Robust controller design for PTP motion of vertical XY positioning systems with a flexible beam

This paper presents a point-to-point (PTP) motion control method to get accurate positioning and to suppress vibration of a vertical XY positioning system with a flexible beam. The proposed method is composed of a feedforward and feedback controller. The, input preshaping based on the analytic modeling and the frequency equation of the system is proposed as a feedforward controller to produce desired responses. The feedback controller based on a robust internal-loop compensator is designed to meet specified performance and to stabilize the whole system in the presence of uncertainties and disturbances. By integrating the input preshaping controller and feedback controller, it is shown that the system is controlled to be stable and the vibration of the flexible beam is suppressed. The proposed algorithm is demonstrated experimentally on a XY positioning system which consists, of a base cart, elastic beam, and moving mass.