Maximization of Gain/Phase Margin: PID Control versus LTI Control
Speaker: 毛奇副研究员，南京师范大学
Title: Maximization of Gain/Phase Margin: PID Control versus LTI Control
Language: Chinese
Time & Venue: 2025.08.22 15:00-16:00 腾讯会议：737386446
Abstract: 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). The goal in this work 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. At last, we also show, reassuringly, that for first-order plants the filtered PID controllers can recover in the limit the best gain and phase margins attainable by the standard PID controllers and more generally, by general, optimal LTI controllers.
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