Switching iterative learning control of a piezoelectric nano motion stage with hysteretic state and parameter...

The control of piezoelectric nano motion stages is one of the key enabling techniques supporting high precision optical scanning tasks in nano-measurement applications. This paper proposes a hysteretic state and parameter estimation scheme for switching iterative learning control of a piezoelectric driven stage, in which the hysteresis nonlinearities of such a motion system are reflected by an asymmetric Bouc-Wen model (ABWM). Aided by only the displacement measurement, the prediction error of the hysteresis model is utilized to devise an update law for obtaining the hysteretic state observation error. The parameters of the entire ABWM are adaptively estimated by the use of the hysteretic state observation error. Based on this, a novel adaptive state observer is presented for hysteretic estimation and inverse compensation. Moreover, both the external perturbation and the unmodeled dynamics of the asymmetric hysteretic system are also considered, and the robust compensation term with an adaptive gain is introduced to address their adverse effects. The convergence of the parameter estimation errors and the state observation errors is rigorously analyzed by the Lyapunov stability theory. To boost the feedforward inverse control performance, a switching iterative learning control framework is developed to seek the high-accuracy trajectory tracking. Comprehensive experiments regarding the adaptive model prediction and the trajectory tracking are conducted on a piezoelectric nano motion stage. Both the excellent model prediction performance and the satisfactory displacement control accuracy are demonstrated by the experimental results.