Adaptivity and Robustness in Automatic Control Systems

  • Ya. Z. Tsypkin
Part of the Progress in Systems and Control Theory book series (PSCT, volume 17)

Abstract

This paper deals with various approaches to the solution of control problems for dynamic plants under uncertainty conditions. It gives a description of the principles for designing discrete-time adaptive and robust control systems and presents a discussion of their properties and specificities. A broader range of possibilities is given by robustly nominal systems that incorporate, together with a feedback loop from the system output, also a feedback that depends on the bias between the system output and the output of a special nominal model.

Robustly nominal systems allow to eliminate or to diminish substantially the effect of input as well as parametric disturbances that are due to parameter fluctuations within the range of uncertainty.

The principles of constructing robustly nominal systems are described together with the conditions for their realization based on criteria for robust stability.

For improving the quality of such systems we use algorithms for identifying the bias between the system output and the nominal model rather than those of identifying the dynamic plant itself. This simplifies the system structure and broadens the range of applications of robustly nominal systems as compared with traditional adaptive systems.

Keywords

Turkey Doyle 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Goodwin G.C., Sin K.S. Adaptive filtering prediction and control. New Jersey: Prentice Hall, 1984.Google Scholar
  2. [2]
    Tsypkin Ya.Z., Aved’yan E.D. Discrete adaptive systems of deterministic plants control. Itogi Nauki i Techniki, Ser. Techn. Kibernetika. Moscow: VINITI, 1985, V. 18, pp. 45-78. (in Russian).Google Scholar
  3. [3]
    Aström K.J. Introduction to stochastic control theory. New York: Academic Press, 1970.Google Scholar
  4. [4]
    Tsypkin Ya.Z., Kelmans G.K. Discrete adaptive control systems. Itogi Nauki i Techniki, Ser. Techn. Kibernetika. Moscow: VINITI, 1984, V. 17, pp. 3-73. (in Russian).Google Scholar
  5. [5]
    Basar T. Theory of stochastic dynamic noncooperative games. Oxford: basil Blackwell, 1990.Google Scholar
  6. [6]
    Kuntsevitch V.M., Lychak M. Guaranteed estimates. Adaption and robustness in control systems. Lecture Notes in Control and Information Sciences. V. 169, Berlin: Springer Verlag, 1992.Google Scholar
  7. [7]
    Voronov A.A., Rutkovsky V.Y. State-of-the-art and prospects of adaptive systems Automatica. The Journal of IFAC. 1984, V. 20, N 5, pp.547-557.Google Scholar
  8. [8]
    Aström K.J., Wittenmark B. Adaptive control systems. Addison-Wesley, Reading, Mass., 1990.Google Scholar
  9. [9]
    Tsypkin Ya.Z. Adaptation and learning in automatic systems. New York: Academic Press, 1971.Google Scholar
  10. [10]
    Landau Y.D. Adaptive control. The model reference approach. New York: Marcel Dekker Inc., 1979.Google Scholar
  11. [11]
    Ortega R., Tang Y. Robustness of adaptive controllers — a survey. Automatica. 1989. V 25, N 5, pp. 651–677.CrossRefGoogle Scholar
  12. [12]
    Morari M., Zafiriorou E. Robust process control. New Jersey: Prentice Hall, 1989.Google Scholar
  13. [13]
    Basar T. Game theory and H∞-optimal control: the discrete-time case. Proceedings of the 1990 International Conference on New Trends in Communication Control and Signal Processing. Ankara, Turkey, July, 1990, pp.669–686, Elsevier.Google Scholar
  14. [14]
    Francis B.A. A course in H∞-control theory. Lecture Notes in Control and Information Sciences. V. 88, Berlin: Springer Verlag, 1987.Google Scholar
  15. [15]
    Francis B.A., Melton J.W., Zames G. H∞-optimal feedback controllers for linear multivariable systems. IEEE Trans. Autom. Control. 1984. V. 29, N 10, pp.888–899.CrossRefGoogle Scholar
  16. [16]
    Tsypkin Ya.Z. Sampling systems theory and its applications. Oxford: Pergamon Press, vol. 1,2, 1964.Google Scholar
  17. [17]
    Kuo B.C. Digital control systems. New York: Halt Rinehart and Winston Inc., 1980.Google Scholar
  18. [18]
    Volgin L.N. Optimal discrete control of dynamic systems. Moscow: Nauka, 1986. (in Russian).Google Scholar
  19. [19]
    Tsypkin Ya.Z. Frequency modality criteria of linear discrete systems. Automatica. 1990, N 3, pp. 3–7.Google Scholar
  20. [20]
    Tsypkin Ya.Z. Synthesis of optimal systems for non-minimum phase plants. International Journal of System Science. 1992, V. 23, N 2, pp. 291–296.CrossRefGoogle Scholar
  21. [21]
    Guerrieri J. Methods of introductions functional relations automatical on different analysers. Thesis MIT, 1932.Google Scholar
  22. [22]
    Shannon C. Mathematical theory of the differential analyzer. Journal of Mathematics and Physics. 1941, V. 20, N 4, pp. 337.Google Scholar
  23. [23]
    Kulebakin B.S. On behavior of constantly disturbed automatization linear systems. Doklady AN SSSR, V. 68, N 5, pp. 73–79.Google Scholar
  24. [24]
    Johnson C.D. Accomodation of external disturbances in linear regulator and servomechanism problems. IEEE Trans. Autom. Control. 1971. V. AC-16, N 6, pp. 635–644.CrossRefGoogle Scholar
  25. [25]
    Johnson C.D. Theory of disturbance-accomodating controllers. In “Advances in Control and Dynamic Systems”. CT. Leondes (ed.), V. 12, N 7, New York: Academic Press. 1976.Google Scholar
  26. [26]
    Davisson E.J. The output control at linear time invariant systems with unmeasurable arbitrary disturbances. IEEE Trans. Autom. Control. 1972. V. AC-17. N 5, pp. 621–630.CrossRefGoogle Scholar
  27. [27]
    Wonham W.M. Linear multivariable control: a geometric approach. Berlin: Springer Verlag, 1979.CrossRefGoogle Scholar
  28. [28]
    Francis B.A., Wonham W.M. THe internal model principle for linear multivariable regulators. Applied Mathematics and Optimization, 1975, V. 22, N 5, pp. 170–194.Google Scholar
  29. [29]
    Francis B.A., Wonham W.M. The internal model principle of control theory. Automatica, 1976, V. 12, N 5, pp. 457–465.CrossRefGoogle Scholar
  30. [30]
    Gonzalez D.R., Autsaklis P.J. Internal models in regulation, stabilizing and tracking. International Journal of Control, 1991, V. 53, N 2, pp. 411–430.CrossRefGoogle Scholar
  31. [31]
    Nikolskii V.A., Sevastjanov LP. K(E)-transformation of sampled functions in the problem of discrete systems research. Avtomatika i elektromekhanika. Moscow: Nauka, 1973, pp. 30–36. (in Russian).Google Scholar
  32. [32]
    Johnson C.D. Discrete-time disturbance accomodating control theory with applications to missile digital control. J. Guidance and Control. 1981, V. 4, N 2, pp. 116–125.CrossRefGoogle Scholar
  33. [33]
    Ulanov G.M. Dynamic accuracy and disturbances compensation in automatic control systems. Moscow: Mashinostroenie, 1971. (in Russian).Google Scholar
  34. [34]
    Tsypkin Ya.Z. Adaptive-invariant discrete control systems. In “Foundations of adaptive control”. Ed. P.V. Kokotovich. Lecture Notes in Control and Information Science. V. 160, Berlin: Springer Verlag, 1991. pp. 239–268.CrossRefGoogle Scholar
  35. [35]
    Zypkin Ja.S. (Tsypkin Ya.Z.) Grunlagen der informationellen Theorie der Identification. Berlin: VEB Verlag Technik, 1987.Google Scholar
  36. [36]
    Aström K.J., Wittenmark B. Computer controlled systems. Theory and design. New Jersey: Prentice Hall, 1984.Google Scholar
  37. [37]
    Anderson B.D.O., Bitmead R.R. et al. Stability of adaptive systems passivity and averaging analysis. Cambridge, Massachusetts, London: MIT Press, 1986.Google Scholar
  38. [38]
    Anderson B.D.O., Johnstone R.M. Adaptive systems and time varying plants. International Journal of Control. 1983. V. 37, N 4, pp. 367–377.CrossRefGoogle Scholar
  39. [39]
    Horowitz I.M. Synthesis of feedback systems. New York: Academic Press, 1963.Google Scholar
  40. [40]
    Francis B., Doyle J. Linear control theory with an H∞-optimality criterion. SIAM Journal of Control. 1987. V. 25, N4, pp. 815–844.CrossRefGoogle Scholar
  41. [41]
    McFarlane D.C., Glover K. Robust controller design using normalized coprime factor plant descriptions. Lecture Notes in Control and Information Sciences. V. 138, Berlin: Springer Verlag, 1990.Google Scholar
  42. [42]
    Kharitonov V.L. Asymptotic stability of systems family of differential equations. Differential Equations, 1978, V. 14, N 11, pp. 2086–2088. (in Russian).Google Scholar
  43. [43]
    Jury E.I. Robustness of discrete systems. A Survey. Avtomatika i telemekhanika, 1990, N 5, pp. 3–28.Google Scholar
  44. [44]
    Tsypkin Ya.Z., Polyak B.T. Frequency criterion of robust modality of linear discrete systems. Avtomatika, Kiev, 1990, N 3, pp. 3–9. (in Russian).Google Scholar
  45. [45]
    Polyak B.T., Tsypkin Ya.Z. Robust stability of discrete linear systems. Soviet Physics Doklady, 1991, V. 36(2), pp. 111–113.Google Scholar
  46. [46]
    Tsypkin Ya.Z. Robust adaptive control systems. Soviet Physics Doklady, 1990, V. 35, N 12, pp. 1013–1014.Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Ya. Z. Tsypkin

There are no affiliations available

Personalised recommendations