Robust multiple frequency trajectory tracking control of piezoelectrically driven micro/nanopositioning systems

A novel modeling and control methodology is proposed in this paper for real-time compensation of nonlinearities along with precision trajectory control of piezoelectric actuators in various range of frequency operation. By integrating a modified Prandtl-lshlinskii hysteresis operator with a second-order linear dynamics, a nonlinear dynamic model and an inverse feedforward controller are developed and experimentally validated for a piezoelectrically driven nanopositioning stage. This modeling and control framework, however, lacks the accuracy due to the hysteresis model limitation, parametric uncertainties, and ever present unmodeled dynamics. Utilizing the sliding mode control strategy coupled with a perturbation estimation technique, a robust controller is then proposed for trajectory tracking of the actuator displacement. The controller gains are adjusted based on an intelligent comparison of the dynamic model and the control law. Eventually, the performance of the proposed controller is verified for the nanopositioning stage which is equipped with a high resolution capacitive position sensor. Experimental results demonstrate that the controller is capable of precisely tracking triangular and multiple frequency sinusoidal trajectories, which are common practices in many scanning probe microscopy systems.