PID auto-tuning for simultaneously fulfilling the requirements of relative stability and steady-state error
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ORIGINAL ARTICLE
PID auto‑tuning for simultaneously fulfilling the requirements of relative stability and steady‑state error Yu‑Sheng Lu1 · Tsang‑Shiuan Tsai1 · Chien‑Chih Huang2 · Chung‑Hsin Cheng2 Received: 29 March 2020 / Accepted: 5 October 2020 © International Society of Artificial Life and Robotics (ISAROB) 2020
Abstract Proportional-integral-derivative (PID) control is commonly used in industrial automatic control systems. However, it is not straightforward to determine control gains in a PID controller for satisfactory closed-loop performance. Many research works have been devoted to the auto-tuning of PID control gains. In contrast to previous studies, this paper develops an auto-tuning rule for PID controllers to simultaneously satisfy specifications of both steady-state error and relative stability, in which stability is specified in terms of phase margin. To illustrate the proposed auto-tuning rule, a focus servo of an optical disk drive is used, in which a voice coil motor drives a lens to focus a laser beam on a data layer of an optical disk. Experimental results show the effectiveness of the proposed PID auto-tuning process. Keywords Auto-tuning · PID control · Relative stability · Phase margin · Low-frequency gain · Steady-state error
1 Introduction Proportional-integral-derivative (PID) control is one of the most important and most popular feedback control laws in both academic and industrial practice because of its simple structure and straightforward microprocessor implementation [1]. Many research efforts have been devoted to the PID controller design. The study [2] proposed a PID controller design for non-overshooting responses. The structure of internal model control can also be used to decide the PID gains [3]. However, these methods [2, 3] require a priori information on the parameters of a plant model for determining the PID gains. The determination of PID gains involves trial and error if a plant model is unavailable. The most famous heuristic PID tuning law is the Ziegler–Nichols rule that tries to obtain appropriate values for the three PID control gains This work was presented in part at the 25th International Symposium on Artificial Life and Robotics (Beppu, Oita, January 22-24, 2020). * Yu‑Sheng Lu [email protected] 1
National Taiwan Normal University, Taipei, Taiwan
National Yunlin University of Science and Technology, Yunlin, Taiwan
2
without using a plant model [4]. This rule is useful but usually yields an output response with excessive overshoots. A set-point weighting technique [5] is proposed to reduce an output overshoot by a Ziegler–Nichols-tuned PID controller. If a plant model is known but its parameters are unknown, an identification process is required for determining the parameter values and subsequently the PID gains using model-based approaches. However, even when the parameter values are identified, there exist uncertainties, and actual parameter values can vary with the aging of a plant, which leads to the necessity of auto-tuning PID gains. Many studies
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