MINIMUM-TIME CONTROL CHARACTERISTICS OF FLEXIBLE STRUCTURES

The time-optimal control for rest-to-rest maneuvers of flexible struct ures is considered, We formulate the general time-optimal control prob lem for single-axis flexible structures, and analytical results are gi ven for the number of control switches for the one-bending-mode case, with and without damping, When there is no damping, it is shown that t he time-optimal control generally has three switches and is an odd fun ction of time about the second switch except in certain isolated cases where there is only one switch. With damping, it is shown that there is always more than one switch. A numerical method is presented for so lving the time-optimal control for general linear systems, and solutio ns are presented for flexible structures with several flexible modes, revealing interesting trends of the time-optimal control switch times as the maneuver sizes and the frequencies and damping ratios of the fl exible modes are varied.