Toosi Univ. of Tech
In this paper, a minimum and near-minimum time optimal control laws are developed and compared for a rigid space platform with flexible links during an orientating maneuver with large angle of rotation. The control commands are considered as typical bang-bang with multiple symmetrical switches, the time optimal control solution for the rigid-body mode is obtained as a bang-bang function and applied to the flexible system after smoothening the control inputs to avoid stimulation of the flexible modes. This will also reflect practical limitations in exerting bang-bang actuator forces/torques, due to delays and non-zero time constants of existing actuation elements. The smoothness of the input command is obtained by reshaping its profile based on consideration of additional derivative constraints. the optimal control problem is converted into parameter optimization problem. The steps of the solution procedure and numerical algorithm to obtain the time optimal control input are discussed next. The developed control law is applied on a given satellite during a slewing maneuver, and the simulation results show that the control input with just few switching times can significantly lessen the vibrating motion of the flexible appendage, which reveals the merits of the developed control law. the modified realistic optimal input compared to the bang-bang solution goes well with the practical limitations and also alleviates the vibrating motion of the flexible appendage, which reveals the merits of the new developed control law.