Simulations and experimental investigations on residual vibration suppression of electromagnetically actuated structures using command shaping methods

The energy-based nonlinear command shaper developed by the authors has been used in this paper to suppress the motion-induced vibration of an electromagnetically actuated flexible structure. Both finite element dynamic simulation and experimental investigation are performed and demonstrated. The results indicate that the performance of the energy-based nonlinear shapers is much superior to that of the traditional linear design such as zero-vibration and zero-vibration-and derivative shapers. However, based on the result of the finite element simulation and its equivalent lumped modeling, it can also be found that the existence of higher order modes would involve the energy interactions which result in slight residual vibration in steady state and cause the sensitivity curves to be slightly deviated from that of their single degree-of-freedom model. Nevertheless, the performance is still acceptable for real applications. Using the concept of system analogy and dimensional analysis, the conclusions obtained from this study would be naturally applicable to electrostatically actuated MEMS structures.