Optimal tracking control of nano-positioner in reciprocal state space framework

This paper introduces novel tracking control algorithms for step command utilizing state derivative output feedback and feedforward in reciprocal state space framework. Linear quadratic regulator (LQR) design of deviation system is used to find state derivative output feedback gain and two methods are developed to find feedforward gain to construct tracking controller in reciprocal state space framework. For the systems with state derivative sensors, applying the proposed algorithms, tracking control designs become straightforward while unnecessary integrations can be avoid to reduce implementation cost. Simulations of a nano-positioner with micro-accelerometer as sensor have been successfully carried out to verify the proposed algorithms. From the simulation results, we find that although the design is based on step response shaping, it also gives good time responses for time varying reference commands such as sine wave and square wave.