Robust H∞ control in nano-positioning

This study considers the use of robust H∞ tracking control in a nano-positioning system. The nano-positioning system uses a high-performance monolithic multilayer piezoelectric stack actuator connected in series with an external capacitor, which is used to provide a measured voltage proportional to the charge on the piezoelectric actuator. The electrical energy applied to the piezoelectric actuator is transferred to mechanical energy leading to nano-scale motion. The mechanical part of this system consists of a spring mass mechanical system and a capacitive sensor is used to measure the displacement. The design of the controller takes into account the existence of hysteresis in the piezoelectric actuator by representing it as a sector-bounded uncertainty. The parameters in a non-linear model of the system are obtained from experimental measurements on the system. Experimental results show that the robust H∞ controller yields accurate tracking of displacement and significantly reduces the hysteresis.