Exact Computation of Delay Margin by PID Control: It Suffices to Solve a Unimodal Problem!

被引:0
作者
Chen, Jianqi [1 ]
Ma, Dan [2 ]
Xu, Yong [3 ]
Chen, Jie [1 ]
机构
[1] City Univ Hong Kong, Dept Elect Engn, Kowloon, Hong Kong, Peoples R China
[2] Northeastern Univ, Coll Informat Sci & Engn, State Key Lab Synthet Automat Proc Ind, Shenyang, Peoples R China
[3] Guangdong Univ Technol, Sch Automat, Guangdong Prov Key Lab Intelligent Decis & Cooper, Guangzhou, Peoples R China
来源
PROCEEDINGS OF THE 38TH CHINESE CONTROL CONFERENCE (CCC) | 2019年
关键词
Delay margin; robust stabilization; PID controller; uncertain time delay; nonlinear programming; pseudo-concavity; TRUNCATED PREDICTOR FEEDBACK; LINEAR-SYSTEMS; TIME-DELAY; BOUNDS; STABILIZATION;
D O I
10.23919/chicc.2019.8865931
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 study delay robustness of PID controllers in stabilizing systems containing uncertain, variable delays. We consider second-order unstable systems and seek analytical characterization and exact computation of the PID delay margin, where by PID delay margin we mean the maximal range of delay values within which the system can be robustly stabilized by a MD controller. Our contribution is threefold. First, we show that the delay margin achieved by PID control coincides with that by PD controllers. Second. we show that other than helping stabilize the delay-free part of a plant, the proportional control contributes no action to increase the delay margin. Finally, we show that the PID delay margin can be computed efficiently by solving a unimodal problem, that is, a univariate optimization problem that admits a unique maximum and hence is a convex optimization problem in one variable. This unimodal problem is one of pseudo-concave optimization and hence can be solved using standard convex optimization or gradient-based methods. As such, from a computational perspective, the ND delay margin problem is completely resolved in this paper! The results not only insure that the PIE) delay margin problem be readily solvable, but also provide fundamental conceptual insights into the PID control of delay systems, and analytical justifications to long-held engineering intuitions and heuristics, thus lending useful guidelines in the tuning and analytical design of PID controllers.
引用
收藏
页码:242 / 249
页数:8
相关论文
共 31 条
[1]  
[Anonymous], 2007, PID controllers for time-delay systems
[2]  
[Anonymous], 2006, Robust Control of Time-Delay Systems
[3]  
Astrom KJ., 1995, PID Controllers: Theory, Design, and Tuning
[4]  
Bertsekas Dimitri P, 2016, Nonlinear Programming, V3rd
[5]   Adaptive control scheme for uncertain time-delay systems [J].
Bresch-Pietri, Delphine ;
Chauvin, Jonathan ;
Petit, Nicolas .
AUTOMATICA, 2012, 48 (08) :1536-1552
[6]   A LOWER-BOUND FOR LIMITING TIME-DELAY FOR CLOSED-LOOP STABILITY OF AN ARBITRARY SISO PLANT [J].
DEVANATHAN, R .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1995, 40 (04) :717-721
[7]  
Doyle J. C., 2013, Feedback control theory
[8]  
FOIAS C, 1996, ROBUST CONTROL INFIN
[9]  
Fridman E, 2014, 2014 EUROPEAN CONTROL CONFERENCE (ECC), P1428, DOI 10.1109/ECC.2014.6862628
[10]   Adaptive stabilization of a class of time-varying systems with an uncertain delay [J].
Gaudette, Darrell L. ;
Miller, Daniel E. .
MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2016, 28 (03)