High-Bandwidth Tracking Control of Piezoactuated Nanopositioning Stages via Active Modal Control

Abstract

Due to the lightly damped resonance and intrinsic nonlinearities, it is difficult for the piezoactuated nanopositioning stage to realize high-bandwidth and high-accuracy control. To handle these limitations, in this work, a dual-loop control scheme based on state-feedback-based modal method is designed to both actively damp and stiffen the resonant mode and to suppress the effects of nonlinearities of the piezoactuated nanopositioning stage. In this scheme, the state-feedback-based modal controller is first designed in the inner loop to enlarge both the damping ratio and natural frequency of the first resonant mode. Then, a proportional–integral (PI) controller is utilized in the outer loop for eliminating the tracking errors caused by other disturbances and nonlinearities including hysteresis and creep. To maximize the control bandwidth of system under the proposed dual-loop scheme, an optimization method is thus proposed for simultaneously tuning the parameters of the inner and the outer loop controllers. Finally, to validate the proposed dual-loop control scheme, comparative experiments are carried out on a piezoactuated nanopositioning stage. Results demonstrate that the proposed control scheme improves the bandwidth of the system from 497 Hz (with PI control) and 1543 Hz (with a commonly used positive acceleration, velocity, and position damping control and a PI controller) to 6546 Hz, which is 664 Hz larger than the first resonant frequency of the original system, validating the effectiveness of the proposed dual-loop scheme on high-bandwidth control. Note to Practitioners—The demand of high-bandwidth and high-accuracy piezoactuated nanopositioning stages increases rapidly. However, the lightly damped resonance of the mechanism and the intrinsic nonlinearities of the piezoelectric actuator limit the tracking performance of the stage. A dual-loop control structure is adopted in this work to improve the tracking performance of the nanopositioning stage. Different from most of the vibration control methods proposed in the literature which aimed only at improving the damping ratio, a state-feedback-based modal controller is designed in the inner-loop for improving both the damping ratio and the stiffness of the system. This task is realized by re-placing the resonant poles of the system to the optimized location. The outer-loop controller adopts the high-gain PI control for eliminating the tracking errors. More importantly, in order to realize the high-bandwidth and high-accuracy control, a numerical optimization method is proposed for simultaneously tuning the parameters of the controllers in inner and outer loops. The controller design is simple, and it can be applied to other systems with second or higher order in which the first resonant mode dominates the system dynamics.