Design of Two-degree-of-freedom H∞ Controller for Three-dimensional Piezo-positioning System

The piezo-positioning stage driven by piezoelectric (PZT) actuators has been widely used in the precision engineering field. In order to control three-dimensional piezo-positioning system with good robustness, high bandwidth and high resolution, a two-degree-of-freedom (2-DOF) H
_∞
control system is given. In this control system, a pre-and post-compensator was designed to shape desired singular values of positioning system. Based on this shaped plant, 2-DOF controller was constructed with a prefilter and a feedback controller, it can obtain desired dynamic performance and robustness. According to simulation results, by comparing with PID controller, the proposed controller obviously reduces the coupling effect, gives an improvement of bandwidth and resolution, and has better robustness. These indicate that the designed controller is effective and feasible.