Coordinated feedforward and feedback control for fast repositioning of uncertain flexible systems

This paper presents a heterogeneous control approach that can facilitate fast repositioning of uncertain flexible systems with limited actuator capacity. By properly distributing the available actuator capacity, the proposed approach can coordinate a feedforward controller and a feedback controller within a robust model-following framework. The controllers are, respectively, derived from (M. Branch and A. Grace, 1996) a linear programming formula of time- and energy-optimal control and (P. Gahinet, et. al., 1995) a sub-optimal H²/μ dynamic synthesis. In particular, the second uniquely leads to a hybrid set of linear matrix inequalities, an algebraic Sylvester equation, and a matrix equation. Since the proposed approach can take advantage of aspects of both feedforward and feedback control, it is shown to facilitate as fast repositioning as the time-optimal control but with much less control energy usage.