Abstract:

At the beginning of this paper, to avoid the potential ill conditioned balanced transformation, Schur methods for generalized singular perturbation approximation (GSPA) method and singular perturbation approximation(SPA) method are obtained, and the robustness of the algorithm is good. And then, compared with other methods, such as balanced truncation model reduction (BTMR) method and optimal Hankel norm approximation (Hankel) method, the Schur methods of GSPA and SPA are applied to controller reduction. The following results are obtained: Firstly, the magnitude of the model reduction error around the bandwidth frequency plays an important role in the controller reduction with consideration of the closed loop stability and performance. Secondly, appropriate selection of the parameter α in GSPA method may be very useful to solving some controller reduction problems.

Key words: generalized singular perturbation approximation, singular perturbation approximation, schurmethod, controller reduction