical applications. To this end, an implementable adaptive controller is developed in the paper, where a minimized parameterization hysteresis model is employed to reduce the computational load. The formulated adaptive control law guarantees the global stability of the controlled positioning system, and the positioning error can approach to zero asymptotically. The advantages of the proposed method making on-line implementation feasible are that the traditional inversion of the hysteresis does not need to be constructed directly; the real values of the parameters of the positioning system neither need to be identified nor measured; only the parameters in the formulation of the controller are estimated online. Comparison with the feedforward plus proportional-integral feedback control scheme is conducted and experimental results show the effectiveness of the proposed method.