Modeling and Control of a Piezoelectric-actuated Nano-positioner: An Hierarchical Composite Anti-disturbance Control Approach

This paper studies the anti-disturbance control for ultra-high precision positioning of a piezoelectric-actuator driven nano-positioner, subjects to nonlinear dynamics and various external disturbances. In this particular study, the multiple-disturbance is supposed to have two parts. One is the undesired vibration resonance, which could be described by an exogenous dynamical system. The other includes model uncertainties and external random disturbances, which can be considered to have bounded norms. The physical model of the nano-positioning stage is discussed and a composite control law is then presented, where disturbance-observer-based control (DOBC) is formulated for feedforward compensation of the vibrations. Then a composite controller consisting of DOBC and an H-infinity controller is developed to achieve the anti-disturbance performance. Finally, simulations and experiments on the nano-stage are deployed to demonstrate the anti-disturbance performance by combining DOBC with H-infinity control.