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Definition d'une methodologie de conception assistee d'asservissements non lineaires continus par l'utilisation de techniques d'agregation par normes vectorielles

  • Dominique Meizel
  • Jean-Claude Gentina
Session 5 Stability II
  • 120 Downloads
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 62)

Abstract

We propose to derive a control-system-design-methodology valuable for non-linear continuous-time processes from a stability-analysis-technique based upon the use of vectorial norms [2] [3]. The design problem is considered from the stability viewpoint and the design methodology is parameter-optimization. A major-difficulty in nonlinear system-stability studies lies in the handling of sufficient stability conditions that can be very conservative with respect to the intrinsic stability properties of the system. A key-point of the proposed method consists in the definition of a scalar criterion the negativity of which implies asymptotic stability of the studied control system. The design-method is thus achieved by minimizing the value of this criterion. The arguments of the stability-criterion consists of both the adjustable parameters and a representation basis in the state-space. The values of former arguments are the real synthesis-objective whereas the latter ones are artificial and are used in order to obtain the least conservative stability conditions as possible with respect to the choosen stability-analysis-theorem [2]. The minimization of the criterion can be helped by the computation of a steepest-descent direction deduced from the simple-eigen-values sensitivity theory. We propose then to implement this design-methodology by the use of a special class of state-space representations of the studied systems. A numerical example illustrates this last design-method.

Keywords

Sufficient Stability Condition Nous Proposons Science Physique Single Output System Nous Permet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliographie

  1. [1]
    BORNE P. 1976 "Contribution à l'étude des systèmes discrets non linéaires de grande dimension. Application aux systèmes interconnectés" Thèse de Doctorat ès Sciences Physiques, no 346, Université de Lille I, Villeneuve d'Ascq (France).Google Scholar
  2. [2]
    GENTINA J.C., BORNE P., BURGAT C., BERNUSSOU J., GRUJIĆ Lj.T. 1979 "Sur la stabilité des systèmes de grande dimension. Normes vectorielles" RAIRO, Vol. 13, no 1.Google Scholar
  3. [3]
    GRUJIĆ Lj.T., GENTINA J.C., BORNE P. 1976 "General aggregation of large scale systems by vector-Lyapunov functions and vector norms" Int. J. of Control, Vol. 24, no 4.Google Scholar
  4. [4]
    GENTINA J.C. 1976 "Contribution à l'analyse et à la synthèse des systèmes continus non linéaires de grande dimension" Thèse de Doctorat ès Sciences Physiques, no 347, Université de Lille I, Villeneuve d'Ascq (France).Google Scholar
  5. [5]
    GUARDABASI G., LOCATELLI A., MAFFEZZONI C., SCHIAVONI N. 1982 "A parameter optimization approach to the computer aided design of structurally constrained multivariable regulators" Congrès IASTED "Modelling, Identification, Control & Robotics", Davos (Suisse).Google Scholar
  6. [6]
    HÖFLER A.B. "A software segmentation technique with high control structure flexibility for optimization by gradients" 8ème Congrès IFAC Mondial Triennal, Kyoto, pp. 1611–1616.Google Scholar
  7. [7]
    SIRISENA H.R., CHOI S.S. 1975 "Pole placement in prescribed regions of the complex plane using output feedback" IEEE Trans. on A.C., Vol. 1C-20, pp. 810–812.Google Scholar
  8. [8]
    GANTMACHER F.R. 1966 "Théorie des matrices" Tome 2, Dunod, Paris.Google Scholar
  9. [9]
    DEIF A.S. 1982 "Advanced matrix theory for scientists and engineers" Abacus Press, Halsted Press.Google Scholar
  10. [10]
    MEIZEL D., GENTINA J.C. 1979 "New aspects on linear single-input single output systems" Int. J. Control, Vol. 30, no 6, pp. 1043–1060.Google Scholar
  11. [11]
    MEIZEL D., GENTINA J.C., DAUPHIN-TANGUY G. 1982 "A parameter optimization design method of robust controllers for large scale non linear processes" IEEE Int. Large Scale System Symposium, Virginia Beach (U. S. A.), pp. 343–348.Google Scholar
  12. [12]
    LECOUTURIER J., DUPUY M. 1971 "Centrale de Loire/Rhône Tranche 3, identification des installations de température et de pression du générateur de vapeur" E. D. F. — D. E. R., Dept Automatique et Moyens de Production, Rapport AMP 84.Google Scholar
  13. [13]
    FADEEV D.K., FADEEVA V.N. 1963 "Computational methods of linear algebra" Freeman, San Francisco.Google Scholar
  14. [14]
    DAVISON A.J., ÖZGÜNER U. 1982 "Synthesis of the decentralized robust servomechanism problem using local models" IEEE Trans. on A.C., Vol. AC-27, pp. 583–599.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Dominique Meizel
    • 1
  • Jean-Claude Gentina
    • 1
  1. 1.Laboratoire d'Automatique et d'Informatique IndustrielleInstitut Industriel du Nord (I. D. N.)Villeneuve D'Ascq CedexFrance

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