Periodic structure controller design

The authors demonstrate via averaging theory an approach whereby any stable linear system can be approximated by a simple periodic-structure system. The control of continuous-time, linear, time-invariant plants via a periodic structure control scheme is proposed. It is established that for continuous-time minimal plants it is possible to design periodic-structure stabilizing first-order controllers which asymptotically approach the performance of an n th-order stabilizing time-invariant controller, such as an optimal (LQG) controller, in the limit as the switching rate increases. The proposed controllers suffer only a small loss of performance compared with the nth-order controller, are attractive from a computational point of view, and may be implemented in either discrete or continuous time. The question of achieving a low-order robust variable-structure controller for a high-order uncertain plant is addressed. Simulation results are shown which demonstrate the efficacy of the periodic structures proposed