Minimum Move-Vibration Control for Flexible Structures

Abstract

In the rest-to-rest motion of a flexible structure with limited torque or force, it is sometimes important to control the vibrations during the move trajectory as well as at the final time. In order to achieve this control, the duration of the move must be set to be longer than the theoretical minimum time. In this paper, three definitions of trajectory vibration performance are given and a new method for input design is described, which is based on switched control. An analytical expression is obtained for the solution for lightly damped fourth-order systems, which enables a very efficient control implementation of approximately time-optimal moves. The switched control approach is generalized for presenting simplified approximate solutions for the tracking problem and other optimal control problems with singular arcs.