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2014 | Vol. 24, no. 4 | 499--513
Tytuł artykułu

Off-line robustification of Generalized Predictive Control for uncertain systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An off-line methodology was proposed for enhancing the robustness of an initial Generalized Predictive Control (GPC) by convex optimization of the Youla parameter. However, this procedure of robustification is restricted with the case of the systems affected only by unstructured uncertainties. This paper proposes an extension of this method to the systems subjected to both unstructured and structured polytopic uncertainties. The main idea consists in adding supplementary constraints to the optimization problem which validates the Lipatov stability condition at each vertex of the polytope. These polytopic uncertainties impose a set of non convex quadratic constraints. The globally optimal solution is found by means of the GloptiPoly3 software. Therefore, this robustification provides stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Finally, an illustrative example is given.
Wydawca

Rocznik
Strony
499--513
Opis fizyczny
Bibliogr. 16 poz., rys.
Twórcy
autor
  • Process Control Laboratory, Ecole Nationale Polytechnique, ENP, Algers, l_nezli@yahoo.fr
autor
  • Industrial Systems Laboratory, University of Sciences and Technology Houari Boumediene, Algiers, nbali@usthb.fr
Bibliografia
  • [1] P. Rodriguez and D. Dumur: Generalized Predictive Control robustification under frequency and time-domain constraints. IEEE Trans. on Control Systems Technology, 13(4), (2005), 577-587.
  • [2] D. Henrion, J. B. Lasserre and J. Löfberg: GloptiPoly 3: Moments, optimization and semidefinite programming. Optimization Methods and Software, 24(4), (2009), 761-779.
  • [3] D. W. Clarke, C. Mohtadi and P. S. Tuffs: Generalized Predictive Control. Part 1 and 2. Automatica, 23(2), (1987), 137-160.
  • [4] H. Demircioglu and D. W. Clarke: Generalised Predictive Control with endpoint state weighting. IEE Proceedings, Part D, 140(4), (1993), 275-282.
  • [5] B. Kouvaritakis, J. A. Rossiter and A. O. T. Chang: Stable Generalised Predictive Control: An algorithm with guaranteed stability. IEE Proceedings, Part D, 139(4), (1992), 349-362.
  • [6] J. R. Gossner, B. Kouvaritakis and J. A. Rossiter: Cautious stable predictive control: A guaranteed stable predictive control algorithm with low input activity and good robustness. Int. l J. of Control, 67(5), (1997), 675-697.
  • [7] K. Hrissagis, O. D. Crisalle and M. Sznaier: Robust design of unconstrained predictive controllers. American Control Conf., Seattle, Washington, (1995).
  • [8] R. A. J. De Vries and T. J. J. Van Den Boom: Constrained robust predictive control. European Control Conf., Rome, Italy, (1995).
  • [9] M. Morari and E. Zafiriou: Robust Process Control. Prentice Hall, Englewood Cliffs, N.J. 1989.
  • [10] M. V. Kothare, V. Balakrishnan and M. Morari: Robust constrained model predictive control using linear matrix in-equalities. Automatica, 32(10), (1996), 1361-1365.
  • [11] A. V. Lipatov and N. I. Sokolov: Some sufficient conditions for stability and instability of continuous linear stationary systems. Automation and Remote Control, 39(9), (1978), 1285-1291.
  • [12] K. Ogata: Discrete-time Control Systems. Prentice Hall, Englewood, Cliffs, USA, 1987.
  • [13] N. K. Bose: Properties of the Qn-matrix in bilinear transformation. Proc. IEEE, 71 (1983), 1110-1111.
  • [14] E. I. Jury: Inners and Stability of Dynamic Systems. Florida: Krieger, 1982, 242-252.
  • [15] D. Henrion and J. B. Lasserre: GloptiPoly: global optimization over polynomials with Matlab and SeDuMi. ACM Trans. on Mathematical Software, 29(2), (2003), 165-194.
  • [16] P. Boucher and D. Dumur: La Commande Prédictive. Collection Méthodes et pratiques de l’ingénieur, Editions Technip, Paris, 1996.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-35a22f0a-38b2-404f-8aa5-df5904fd4cd5
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