Multi-model approaches to robust control system design

  • J. Ackermann
Conference paper
First Online:
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 70)

Abstract

The problem of control system design is stated with explicit uncertainty bounds for physical parameters in the plant model and performance bounds as design objectives. A finite number of typical plant parameter values is used to define a multi-model problem. Two design methods for fixed-gain controllers for this problem are reviewed: i) the simultaneous assignment of the poles to a given region for all members of the plant family by parameter space methods, ii) the interactive Pareto-optimization of a vectorial performance index. The controller for the representative family of plant models may then be tested for continuous intervals of the parameter uncertainties. Only few results are available on stability of interval polynomials and matrices. Also the problem of a systematic choice of a feasible controller structure has not yet been solved. The interactive multi-model approaches will particularly profit from the progress in computer graphics.

Keywords

Plant Parameter Pole Assignment Simultaneous Stabilization Admissible Region Interval Matrice 
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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8. Literature

  1. [1]
    Christ, H., Darenberg, W., Panik, F., Weidemann, W.: Automatic track control of vehicles. 5th VSD and 2nd IUTAM Symposium, Vienna, Sept. 1977.Google Scholar
  2. [2]
    Darenberg, W., Gipser, M., Türk, S.: Probleme der robusten Regelung aus dem Bereich der Kraftfahrzeugforschung. Interkama Congress, Düsseldorf, Oct. 1983., Springer, Berlin 1983, 319–330.Google Scholar
  3. [3]
    Ackermann, J., Türk, S.: A common controller for a family of plant models. 21st IEEE Conference on Decision and Control, Orlando, Dec. 1982, 240–244.Google Scholar
  4. [4]
    Berger, R.L., Hess, J.R., Anderson, D.C.: Compatibility of maneuver load control and relaxed static stability applied to military aircraft. AFFDL-TR-73-33, 1973.Google Scholar
  5. [5]
    Franklin, S.N., Ackermann, J.: Robust flight control: a design example. AIAA Journal of Guidance and Control 1981, vol. 4, 597–605.Google Scholar
  6. [6]
    Gruebel, G., Joos, D., Kaesbauer, D., Hillgren, R.: Robust back-up stabilization for artificial-stability aircraft. 14th ICAS Congress, Toulouse, Sept. 84.Google Scholar
  7. [7]
    Horowitz, I.: Quantitative synthesis of uncertain multiple input-output feedback systems. Int. J. Control 1979, vol. 30, 81–106.Google Scholar
  8. [8]
    Kailath, T.: Linear systems. Englewood Cliffs, N.J.: Prentice Hall 1980.Google Scholar
  9. [9]
    Ackermann, J.: Der Entwurf linearer Regelungssysteme im Zustandsraum. Regelungstechnik 1972, vol. 20, 297–300.Google Scholar
  10. [10]
    Ackermann, J.: Parameter space design of robust control systems. IEEE Trans. Aut. Control 1980, vol. 25, 1058–1980.Google Scholar
  11. [11]
    Ackermann, J., Kaesbauer, D.: D-decomposition in the space of feedback gains for arbitrary pole regions. 8th IFAC Congress, Kyoto, Aug. 1981, vol. IV, 12–17.Google Scholar
  12. [12]
    Ackermann, J.: Abtastregelung. Berlin, Springer 1983. English version "Sampled-data control systems", to appear 1985.Google Scholar
  13. [13]
    Putz, P.: Algorithms for modeling and display of 2D and 3D projections of parameter space regions for siso control. Center of Interactive Computer Graphics, Rensselaer Polytechnic Institute, Troy, N.Y., Technical Report No. 84001.Google Scholar
  14. [14]
    Sondergeld, K.P.: A generalization of the Routh-Hurwitz stability criteria and an application to a problem in robust controller design. IEEE Trans. Aut. Control 1983, vol. 28, 965–970.Google Scholar
  15. [15]
    Kreisselmeier, G., Steinhauser, R.: Systematische Auslegung von Reglern durch Optimierung eines vektoriellen Gütekriteriums. Regelungstechnik 1979, vol. 27, 76–79.Google Scholar
  16. [16]
    Kreisselmeier, G., Steinhauser, R.: Application of vector performance optimization to a robust control loop design for a fighter aircraft. Int. J. Control 1983, vol. 37, 251–284.Google Scholar
  17. [17]
    Björnsson, B., Cuno, B., Handschin, E., Voss, J.: Auslegung robuster Regelsysteme in der elektrischen Energieversorgung. Interkama Congress, Düsseldorf, Oct. 1983, Springer, Berlin 1983, 308–318.Google Scholar
  18. [18]
    Steinhauser, R.: Reglerentwurf für einen Tieftemperatur-Windkanal mittels Gütevektor-Optimierung. Dissertation TU Karlsruhe 1984, and DFVLR-Forschungsbericht, to appear 1985.Google Scholar
  19. [19]
    Kharitonov, V.L.: Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differentsial'nye Uraveniya 1978, vol. 14, 2080–2088. English translation Plenum Publishing Corporation 1979, 1483–1485.Google Scholar
  20. [20]
    Barmish, B.R., Hollot, C.V.: Counter-example to a recent result on the stability of interval matrices by S. Bialas. Int. J. Control 1984, vol. 39, 1103–1104.Google Scholar
  21. [21]
    Kiendl, H.: Stabilitätsnachweis für den Multimodellansatz mit einem Kontinuum von möglichen Parameterwerten. Fifth GMR Workshop on Robust Control, Interlaken, Oct. 1984.Google Scholar
  22. [22]
    Zeheb, E., Hertz, D.: Robust control of the characteristic values of systems with possible parameter variations. Int. J. Control 1984, vol. 40, 81–96.Google Scholar
  23. [23]
    Saeks, R., Murray, J.: Fractional representation, algebraic geometry, and the simultaneous stabilization problem. IEEE Trans. Aut. Control 1982, vol. 27, 895–903.Google Scholar
  24. [24]
    Vidyasagar, M., Viswanadham, N.: Algebraic design techniques for reliable stabilization. IEEE Trans. Aut. Control 1982, vol. 27, 1085–1095.Google Scholar
  25. [25]
    Desoer, C.A., Lin, C.A.: Simultaneous stabilization of nonlinear systems. IEEE Trans. Aut. Control 1984, vol. 29, 455–457.Google Scholar
  26. [26]
    Olbrot, A.W.: A simple method of robust stabilization of linear uncertain systems. Proc. Conf. Measurement and Control, Athens, Sept. 1983.Google Scholar
  27. [27]
    Ackermann, J.: Simultaneous stabilization of two plant models. Proc. Pre-IFAC Meeting on Current Trends in Control, Dubrovnik-Cavtat, June 1984.Google Scholar
  28. [28]
    Ackermann, J.: Robustness against sensor failures. Automatica 1984, vol. 20, 31–38.Google Scholar
  29. [29]
    Kwakernaak, H.: Uncertainty models and the design of robust control systems. This volume.Google Scholar
  30. [30]
    Åström, K.J.: Adaptive control — a way to deal with uncertainty. This volume.Google Scholar
  31. [31]
    Tsypkin, Ya.: Optimality in adaptive control systems. This volume.Google Scholar
  32. [32]
    Gruebel, G.: Uncertanty and control — some activities at DFVLR. This volume.Google Scholar
  33. [33]
    Klickow, H.H., Franke, D.: Eigenwerteinschließung für kontinuierliche und diskrete Regelungen bei Berücksichtigung von Parameterstörungen. XIX Regelungstechnisches Kolloquium, Boppard, Feb. 1985.Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • J. Ackermann
    • 1
  1. 1.DFVLR-Institut für Dynamik der FlugsystemeOberpfaffenhofenFRG

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