Advanced Tuning for Ziegler-Nichols Plants

Abstract

In this paper, we describe an advanced tuning approach for the design of PI (Proportional-Integral) and PID (Proportional-Integral-Derivative) controllers for the Ziegler-Nichols plants, that is First Oder Plus Time-Delay (FOPTD) continuous-time LTI (Linear Time Invariant) systems. The objective is to provide to the designer an efficient tool to design PI or PID controllers where it is possible to select simultaneous performance specifications of gain margin, phase margin, and gain crossover frequency from a set of achievable performance design curves for Ziegler-Nichols plants. To succeed in this, we first construct the stabilizing set of PI or PID controllers corresponding to the Ziegler-Nichols plant. Next, we generate an achievable performance set displayed as design curves in the gain and phase margin plane, indexed by gain crossover frequencies. Each point in this achievable performance plot represents a prescribed gain margin, phase margin, and crossover frequency, obtained by a PI or PID controller contained in the stabilizing set. Then, by selecting a point from the achievable performance set, a unique PI or PID controller achieving these simultaneous specifications is found from the intersection of an ellipse and straight line parametrized from constant magnitude and constant phase loci in the space of controller gains. We present illustrative examples to validate the proposed approach.