PI Control of First Order Time-Delay Systems via Eigenvalue Assignment

A new approach to design PI controllers for time-delay systems is presented. A time-delay can limit and degrade the achievable performance of the controlled system, and even induce instability. This paper presents a new method, based on the Lambert W function [20], for design of PI feedback controllers as an alternative to the well-known Smith predictor. PI controllers for first-order plants with time-delays are designed by obtaining the rightmost (i.e., dominant) eigenvalues in the infinite eigenspectrum of time-delay systems, and assigning them to desired positions in the complex plane. The process is possible due to a novel property of the Lambert W function. Using the controllers designed by using the presented approach, system performance can be improved as well as successfully stabilized. Also, sensitivity analysis of the rightmost eigenvalues is conducted to show that robustness compares favorably to the Smith predictor.