Abstract
In this paper a new design procedure is proposed that combines linear quadratic optimal control (LQ) with pole assignment. In LQ-problems the quadratic weights are usually found by trial and error to get good time behavior. In contrast the proposed method modifies a given state weighting matrix such that all closed-loop poles are located in a specified region of the complex s-plane. It is shown that this can be done with the smallest possible increase of the quadratic performance index under consideration. The procedure is extended to the design of robust control systems where the plant is described by a family of linear systems according to different operational conditions. The control of a F4E aircraft demonstrates the achievements of the new procedure.
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References
H. Kwakernaak; R. Sivan, Linear Optimal Control Systems, New York, Wiley Interscience, 1972.
B.D.O. Anderson; J.B. Moore, Linear Optimal Control, Prentice Hall Inc., 1971.
R.E. Kalman, ‘When is a Linear Control System Optimal?’ J. Basic Eng., Vol. 86, 1964.
M.G. Safonov; M. Athâns, ‘Gain and Phase Margin for Multiloop LQR Regulators’, IEEE Trans. Autom. Contr. Vol. AC-22, 1977.
H. Kobayashi; E. Shimemura, ‘Some Propertis of optimal Regulators and their Applications’, Int. J. Contr., 1981.
J. Ackermann, ‘Entwurf durch Polvorgabe’, Regelungstechnik 25, 1977.
D. Graupe, ‘Derivation of Weighting Matrices Towards Satisfying Eigenvalue Requirements’, Int. J. Contr., Vo1, 16, 1972.
N. Kawasaki; E. Shimemura, ‘A Method of Deciding Weighting Matri-ces in an LQ-problem to Locate all Poles in the Specified Region’, Proc. of the 8th IFAC WorldCongress, Kyoto, 1981.
F. Heger, Entwurf robuster Regelungen für Strecken mit großen Parametervariationen, Ph.D. Thesis, University Duisburg, 1983.
O.A. Solheim, ‘Design of Optimal Control Systems with Prescribed Eigenvalues’, Int. J. Contr., Vol. 15, 1972.
K. Heym, ‘The Influence of Weghting—Matrices on the Optimal Regulator’, Proc. of the 2nd IFAC-Symp. on “MultivariableTechnical Control Systems”. Düsseldorf, 1971.
K.P. Sondergeld, ‘A Collection of Plant Models and Design Specifications for Robust Control’, DFVLR Institute for Flight System Dynamics, Oberpfaffenhofen, 1982.
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© 1984 D. Reidel Publishing Company, Dordrecht, Holland
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Heger, F., Frank, P.M. (1984). Linear Quadratic Regulators with Prescribed Eigenvalues for a Family of Linear Systems. In: Tzafestas, S.G. (eds) Multivariable Control. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6478-5_15
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DOI: https://doi.org/10.1007/978-94-009-6478-5_15
Publisher Name: Springer, Dordrecht
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