Reference-dependent variable-gain control for a nano-positioning motion system*

In this paper, we develop a variable-gain (VG) control strategy that allows for a reference-dependent ‘bandwidth’ of the feedback controller. The proposed controller architecture can achieve improved performance given time-varying, reference-dependent performance requirements compared to linear time-invariant control, which suffers from design trade-offs between low-frequency tracking performance and sensitivity to higher-frequency disturbances. The VG controller consists of frequency-domain loop-shaped linear filters and a VG element. The gain of this element depends on reference information and determines the desired reference-dependent bandwidth of the resulting controller. We present data-based frequency-domain conditions to verify stability and convergence of the closed-loop system. The complete controller design process and the ability of the ‘bandwidth-on-demand’ controller to outperform linear time-invariant controllers are illustrated through experiments on an industrial nano-positioning motion system.