PID Tuning of Plants With Time Delay Using Root Locus

Abstract

PID-TUNING OF PLANTS WITH TIME DELAY USING ROOT LOCUS by Greg Baker This thesis research uses closed-loop pole analysis to study the dynamic behavior of proportional-integral-derivative (PID) controlled feedback systems with time delay. A conventional tool for drawing root loci, the MATLAB function rlocus() cannot draw root loci for systems with time delay, and so another numerical method was devised to examine the appearance and behavior of root loci in systems with time delay. Approximating the transfer function of time delay can lead to a mismatch between a predicted and actual response. Such a mismatch is avoided with the numerical method developed here. The method looks at the angle and magnitude conditions of the closedloop characteristic equation to identify the true positions of closed-loop poles, their associated compensation gains, and the gain that makes a time-delayed system become marginally stable. Predictions for system response made with the numerical method are verified with a mathematical analysis and cross-checked against known results. This research generates tuning coefficients for proportional-integral (PI) control of a first-order plant with time delay and PID control of a second-order plant with time delay. The research has applications to industrial processes, such as temperature-control loops. ACKNOWLEDGEMENTS This thesis was produced with the help of several individuals. First, the author is indebted to the inspirational instruction of Dr. Peter Reischl, and the willingness of Mr. Owen Hensinger to share his experience in process control, the source of the overshootreduction technique suggested in the text. Sincere appreciation is expressed for the guidance and counsel of Dr. Ping Hsu and Dr. Julio Garcia. Lifelong thanks are due for the patience and support of my wife Adrienne Harrell.