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A method to stabilize linear systems using eigenvalue gradient informationFormal optimization methods and eigenvalue gradient information are used to develop a stabilizing control law for a closed loop linear system that is initially unstable. The method was originally formulated by using direct, constrained optimization methods with the constraints being the real parts of the eigenvalues. However, because of problems in trying to achieve stabilizing control laws, the problem was reformulated to be solved differently. The method described uses the Davidon-Fletcher-Powell minimization technique to solve an indirect, constrained minimization problem in which the performance index is the Kreisselmeier-Steinhauser function of the real parts of all the eigenvalues. The method is applied successfully to solve two different problems: the determination of a fourth-order control law stabilizes a single-input single-output active flutter suppression system and the determination of a second-order control law for a multi-input multi-output lateral-directional flight control system. Various sets of design variables and initial starting points were chosen to show the robustness of the method.
Document ID
19860004477
Acquisition Source
Legacy CDMS
Document Type
Technical Publication (TP)
Authors
Wieseman, C. D. (NASA Langley Research Center Hampton, VA, United States)
Date Acquired
September 5, 2013
Publication Date
November 1, 1985
Subject Category
Cybernetics
Report/Patent Number
L-15964
NASA-TP-2479
NAS 1.60:2479
Accession Number
86N13946
Funding Number(s)
PROJECT: RTOP 505-33-43-13
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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