PID Controller Tuning Based on the Classification of Stable, Integrating and Unstable Processes in a Parameter Plane

Abstract

A quadruplet, defined by the ultimate frequency ??u, the ultimate gain ku, the angle ?? of the tangent to the Nyquist curve at the ultimate frequency and the gain Gp(0), is sufficient for classification of a large class of stable processes, processes with oscillatory dynamics, integrating and unstable processes Gp(s). From the model defined by the above quadruplet, a two parameter model Gn(s n) is obtained by the time and amplitude normalizations. Two parameters of Gn(sn), the normalized gain ?? and the angle ??, are coordinates of the classification ??-?? parameter plane. Model Gn(sn) is used to obtain the desired closed-loop system performance/robustness tradeoff in the desired region of the classification plane. Tuning procedures and tuning formulae are derived guaranteeing almost the same performance/robustness tradeoff as obtained by the optimal PID controller, applied to Gp(s) classified to the same region of the classification plane. Validity of the proposed method is demonstrated on a test batch consisting of stable processes, processes with oscillatory dynamics, integrating and unstable processes, including dead-time. ?? 2010 Elsevier Ltd. All rights reserved.