Robust Input Shaping Control for Multi-Mode Flexible Structures

Input shaping provides an effective method for suppressing residual vibration of flexible structure systems. However, robustness is not possible without a time penalty. In this paper, a robust input shaping method is developed for suppressing residual vibration of multi-mode flexible structure systems with parameter uncertainties and external disturbances. The proposed scheme integrates both input shaping control and sliding mode output feedback control. The input shaper is designed for the reference model and implemented outside of the feedback loop to reduce the residual vibration. In the feedback loop, the SMOFC technique is employed to make the closed-loop system behave like the reference model with input shaper, where the residual vibration is suppressed. The selection of switching surface and the existence of sliding mode have been addressed. The knowledge of upper bound of uncertainties is not required. Furthermore, it is shown that increasing the robustness to parameter uncertainties does not lengthen the duration of the impulse sequence. Simulation results demonstrate the efficacy of the proposed control scheme.