Minimum-time Control Characteristics of Flexible Structures

The time-optimal control of exible structures is considered. We formulate the general time-optimal control problem for single-axis exible 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 3 switches and is an odd function of time about the second switch except in certain isolated cases where there is only 1 switch. With damping, it is shown that there is always more than 1 switch. A numerical method is presented for solving the time-optimal control for general linear systems, and solutions are presented for exible structures with several exible modes, revealing interesting trends of the time-optimal control switch times as the maneuver sizes and the frequencies and damping ratios of the exible modes are varied.