INPUT-SHAPING FOR VIBRATION REDUCTION: AN OPTIMIZATION FORMULATION

Abstract It is well known that flexible structures exhibit vibratory behavior. In this article, a method of preshaping the input to such structures for the suppression of residual vibration is presented. This problem is formulated as an optimization problem that seeks to minimize the time taken for a point-to-point motion. Suitable constraints are imposed to produce zero residual vibration. The formulation allows for easy specification of constraints on the system such as controller saturation and others. In addition, conditions which reduce the sensitivity of the solution with respect to variations in system parameters are included. The robustness of the system performance is verified through simulation results. The results show that the proposed method can cancel the residual vibrations effectively while minimizing the time taken for travel subject to system constraints such as limits of actuators.