Gain scheduling control of a walking piezo actuator

Piezoelectric actuators are commonly used to drive high-precision stages. In this paper, a walking piezo actuator containing four piezoelectric legs is used to drive a high-precision nanomotion stage with constant velocity and point-to-point reference signals. The gain of the system is dependent on the momentary orientation of the piezo legs during the walking movement. The aim of this paper is to design a feedback controller that employs knowledge of the varying gain of the drive legs over one drive cycle. The gain variation is determined by a combination of local and global identification and modeling techniques. The excitation signal for the local frequency response function measurements at different positions of the legs in the drive cycle is designed to avoid stick--slip effects between the drive legs and the drive surface of the stage. Using the knowledge of the system variations, a linear parameter-varying model and a gain scheduling feedback controller are designed for the nanomotion stage. Experiments show that the designed gain scheduling controller reduces the tracking error and settling time compared to a robust ${cal H}_infty$ controller with a comparable closed-loop bandwidth up to 53% and 80%, respectively.