Stability of PID-Controlled Linear Time-Delay Feedback Systems

2008/02/15 by Gianpasquale Martelli, Martelli, Gianpasquale
Engineering · #34K20 #93D05 #Advanced Control Systems Design #Advanced Control Systems Optimization #Extremum Seeking Control Systems #FOS: Mathematics #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.0802.2165

openalex publication_date 2008/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Beyond the PI Controllers in First-Order Time-Delay Systems

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