High-bandwidth control design for a piezoelectric nanopositioning stage

To achieve fast and accurate tracking of a wideband reference trajectory, the piezoelectric (PZT) actuator requires a high-bandwidth control system, which is however restricted by the resonant mode of the PZT positioning stage. In this paper, we study two resonant compensation techniques to damp the resonant mode for increased servo bandwidth. First, we present a feedback control system using a conventional notch filter (NF). Subsequently, we develop a complex lead compensator (CLC) using the phase-stabilized compensation method. Unlike the NF that is aimed at reducing the resonant peak gain, the CLC specializes in shaping the phase of open-loop system at the resonant frequency. The analysis shows that the closed-loop bandwidth achieved by the CLC is around four times higher than that of the NF without sacrificing the stability margin. Finally, we propose a multi-resonant filter (MRF) to suppress periodic tracking errors by significantly attenuating the gains at specified frequencies in the sensitivity function. The experimental results verify that the CLC is superior in disturbance compensation and periodic trajectory tracking as compared to the NF, and the add-on MRF can greatly reduce the tracking error.