An H∞ optimization-based high-gain loop-shaping method for precision motion control of nano-positioning systems

Abstract

In this paper, an enhanced high-gain loop-shaping (E-HGLS) method is proposed based on the H_∞ optimization design scheme for precision motion control of nano-positioning systems. In the conventional HGLS method, a simple first-order low-pass filter is chosen to generate high control gain due to its simple structure. To improve the performance of the HGLS method, a more sophisticated filter is designed using H_∞ based optimization method to provide higher gains across a broader frequency range which can enhance the robust stability, tracking accuracy and disturbance rejection capability. To verify the superiority of the proposed E-HGLS method, comparative experiments are conducted on a nano-positioning system. Experimental results demonstrate that both the maximum tracking error and the root-mean-squared tracking error are reduced significantly as compared with the conventional HGLS method and the proportional-integral controller with the same phase margin. In particular, the maximum tracking error is reduced from 138.8 nm to 64.4 nm as compared with the conventional HGLS method when tracking a 10 Hz sinusoidal trajectory. The E-HGLS method is promising to improve the control performance of high-precision motion systems for nano-positioning applications.