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 Ž rst time derivative for the resulting control input. If the Ž 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.