Position control with zero residual vibration for two degrees-of-freedom flexible systems based on motion trajectory optimization

Abstract

Zero residual vibration (RV) in the position control of a flexible system is difficult to achieve because this system has low stiffness and underactuated feature. In this paper, we present a position control strategy to achieve zero RV in the position control of two degrees-of-freedom (DOF) flexible systems. First, a general dynamic model for two-DOF flexible systems is established. Next, we transform the position control with zero RV to motion planning and tracking control. Based on the position control objective with zero RV, three constraints for the desired system trajectory are given. To make the desired system trajectory satisfy these three constraints, we propose a motion trajectory optimization method. Specifically, we plan a forward system trajectory and a reverse system trajectory based on bidirectional trajectory planning method. Then, the rewinding strategy and the trajectory optimization based on genetic algorithm are used to connect these two system trajectories and to obtain a complete desired system trajectory. Finally, a sliding mode tracking controller is designed to make the system track this desired system trajectory. In this way, the system can reach its target-rest-position with zero RV. The effectiveness and superiority of the proposed control strategy are demonstrated in simulations.