Time-varying impulse shaping to reduce vibration of flexible systems

Abstract

When a flexible mechanical system moves, the motion excites the vibrational modes of the system. The performance of a precise system is limited by the vibration. In this study, time-varying impulse shaping method is presented to reduce the motion-induced vibration for time-varying mechanical systems in a feedforward way. Firstly, an approximation method is studied to compute decoupled modal responses in a linear time-varying structure. A stream of time-varying impulse sequence can be obtained by finding the modal responses vanished. Then, the reference inputs are shaped by being convoluted with the time-varying impulse sequence so that the multi-mode vibration is suppressed during and after a motion. This time-varying impulse shaping method is very robust to modeling error, and applicable to nonlinear multibody systems through linearization. An experimental two-link flexible manipulator system has been built and tested to demonstrate the effectiveness of this shaping method on the vibration suppression. The setup can perform a vertical planar motion, and exhibits time-varying modal properties due to its time-dependent configuration. Some experiments have been successfully conducted in showing the effectiveness and superiority of the proposed method. Consequently, it is believed that this time-varying impulse shaping method provides excellent vibration reduction in broader classes of flexible systems.