Abstract
In this chapter, we introduce an approach to the robust design of PID controllers for continuous-time plants based on gain and phase margin specifications. This design is based on a simple parametrization of constant magnitude and constant phase loci of the PID controller. This parametrization produces ellipses and straight lines for first-order and PI controllers and cylinder and plane for PID controllers. These geometric figures are computed by considering a prescribed but arbitrary gain crossover frequency and prescribed but arbitrary phase margin for the closed-loop system with the given plant. These graphical representations enable the retrieval of PI, PID, and first-order controller designs with simultaneous specifications on gain and phase margins.
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