Vibration Reduction Using Near Time Optimal Commands for Systems With Nonzero Initial Conditions

Abstract

The control of flexible systems has been an active area of research for many years because of its importance to a wide range of applications. The majority of previous research on timeoptimal control has concentrated on the resttorest problem. However, there are many cases when flexible systems are not at rest or are subjected to disturbances. This paper presents an approach to design optimal vibrationreducing commands for systems with nonzero initial conditions. The problem is first formulated as an optimal control problem, and the optimal solution is shown to be bangbang. Once the structure of the optimal command is known, a parametric problem formulation is presented for the computation of the switching times. Solutions are experimentally verified using a portable bridge crane by moving the payload through a commanded motion while removing initial payload swing.