Motion Control of Piezoelectric Positioning Stages: Modeling, Controller Design, and Experimental Evaluation

In this paper, a general skeleton on modeling, controller design, and applications of the piezoelectric positioning stages is presented. Toward this framework, a general model is first proposed to characterize dynamic behaviors of the stage, including frequency response of the stage, voltage-charge hysteresis and nonlinear electric behavior. To illustrate the validity of the proposed general model, a dynamic backlash-like model is adopted as one of hysteresis models to describe the hysteresis effect, which is confirmed by experimental tests. Thus, the developed model provides a general frame for controller design. As an illustration to this aspect, a robust adaptive controller is developed based on a reduced dynamic model under both unknown hysteresis nonlinearities and parameter uncertainties. The proposed control law ensures the boundedness of the closed-loop signals and desired tracking precision. Finally, experimental tests with different motion trajectories are conducted to verify the proposed general model and the robust control law. Experimental results demonstrate the excellent tracking performance, which validates the feasibility and effectiveness of the proposed approach.