Abstract
An H ∞ based control system design procedure is developed. The basic idea is to produce a two degree of freedom controller in which the closed-loop portion is designed, via H ∞ methods similar to those of Kwakernaak, to be robust with respect to both disturbance rejection and insensitivity to parameter variations. The pre-compensator is designed, via vector-valued performance criteria methods, so as to cause the entire system to meet all the design criteria. The resulting design is close to optimal but not necessarily practically useful. Procedures to approximate the nearly optimal controller by lower order, practical controllers are also developed.
This design procedure is then used to design a pitch axis controller for a linearized model of the F − 14 aircraft. The resulting optimal controller as well as its more practical approximations are compared with two other designs, one an LQ based-design from Grumman and the other based on DELIGHT.Marylin.
Research supported in part by the SRC, Contract No. OIR-85-00108.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
G. Zames, “Feedback and Optimal Sensitivity: Model Reference Transformation, Multiplicative Seminorms, and Approximate Inverses,” IEEE Trans. Automatic Control, vol. 26, no.2, pp.301–320, April, 1981.
B.A. Francis and J.C. Doyle, “Linear Control Theory with an H ∞ Optimality Criterion,” SIAM J. Control and Optimization, vol.25, no.4, pp.815–844, July, 1987.
B.A. Francis, “A Course in H ∞ Control Theory,” Springer-Verlag, 1987.
H. Kwakernaak, “Minimax Frequency Domain Optimization of Multivariable Linear Feedback Systems,” IFAC 9th Triennial World Congress, Budapest, Hungary, pp.19–24, 1984.
H. Kwakernaak, “A Polynomial Approach to Minimax Frequency Domain Optimization of Feedback Systems,” Int. J. Control, vol.44, no.1, pp.117–156, 1986.
C.A. Desoer, R.W. Liu, J. Murry and R. Saeks, “Feedback System Design: The Fractional Representation Approach to Analysis and Synthesis,” IEEE Trans. Automatic Control, vol.25, no.3, pp.399–412, 1980.
J.S. Yang, Ph.D. Thesis, University of Maryland, College Park, 1987.
J.W. Helton, “Broadbanding: Gain Equalization Directly From Data,” IEEE Trans Circuits & Systems, vol.28, no.12, pp.1125–1137, 1981.
W.A. Wolovich, P. Antsaklis and H. Elliot, “On the Stability of Solutions to Minimal and Nonminimal Design Problems,” IEEE Trans. Automatic Control, vol.22, pp.88–94, Feb., 1977.
A.K. Packard and S.S. Sastry, “Solving Rational Matrix Equations in the State Space with Applications to Computer-Aided Control System Design,” Int. J. Control, vol.43, no.1, pp.65–90, 1986.
Brian D.O. Anderson and Yi Liu, “Controller Reduction: Concepts and Approaches,” Proceedings of American Control Conference, pp.1–9, 1987.
U.M. Al-Saggaf and G.F. Franklin, “On Model Reduction,” Proceedings of 25th Conference on Decision and Control, pp.1064–1069, Dec., 1986.
“User Data Package for Interim Cascade Program: CSCDEO.1,” Memorandum No. EG-FC-83-39, Oct., 1983, Grumman Aerospace Corporation.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Yang, JS., Levine, W.S. (1988). An H ∞ method for the design of linear time-invariant multivariable sampled-data control systems. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042205
Download citation
DOI: https://doi.org/10.1007/BFb0042205
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19237-4
Online ISBN: 978-3-540-39161-6
eBook Packages: Springer Book Archive