Brief Accuracy-enhancing methods for balancing-related frequency-weighted model and controller reduction

Authors:
Andras Varga;Brian D. O. Anderson
Affiliations:
German Aerospace Center, DLR-Oberpfaffenhofen, Institute of Robotics and Mechatronics, D-82234 Wessling, Germany;Research School of Information Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia
Venue:
Automatica (Journal of IFAC)
Year:
2003

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Abstract

We consider the solution of the balancing-related frequency-weighted model and controller reduction problems using accuracy enhanced numerical algorithms. We propose first new stability-enforcing choices of the frequency-weighted grammians which can guarantee the stability of reduced models for two-sided frequency weights. Then we show that for the frequency-weighted controller reduction problems with standard stability and performance-enforcing frequency weights the computation of the frequency-weighted grammians can be done by solving reduced order Lyapunov equations. For both frequency-weighted model and controller reduction problems we indicate how to compute the grammians directly in terms of their Cholesky factors. This allows the extension of the square-root and balancing-free accuracy-enhancing techniques to the frequency-weighted case.