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 for accurate positioning and vibration suppression 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 frequency equation of the system is proposed as a feedforward controller to produce the desired responses. The feedback controller based on a robust internal-loop compensator is designed to meet the 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 stable and the vibration of the flexible beam is suppressed. The proposed algorithm is demonstrated experimentally on an XY positioning system which consists of a base cart, elastic beam and moving mass.