Implementation-oriented filtered PID control: Optimization of robustness margins

被引:15
作者
Mao, Qi [1 ]
Xu, Yong [2 ]
Chen, Jie [1 ]
Georgiou, Tryphon T. [3 ]
机构
[1] City Univ Hong Kong, Dept Elect Engn, Hong Kong, Peoples R China
[2] Guangdong Univ Technol, Sch Automat, Guangdong Prov Key Lab Intelligent Decis & Coopera, Guangzhou, Peoples R China
[3] Univ Calif Irvine, Dept Mech & Aerosp Engn, Irvine, CA 92697 USA
关键词
Gain margin; Phase margin; Robust stabilization; Filtered PID control; GAIN; STABILIZATION; PLACEMENT; PHASE;
D O I
10.1016/j.automatica.2023.110974
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this paper, we investigate the gain and phase robustness of PID control in stabilizing linear timeinvariant (LTI) systems subject to gain and phase variations. We consider specifically filtered PID controllers, out of the necessity in practical implementation of PID controllers. We examine firstorder unstable systems and seek to find analytical expressions of the maximal gain and phase margins achievable by filtered PID control, where the maximal gain and phase margins are referred to as the largest ranges of gain and phase variations within which the system is guaranteed to be stabilizable. Our results show that the maximal gain margin can be determined explicitly, while the maximal phase margin can be computed by solving a third-order polynomial, which in turn can be solved explicitly. We also investigate the gain and phase maximization problems subject to a performance constraint, which has direct linkages to the steady-state and transient performances of a system. Our results show how in a practically implementable PID control scheme the gain and phase margins may be confined by the plant characteristics, and how in the limit it can perform equally well as other optimal controllers. The results also shed light into the tradeoff between performance and robustness of PID controllers.(c) 2023 Elsevier Ltd. All rights reserved.
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页数:10
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