Singular Perturbation Systems Based On Filter Decomposition H_ ¡Þ / H_ Control

Singularly perturbed system (SPS) is a class of system with two-time-scale. Usually, we decompose of the SPS into fast subsystem and slow subsystem in time domain. Actually, two-time-scale in time domain is corresponding to dual-frequency-scale in frequency domain, which includes low frequency and high frequency. In the difference limited frequency ranges, we will design controllers, such that satisfies performance respectively.Firstly, low pass filter and high pass filter are used to decompose the SPS into low frequency subsystem and the high frequency subsystem in this paper. The traditional rule of combination can not be used about the system on frequency domain. As a result, a new method of combination is introduced, and the simulation result is showed the feasibility of the method.Secondly, H∞/ H_ control for SPS is discussed. For general linear SPS, based on GKYP lemma, sufficient and necessary condition is derived about controller existence, which makes the closed-loop control system stable and satisfies the performance. The simulation results show the effectiveness and feasibility of this method.Finally, mixed sensitivity problem is studied using the H∞/ H_ method. Sub-controllers are designed for the dual-frequency subsystems respectively. The low frequency subsystem satisfies minimum sensitivity function and high frequency subsystem satisfies minimum complementary sensitivity function. Then sub-controllers are combined with the controller for the SPS. The simulations show effectiveness of this method.