“An Algorithm for Design of Decentralized Suboptimal Controllers with Specified Structure”
Authors: David Di Ruscio and Jens G. Balchen,Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 1990, Vol 11, No 3, pp. 155-167.
Keywords: Control system design, decentralized control, linear optimal control, optimization
Abstract: In this paper we present a method for the design of controllers with a specified arbitrary structure for linear multivariable time invariant systems. Both decentralized controllers as well as feedback from a reduced state vector can be designed by this method. The controller will become optimal in the sense that it yields a minimum of a quadratic cost criterion and suboptimal in the sense that it yields a higher value of this criterion than a controller without restrictions. The algorithm makes it possible to specify a stability margin on the feedback system. This means that the feedback system will have eigenvalues located to the left of a certain line (-alpha) in the complex plane. The unknown parameters of the controller are collected in a parameter vector. The algorithm is based upon a modified Newton-method for searching towards the ´optimal´ parameter vector. The algorithm ensures that the closed loop system is stable at any iteration in the case of an initially stable plant, and after the final iteration in the case of an initially unstable plant.
PDF (1552 Kb) DOI: 10.4173/mic.1990.3.3
DOI forward links to this article:
[1] D. Di Ruscio (1992), doi:10.1109/CDC.1992.371609 |
[1] ANDERSON, B.D.O. MOORE, J.B. (1971). Linear Optimal Control, Prentice-Hall.
[2] ANDERSON, B.D.O., BOSU, N.K. JURY, E.I. (1975). Output feedback stabilization and related problems - solution via decision methods, IEEE Trans. on Automatic Control, 20, 53-66 doi:10.1109/TAC.1975.1100846
[3] ANDERSON, B.D.O. SCOTT, R.W. (1977). Output feedback stabilization - solution by algebraic geometry methods, Proc. of the IEEE, 65, 849-861 doi:10.1109/PROC.1977.10581
[4] BALCHEN, J.G. MUMMÉ, K.I. (1988). Process Control; Structures and Applications, Van Nostrand Reinhold Company Inc., New York, Chap. 2.11, pp. 63-65.
[5] BRYSON, A.F. HO, Y.C. (1969). Applied Optimal Control, Blaisdell, New York.
[6] BARTELS, R.H. STEWART, G.W. (1972). A solution of the equation AX + XB = C, Commun. ACM, 15, 820-826 doi:10.1145/361573.361582
[7] CHEN, C.F. SHIEH, L.S. (1968). A note on expanding PA + BP= -Q, IEEE Trans. on Automatic Control, 122-123 doi:10.1109/TAC.1968.1098819
[8] DI RUSCIO, D. (1987). Dynamic models for a binary distillation column, Report 87-64-U, Division of Engineering Cybernetics. Norwegian Institute of Technology, N-7034 Trondheim.
[9] DI RUSCIO, D. (1988). Solution methods for the Liapunov matrix equation, Internal note, Division of Engineering Cybernetics. Norwegian Institute of Technology, N-7034 Trondheim.
[10] DOYLE, J.C., WALL, J.E. STEIN, G. (1982). Performance and robustness analysis for structured uncertainty, Proc. 21th IEEE Conf. Decision and Control, Orlando, Florida, 629-636.
[11] GEROMEL, J.C. BERNUSSOU, J. (1979). An algorithm for optimal decentralized regulation of linear quadratic interconnected systems, Automatica, 15, 489-491 doi:10.1016/0005-1098(79)90025-6
[12] GILL, P.E., MURRAG, W., SAUNDERS, M.A. WRIGHT, M.H. (1986). Users guide for NPSOL: A Fortran package for nonlinear programming, Technical report SOL 86-2. Department of Operational Research, Stanford University, Stanford, CA 94305.
[13] GLUB, G.H., NASH, S. VAN LOAN C. (1979). A Hessenberg Schur method for the problem AX + XB = C, IEEE Trans. on Automatic Control, 24, 909-913 doi:10.1109/TAC.1979.1102170
[14] KOSUT, R.L. (1970). Suboptimal control of linear time-invariant systems subject to control structure constraints, JACC, session 31-B.
[15] LEVINE, W.S. ATHANS, M. (1970). On the determination of the optimal constant output feedback gain for linear multivariable systems, IEEE Trans. on Automatic Control, 15, 44-48 doi:10.1109/TAC.1970.1099363
[16] SCHITTKOWSKI, K. (1984). NLPQL: A FORTRAN subroutine solving constrained nonlinear programming problems, Working paper, University of Stuttgart, Stuttgart.
[17] SOLHEIM, O.A. (1976). Optimal Control, Tapir. Norweigan Institute of Technology, N-7034 Trondhaim.
[18] VALDERHAUG, AA., DI RUSCIO, D. BALCHEN, J.G. (1990). Synthesis of Robust LQ controllers, 11th IFAC Word Congress, Tallin, Aug. 13-17 1990.
[19] WOLFE, M.A. (1978). Numerical Methods for Unconstrained Optimization, Van Nostrand Reinhold Company Ltd.
BibTeX:
@article{MIC-1990-3-3,
title={{An Algorithm for Design of Decentralized Suboptimal Controllers with Specified Structure}},
author={Di Ruscio, David and Balchen, Jens G.},
journal={Modeling, Identification and Control},
volume={11},
number={3},
pages={155--167},
year={1990},
doi={10.4173/mic.1990.3.3},
publisher={Norwegian Society of Automatic Control}
};