Tracking control of a compliant XY nano-positioner under plant uncertainty using a transfigured loop-shaping H∞ controller

This paper presents tracking control of a compliant XY nano-positioner using a transfigured loop-shaping H∞ (TLSH) control strategy, which is capable of achieving satisfied positioning performance. The employed compliant nano-positioner is featured with a symmetric 4-PP (P represents prismatic joint) structure in which four-bar flexures are designed as the prismatic joints, meanwhile two embedded piezoelectric ceramic actuators (PZT) are adopted. Based on the identified plant transfer function of the nano-positioner, the presented control strategy and the traditional PID controller are implemented with different input scanning frequencies of 0.5 Hz and 2.5 Hz for comparisons. Both the simulation results and the practical experimental results demonstrate that the presented TLSH control method obviously performs better than the traditional PID method in the presence of plant model uncertainty, which will be applied to perform practical micromanipulation tasks.