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Analysis and Synthesis in the Frequency Domain

  • André Preumont
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 246)

Abstract

This chapter begins with a brief discussion of the Nyquist stability criterion and recalling the important concepts of gain and phase margins. Next, the feedback specification for single-input single-output system is discussed, together with various representations of the unstructured uncertainty, robust performance, and robust stability. It is followed by a discussion of Bode’s gain–phase relationships (Bode integrals) and how they can be used in design (Bode Ideal Cutoff). Next, the penalty associated with a non-minimum phase system is examined, followed by a brief discussion of usual compensators (Lead, PI, PID). Finally, the discussion is extended to multi-input multi-output system; the small gain theorem allows to derive sufficient conditions for stability. These robustness tests are useful to evaluate a lower bound to the stability margin with respect to spillover (when the high order dynamics is neglected). The chapter concludes with a short list of references and a set of problems.

Keywords

Gain margin Phase margin Nyquist stability Nichols chart Feedback specification Uncertainty Robustness Bode integrals Bode Ideal Cutoff Non-minimum phase system Lead PI PID Small gain theorem Stability robustness Spillover 

References

  1. 1.
    Bode HW (1940) Relations between attenuation and phase in feedback amplifier design. Bell Syst Tech J 19:421–454CrossRefGoogle Scholar
  2. 2.
    Bode HW (1945) Network analysis and feedback amplifier design. Van Nostrand, New YorkGoogle Scholar
  3. 3.
    D’Azzo JJ, Houpis CH (1966) Feedback control system analysis & synthesis, 2nd edn. McGraw-Hill, New YorkzbMATHGoogle Scholar
  4. 4.
    Distefano JJ, Stubberud AR, Williams IJ (1967) Feedback and control systems. Shaum’s outline series, McGraw-Hill, New YorkGoogle Scholar
  5. 5.
    Doyle JC, Stein G (1981) Multivariable feedback design: concepts for a classical/modern synthesis. IEEE Trans Autom Control AC-26(1):4–16Google Scholar
  6. 6.
    Franklin GF, Powell JD, Emami-Naeini A (1986) Feedback control of dynamic systems. Addison-Wesley, ReadingGoogle Scholar
  7. 7.
    Horowitz IM (1963) Synthesis of feedback systems. Academic Press, New YorkzbMATHGoogle Scholar
  8. 8.
    Kissel GJ (1990) The Bode integrals and wave front tilt control. In: AIAA guidance, navigation & control conference, Portland OregonGoogle Scholar
  9. 9.
    Kosut RL, Salzwedel H, Emami-Naeini A (1983) Robust control of flexible spacecraft. AIAA J Guid Control Dyn 6(2):104–111CrossRefzbMATHGoogle Scholar
  10. 10.
    Lurie BJ, Enright PJ (2000) Classical feedback control. Marcel Dekker, New YorkGoogle Scholar
  11. 11.
    Maciejowski JM (1989) Multivariable feedback design. Addison-Wesley, ReadingGoogle Scholar
  12. 12.
    Skelton RE (1989) Model error concepts in control design. Int J Control 49(5):1725–1753MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Strang G (1988) Linear algebra and its applications, 3rd edn. Harcourt Brace Jovanovich, San DiegozbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Active Structures LaboratoryUniversité Libre de BruxellesBrusselsBelgium

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