Sensitivity and Robustness with Constant Controllers

  • Rolf Isermann

Abstract

The preceding controller design methods assumed that the process model is exactly known. However, this is never the case in practice. In theoretical modelling as well as in experimental identification one must always take into account both the small and often the large differences between the derived process model and the real process behaviour. If, for simplicity, it is assumed that the structure and the order of the process model are chosen exactly then these differences are manifested as parameter errors. Moreover, during most cases of normal operation, changes of process behaviour arise for example through changes of the operating point (the load) or changes of the energy- mass- or momentum storages or flows. When designing controllers one must therefore assume
  • the assumed process model is inexact;

  • the process behaviour changes with time during operation.

Keywords

Steam Settling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 10.1
    Horowitz, I.M.: Synthesis of feedback systems. New York: Academic Press 1963MATHGoogle Scholar
  2. 10.2
    Kreindler, E.: Closed-loop sensitivity reduction of linear optimal control systems. IEEE Trans. AC 13 (1968) 254–262CrossRefGoogle Scholar
  3. 10.3
    Perkins, W.R.; Cruz, J.B.: Engineering of dynamic systems. New York: Wiley 1969Google Scholar
  4. 10.4
    nd IFAC-Symp on System Sensitivity and Adaptivity, Dubrovnik (1968). Preprints Yugoslav Committee for Electronics and Automation (ETAN ), Belgrad/JugoslawienGoogle Scholar
  5. 10.5
    rd IFAC-Symp. on Sensitivity, Adaptivity and Optimality, Ischia (1973). Proceedings instrument Soc. of America (ISA), Pittsburgh.Google Scholar
  6. 10.6
    Tomovic, R.; Vucobratovic, M.: General sensitivity theory. New York: Elsevier 1972MATHGoogle Scholar
  7. 10.7
    Frank, P.M.: Empfindlichkeitsanalyse dynamischer Systeme. München: Oldenbourg 1976MATHGoogle Scholar
  8. 10.8
    Anderson, B.D.O.; Moore, J.B.: Linear optimal control. Englewood Cliffs, N.J.: Prentice Hall 1971MATHGoogle Scholar
  9. 10.9
    Cruz, J.B.: System sensitivity analysis. Stroudsburg: Dowen, Hutchinson and Ross 1973Google Scholar
  10. 10.10
    Andreev, Y.N.: Algebraic methods of state space in linear object control theory. Autom. and Remote Control 39 (1978) 305–342Google Scholar
  11. 10.11
    Frank, P.M.: The present state and trends using sensitivity analysis and synthesis in linear optimal control. Acta polytechnica, Prâce CVUT v Praze, Vedeekâ Konference 1982Google Scholar
  12. 10.12
    Kreindler, E: On minimization of trajectory sensitivity. Int. J. Control 8 (1968) 89–96CrossRefGoogle Scholar
  13. 10.13
    Elmetwelly, M.M.; Rao, N.D.: Design of low sensitivity optimal regulators for synchroneous machines. Int. J. Control 19 (1974) 593–607CrossRefGoogle Scholar
  14. 10.14
    Byrne, P.C.; Burke, M.: Optimization with trajectory sensitivity considerations. IEEE Trans. Autom. Control 21 (1976) 282–283MATHCrossRefGoogle Scholar
  15. 10.15
    Rillings, J.H.; Roy, R.J.: Analog sensitivity design of Saturn V launch vehicle. IEEE Trans. AC 15 (1970) 437–442CrossRefGoogle Scholar
  16. 10.16
    Graupe, D.: Optimal linear control subject to sensitivity constraints. IEEE Trans. AC 19 (1974) 593–594MathSciNetMATHCrossRefGoogle Scholar
  17. 10.17
    Subbayyan, R.; Sarma, V.V.S.; Vaithiluigam, M.C.: An approach for sensitivity reduced design of linear regulators. Int. J. Control 9 (1978) 65–74MATHGoogle Scholar
  18. 10.18
    Krishnan, K.R.; Brzezowski, S.: Design of robust linear regulator with prescribed trajectory insensitivity to parameter variations. IEEE Trans. AC 23 (1978) 474–478MATHCrossRefGoogle Scholar
  19. 10.19
    Verde, C.; Frank, P.M.: A design procedure for robust linear suboptimal regulators with preassigned trajectory insensitivity. CDC-Conference, Florida 1982Google Scholar
  20. 10.20
    Verde, M.C.: Empfindlichkeitsreduktion bei linearen optimalen Regelungen. Diss. GH Duisburg 1983Google Scholar
  21. 10.
    Kalman, R.E.: When is a linear system optimal? Trans. ASME, J. Basic Eng. 86 (1964) 51–60Google Scholar
  22. 10.22
    Safonov, M.G.; Athans, M.: Gain and phase margin for multivariable. I OR Regulators. IEEE Trans AC 22 (1977) 173–179MathSciNetMATHCrossRefGoogle Scholar
  23. 10.23
    Safonov, M.G.: Stability and robustness of multivariable feedback systems. Boston: MIT-Press, 1980MATHGoogle Scholar
  24. 10.24
    Frank, P.M.: Entwurf parameterunempfindlicher und robuster Regelkreise im Zeitbereich-Definitionen, Verfahren und ein Vergleich. Automatisierungstechnik 33 (1985) 233–240MATHGoogle Scholar
  25. 10.
    Horowitz, 1; Sidi, M.: Synthesis of cascaded multiple-loop feedback systems with large plantparameter ignorance. Automatica 9 (1973) 588 — 600Google Scholar
  26. 10.26
    Ackermann, J.: Entwurfsverfahren für robuste Regelungen. Regelungstechnik 32 (1984) 143–150MATHGoogle Scholar
  27. 10.27
    Ackermann, J (Ed.): Uncertainty and control. Lecture Notes 76. Berlin: Springer-Verlag (1985)Google Scholar
  28. 10.28
    Tolle, H.: Mehrgrößen-Regelkreissynthese, Bd. I und II, München: Oldenbourg 1983 und 1985Google Scholar
  29. 10.29
    Kofahl, R.: Robustheitsanalyse zeitdiskreter, optimaler Zustandsregler. Interner Ber. Inst. f. Regelungstechnik, T.H. Darmstadt (1984)Google Scholar
  30. 10.30
    Bux, D.: A new closed solution design of constant feedback control for systems with large parameter variations. 3rd IFAC-Symp. on Sensitivity, Adaptivity and Optimality, Ischia, Haly (1973), Inst. Soc. Am.Google Scholar
  31. 10.31
    Bux, D.: Anwendung und Entwurf konstanter, linearer Zustandsregler bei linearen Systemen mit langsam veränderlichen Parameter. Diss. Univ. Stuttgart. Fortschritt Ber. VDI—Z. Reihe 8 Nr. 21. Düsseldorf: VDI-Verlag 1975Google Scholar
  32. 10.32
    Isermann, R.; Eichner M.: Über die Lastabhängigkeit der Dampftemperatur-Regelung des Mehrgrößen-Regelsystems „Trommelkessel“. Brennstoff, Wärme, Kraft 20 (1968) 453–459Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Rolf Isermann
    • 1
  1. 1.Institut für RegelungstechnikTechnische Hochschule DarmstadtDarmstadtWest Germany

Personalised recommendations