Stability of PID-Controlled Linear Time-Delay Feedback Systems

Details Stability of PID-Controlled Linear Time-Delay Feedback Systems Stability of PID-Controlled Linear Time-Delay Feedback Systems

2008-02-15

arxiv.org/abs/0802.2165v1

Mathematics

Optimization and Control

AMS-LaTex version 2.20 11 pages with 5 figures

Scientific paper

The stability of feedback systems consisting of linear time-delay plants and PID controllers has been investigated for many years by means of several methods, of which the Nyquist criterion, a generalization of the Hermite-Biehler Theorem, and the root location method are well known. The main purpose of these researches is to determine the range of controller parameters that allow stability. Explicit and complete expressions of the boundaries of these regions and computation procedures with a finite number of steps are now available only for first-order plants, provided with one time delay. In this note, the same results, based on Pontryagin's studies, are presented for arbitrary-order plants.

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