Settling Time Optimization of a Critically Damped System with Input Shaping for Vibration Suppression Control

Abstract

The input shaping technique is widely used as feedforward control for vibration suppression of flexible dynamic systems. The main disadvantage of the input shaping technique is the increasing system time response since the input shaper contains time delay parts. However, with the same reference input, the actuator effort in the case of using an input shaper is smaller than the one in the case without an input shaper. Thus, it is possible to decrease the system response time by designing the feedback controller to maximize the actuator effort. This paper proposes a design approach to design the Proportional-Derivative (PD) controller for position control of the actuator so that the settling time of the flexible system with input shaper is minimized. The actuator system with a PD controller is equivalent to a critically damped system, and the condition for the controller gains is established. In addition, the settling time and actuator effort with shaped step input are calculated. The controller gains can be determined by solving the settling time optimization problem with the actuator effort constraint. The effectiveness of the proposed approach is verified via experiments with an overhead crane model.