PI controller design in the achievable gain-phase margin plane

In this paper, we present a new approach to the design of Proportional-Integral (PI) controllers. The focus is on a simultaneous achievement of the design specifications most often required in applications. These are a) gain margin, b) phase margin, and c) gain crossover frequency. To accomplish this, we develop a set of design curves in the gain and phase margin plane, indexed by gain crossover frequencies. These curves are constructed from the stabilizing set of PI controllers corresponding to the given plant. Each point in this space represents a prescribed gain margin, phase margin, and crossover frequency, achievable by some PI controller in the stabilizing set. The specific and unique PI achieving these specifications can be found from the intersection of constant magnitude and constant phase loci in the space of controller gains, which consist of ellipses and straight lines. Illustrative examples are presented.