In this chapter, it will be shown how the Nyquist stability criterion can be used to synthesize a PID controller so that the feedback system is in a certain sense robustly stable and fulfills also some specified performance requirements. These properties are typically measured by the phase margin and the gain crossover frequency. The method will be most successfully applied if the plant is stable with the possible exception of a pole at the origin, but even in this case it has limitations if the performance requirements become too complex. We show that in such a situation an improvement can be achieved by generalizing the structure of the classical SISO feedback loop. This leads to a cascade of several controllers, to a two degrees-of-freedom control configuration or to feedforward of the disturbance.
KeywordsController Design Nyquist Plot Step Response Phase Margin Phase Plot
Unable to display preview. Download preview PDF.
Notes and References
- Most of the material presented in the Chaps. 1 – 4 can be found in much greater detail in any introductory textbook on control. We mention here only Dorf and Bishop  and Föllinger , but there are many further excellent books on classical control. Some effort has been made to introduce the basic ideas of H ∞ and robust control for SISO systems and to relate them as far as possible to well-known classical concepts. In particular, this holds for Chap. 3. Concerning these questions, the reader is referred to Doyle, Francis and Tannenbaum , where H ∞ and robust control for SISO systems in the frequency domain is introduced in detail.Google Scholar