Optimal Near-Minimum-Time Control Design for Flexible Structures

Amethod for generating a near-minimum-time control input for exible structures is presentedwith the objective of minimizing the maneuver time and the residual energy of the exible modes. The method is based on smoothing the bang–bang, time-optimal control input designed for the rigid-body mode. Smoothing is accomplished through the addition, to the basic time-optimal control problem for the rigid-body mode, of a constraint that limits the rst time derivative for the resulting control input. If the rst time-derivative constraint is replaced with the second time-derivative constraint, then smoother control input is generated. The necessary conditions of optimality for the resulting time-optimal control problem, with control and state constraints, are derived, which leads to forming a boundary-value problem. The resulting boundary-value problem is solved using the shooting method. The capability of this method is demonstrated through a numerical example in which the smooth control input is able to eliminate the residual energy of the exible modes at the expense of a slight increase in maneuver time. I