On Robust Stability of Uncertain Control Systems With Time Delay: An Approach Based on the Overlap of Value Sets

• 成果类型: Article
• 署名作者: Ghorbani, Majid; Tepljakov, Aleksei; Petlenkov, Eduard
• 署名单位: Tallinn University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3381912
• 发表日期: 2024
• 页码: 6349-6356
• 关键词: Delay effects; robust stability; uncertainty; DELAYS; control systems; stability analysis; Transfer functions; delay systems; interval time delay; real parametric uncertainties; robust controllers

摘要

This study provides some methods to analyze robust stabilizability of uncertain plants with an uncertain time delay using arbitrary linear controllers. In this work, an uncertain plant with an uncertain time delay means that the numerator and denominator coefficients and the time delay term of the transfer function of the plant have interval uncertainties. Towards solving the abovementioned problem, first, robust stability is investigated for the closed-loop system in terms of a general class of linear controllers and uncertain plants with an uncertain time delay. Then, by using some interesting geometric features, a robust stability checking function and frequency bounds are provided to improve the computational efficiency of robust stability analysis. Furthermore, due to the widespread industrial use of the well-known proportional-integral-derivative (PID) controller structure, the robust stability region of PID controllers has been determined for an uncertain plant with an uncertain time delay. Finally, two numerical examples are given to verify the obtained results.