Efficient modal control for vibration suppression of a flexible parallel manipulator

To achieve high speed and high acceleration, flexible planar parallel manipulators (PPM) are typically designed with lightweight linkages, but hence suffer from unwanted structural vibration, diminishing positioning accuracy. This paper addresses the dynamic modeling and efficient modal control for vibration suppression of a PPM with three flexible linkages actuated by linear ultrasonic motors (LUSM). To achieve active vibration control, multiple lead zirconate titanate (PZT) transducers are mounted on the flexible links as vibration sensors and actuators. Based on Lagrange's equations, the dynamic model of the flexible links is derived with the dynamics of PZT actuators incorporated. Using the assumed mode method, the elastic motion of the flexible links are discretized under the assumptions of pinned-free boundary conditions, and the assumed mode shapes are validated through experimental modal test. Efficient modal control, in which the feedback forces in different modes are determined according to the vibration amplitude or energy of their own, is employed to control the PZT actuators to realize active vibration suppression. Computer simulations and vibration control experiments are conducted, and the results demonstrate that the presented dynamic model and the proposed active vibration control strategy are effective.