Robust H Infinity Control of Piezoelectric Actuators in Nano-positioning and Atomic Force Microscopy

The aim of this thesis is to show how the robust H infinity control method can be applied to fast tracking position control problems in nano-positioning and atomic force microscopy. The key component used in the nano-positioning system and atomic force microscope positioning system is a piezoelectric actuator which makes motion control at the sub-nanometer level possible. A significant challenging issue in the use of piezoelectric actuators is the existence of hysteresis nonlinearity which limits the accuracy of position control. This research involves designing three robust H infinity tracking controllers for three different systems: controlling hysteresis nonlinearity in a piezoelectric stack actuator using a charge output, controlling displacement tracking in a nano-positioning system, and improving fast tracking in a position control problem for an atomic force microscope (AFM). The approach considered in this research is to utilize H infinity control theory to control piezoelectric actuator systems with hysteresis nonlinearity. These robust H infinity controllers were designed based on physical models for these three systems considering both mechanical and electrical sides separately. The parameters used in the nonlinear models were obtained from experimental measurements. Experimental results showed that the robust H infinity controller yields highly accurate tracking of displacement and also significantly reduces the nonlinear hysteresis. Each robust H infinity controller was implemented in a dSpace DSP system. The experimental results obtained using the robust H infinity controllers have been analysed and discussed in this thesis. This research has provided good evidence to demonstrate that high levels of accuracy in tracking displacement can be achieved by using the robust H infinity control method in nano-positioning systems