Maximization of Gain/Phase Margins by PID Control

• 成果类型: Article
• 署名作者: Mao, Qi; Xu, Yong; Chen, Jianqi; Chen, Jie; Georgiou, Tryphon T.
• 署名单位: Nanjing Normal University; City University of Hong Kong; Guangdong University of Technology; Nanjing University; City University of Hong Kong; University of California System; University of California Irvine
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3417717
• 发表日期: 2025
• 页码: 34-49
• 关键词: PD control; PI control; Linear systems; Stability criteria; Robustness; Tuning; Robust control; Gain margin; nonminimum-phase dynamics; proportional-integral-derivative (PID) control; phase margin; robust stabilization

摘要

Proportional-integral-derivative (PID) control has been the workhorse of control technology for about a century. Yet to this day, designing and tuning PID controllers relies mostly on either tabulated rules (Ziegler-Nichols) or on classical graphical techniques (Bode). Our goal in this article is to take a fresh look on PID control in the context of optimizing stability margins for low-order (first- and second-order) linear time-invariant systems. Specifically, we seek to derive explicit expressions for gain and phase margins that are achievable using PID control, and thereby gain insights on the role of unstable poles and nonminimum-phase zeros in attaining robust stability. In particular, stability margins attained by PID control for minimum-phase systems match those obtained by more general control, while for nonminimum-phase systems, PID control achieves margins that are no worse than those of general control modulo to a predetermined factor. Furthermore, integral action does not contribute to robust stabilization beyond what can be achieved by PD control alone.