Semidefinite Programming Techniques for Reduced Order Systems with Guaranteed Stability Margins

Authors:
Belinda B. King;Ekkehard W. Sachs
Affiliations:
Interdisciplinary Center of Applied Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA. bbking@math.orst.edu;Universität Trier, Fachbereich IV/Mathematik, 54286 Trier, Germany. sachs@uni-trier.de
Venue:
Computational Optimization and Applications
Year:
2000

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Abstract

In this paper, the compensator based reduced order control design framework of Burns and King (J. Vibrations and Control, vol. 4, pp. 297–323, 1998) is modified to yield low order systems with guaranteed stability margins. This result is achieved through use of a logarithmic barrier function. In addition, a reduced basis method is formulated in which the compensator equations are approximated on uneven grids; guaranteed stability margins are also included. The methods are tested numerically on a one dimensional, nonlinear, damped, hyperbolic structural control problem. Examples are provided to illustrate differences between systems designed by both reduced basis methods.