Controller reduction using optimal Hankel norm approximation with guaranteed closed-loop performance

Abstract

The present work deals with the problem of frequency weighted controller reduction using optimal Hankel norm approximation. The advanced controller designs methods like LQG/LTR or H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> based synthesis methods leads to controllers of order comparable to the plant and sometimes unstable controller whereas lower order controller should be sought out to keep the closed-loop stability and system performance within acceptable limit. For unstable controller reduction a controller decomposition algorithm is developed using two stage transformations. The algorithm discussed for computation of balancing transform is based on orthogonal transformation which circumvents the ill-conditioned cases due to numerical errors. Resulting closed-loop system with reduced order controller is guaranteed to preserve the dominant time domain and frequency domain characteristics.