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Minimum-time control characteristics of flexible structures

The time-optimal control for rest-to-rest maneuvers of flexible structures is considered. We formulate the general time-optimal control problem for single-axis flexible structures, and analytical results are given 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 the time-optimal control generally has three switches and is an odd function 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 solving the time-optimal control for general linear systems, and solutions 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 flexible modes are varied.