×

Design of predictive LQ controller. (English) Zbl 1274.93089

Summary: A single variable controller is developed in the predictive control framework based upon minimization of the LQ criterion with infinite output and control horizons. The infinite version of the predictive cost function results in better stability properties of the controller and still enables to incorporate constraints into the control design. The constrained controller consists of two parts: time-invariant nominal LQ controller and time-variant part given by the Youla-Kučera parametrization of all stabilizing controllers.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93B51 Design techniques (robust design, computer-aided design, etc.)
93C55 Discrete-time control/observation systems
49N10 Linear-quadratic optimal control problems
PDFBibTeX XMLCite
Full Text: Link

References:

[1] Clarke D. W., Mohtadi, C., Tuffs P. S.: Generalized predictive control. Part I. The basic algorithm. Automatica 23 (1987), 2, 137-148 · Zbl 0621.93033 · doi:10.1016/0005-1098(87)90088-4
[2] Clarke D. W., Mohtadi, C., Tuffs P. S.: Generalized predictive control. Part II: Extensions and interpretations. Automatica 23 (1987), 2, 149-160 · Zbl 0621.93033 · doi:10.1016/0005-1098(87)90088-4
[3] Clarke D. W., Scattolini R.: Constrained receding-horizon predictive control. IEE Proc. D 138 (1991), 4, 347-354 · Zbl 0743.93063 · doi:10.1049/ip-d.1991.0047
[4] Fikar M., Engell S.: Receding horizon predictive control based upon Youla - Kučera parametrization. European J. Control 3 (1997), 4, 304-316 · Zbl 0895.93019 · doi:10.1016/S0947-3580(97)70088-8
[5] Horn R. A., Johnson C. R.: Matrix Analysis. Cambridge University Press 1985 · Zbl 0801.15001
[6] Hunt K. J., Šebek M.: Implied polynomial matrix equations in multivariable stochastic optimal control. Automatica 27 (1991), 2, 395-398 · Zbl 0729.93083 · doi:10.1016/0005-1098(91)90088-J
[7] Kučera V.: Discrete Linear Control: The Polynomial Equation Approach. Wiley, Chichester 1979 · Zbl 0432.93001
[8] Kučera V.: Analysis and Design of Discrete Linear Control Systems. Prentice Hall, Englewood Cliffs, N. J. 1991 · Zbl 0762.93060
[9] McIntosh A. R., Shah S. L., Fisher D. G.: Analysis and tuning of adaptive generalized predictive control. Canad. J. Chem. Engrg. 69 (1991), 97-110 · doi:10.1002/cjce.5450690112
[10] Middleton R., Goodwin G. C.: Digital Control and Estimation. A Unified Approach. Prentice Hall, Englewood Cliffs, N. J. 1990 · Zbl 0754.93053
[11] Mosca E., Zhang J.: Stable redesign of predictive control. Automatica 28 (1992), 1229-1233 · Zbl 0775.93056 · doi:10.1016/0005-1098(92)90065-N
[12] Rawlings J. B., Muske K. R.: The stability of constrained receding horizon control. IEEE Trans. Automat. Control 38 (1993), 10, 1512-1516 · Zbl 0790.93019 · doi:10.1109/9.241565
[13] Rossiter J. A., Gossner J. R., Kouvaritakis B.: Infinite horizon stable predictive control. IEEE Trans. Automat. Control 41 (1996), 10, 1522-1527 · Zbl 0863.93037 · doi:10.1109/9.539437
[14] Rossiter J. A., Kouvaritakis B.: Constrained stable generalised predictive control. IEE Proc. D 140 (1993), 4, 243-254 · Zbl 0786.93005 · doi:10.1049/ip-d.1993.0033
[15] Rossiter J. A., Kouvaritakis, B., Gossner J. R.: Feasibility and stability results for constrained stable predictive control. Automatica 31 (1995), 3, 863-877 · Zbl 0830.93067 · doi:10.1016/0005-1098(94)00166-G
[16] Scokaert P. O. M., Clarke D. W.: Stabilizing properties of constrained predictive control. IEE Proc. - Control Theory Appl. 141 (1994), 5, 295-304 · Zbl 0925.93555 · doi:10.1049/ip-cta:19941361
[17] Scokaert P. O. M., Rawlings J. B.: Infinite horizon linear quadratic control with constraints. 13th Triennal World Congress IFAC, San Francisco 1996, Volume M, pp. 109-114
[18] Šebek M.: Direct polynomial approach to discrete-time stochastic tracking. Problems Control Inform. Theory 12 (1983), 293-302 · Zbl 0517.93067
[19] Zafiriou E., Chiou H. W.: On the dynamic resiliency of constrained processes. Comput. Chem. Engrg. 20 (1996), 4, 347-355 · doi:10.1016/0098-1354(95)00038-0
[20] Zheng A., Morari M.: Stability of model predictive control with mixed constraints. IEEE Trans. Automat. Control 40 (1995), 10, 1818-1823 · Zbl 0846.93075 · doi:10.1109/9.467664
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.