Analysis and Synthesis in the Frequency Domain

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


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.


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 


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Active Structures LaboratoryUniversité Libre de BruxellesBrusselsBelgium

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