Genuine feasible stability margin region for integrating unstable processes with PD control

Author(s): M.W. Sun ; R.G. Yang ; Z.Q. Chen
DOI: 10.1049/iet-cta.2010.0325

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Author(s): M.W. Sun ¹ ; R.G. Yang ¹ ; Z.Q. Chen ¹
- Affiliations: 1: College of Information Technology and Science, Department of Automation, Nankai University, Tianjin, People's Republic of China
Source: Volume 5, Issue 10, 7 July 2011, p. 1228 – 1234
DOI: 10.1049/iet-cta.2010.0325 , Print ISSN 1751-8644, Online ISSN 1751-8652

PID control is widely used to control stable processes; however, its application to integrating unstable processes is less common. Integrating unstable process is often approximated by an integrating-unstable-first-order-plus-dead-time model based on which the simple analytical tuning formulae of PD control are derived to meet gain and phase margin (GPM) specifications. The previous tuning approach based on GPM only takes the increasing gain margin into account; however, the decreasing gain margin is commonly more critical. Using Routh stability criterion, the decreasing gain margin is obtained by Pade approximation of the delay based on the established tuning rule. The numerical polynomial solving approach is employed to seek the feasible stability margin region, which is explicitly plotted in the 2-D plane. At the same time, a novel tuning rule based on the decreasing gain margin is presented. The results demonstrate that the feasible GPM region is a small portion of the original one. Finally, some numerical examples are provided to validate the analysis result.

References

1. 1)
  - K.J. Astrom , T. Hagglund . Automatic tuning of simple regulators with specifications on phase and amplitude margins. Automatica , 5 , 645 - 651
2. 2)
  - C.-H. Lee . A survey of PID controller design based on gain and phase margins. Int. J. Comput. Cogn. , 3 , 63 - 100
3. 3)
  - P.N. Paraskevopoulos , G.D. Pasgianos , K.G. Arvanitis . PID-type controller tuning for unstable first order plus dead time processed based on gain and phase margin specifications. IEEE Trans. Control Syst. Technol. , 5 , 926 - 936
4. 4)
  - W.K. Ho , C.C. Hang , L.S. Cao . Tuning of PID controllers based on gain and phase margin specifications. Automatica , 3 , 497 - 502
5. 5)
  - W.K. Ho , C.C. Hang , J. Zhou . Self-tuning PID control of a plant with under-damped response with specifications on gain and phase margins. IEEE Trans. Control Syst. Technol. , 4 , 446 - 452
6. 6)
  - C.H. Chang , K.W. Han . Gain margins and phase margins for control systems with adjustable parameters. J. Guid. Control Dyn. , 3 , 404 - 408
7. 7)
  - P.N. Paraskevopoulos , G.D. Pasgianos , K.G. Arvanitis . New tuning and identification methods for unstable first order plus dead time processes based on pseudo-derivative feedback control. IEEE Trans. Control Syst. Technol. , 3 , 455 - 464
8. 8)
  - Y.G. Wang , W.J. Cai . Advanced proportional-integral-derivative tuning for integrating and unstable processes with gain and phase margin specifications. Ind. Eng. Chem. Res. , 12 , 2910 - 2914
9. 9)
  - A. Leva , F. Donida . Quality indices for the autotuning of industrial regulators. IET Control Theory Appl. , 2 , 170 - 180
10. 10)
  - Y. Li , H.A. Kiam , G.C.Y. Chong . Patents, software, and hardware for PID control: an overview and analysis of the current art. IEEE Control Syst. Mag. , 1 , 42 - 54
11. 11)
  - Y.G. Wang , H.H. Shao . PID autotuner based on gain- and phase margin specifications. Ind. Eng. Chem. Res. , 8 , 3007 - 3012
12. 12)
  - S. Vivek , M. Chidambaram . An improved relay auto tuning of PID controllers for unstable FOPTD systems. Comput. Chem. Eng. , 2060 - 2068
13. 13)
  - W.L. Bialkowski . Dreams versus reality: a view from both sides of the gap: manufacturing excellence with come only through engineering excellence. Pulp Pap , 11 , 19 - 27
14. 14)
  - S.Y. Chu , C.C. Teng . Tuning of PID controllers based on gain and phase margin specifications using fuzzy neural network. Fuzzy Sets Syst. , 1 , 21 - 30
15. 15)
  - W.K. Ho , K.W. Lim , C.C. Hang , L.Y. Ni . Getting more phase margin and performance out of PID controllers. Automatica , 9 , 1579 - 1585
16. 16)
  - R. Toscano . A simple robust PI/PID controller design via numerical optimization approach. J. Process Control , 81 - 88
17. 17)
  - R.P. Sree , M.N. Srinivas , M. Chidambaram . A simple method of tuning PID controllers for stable and unstable FOPTD systems. Comput. Chem. Eng. , 2201 - 2218
18. 18)
  - K.J. Astrom , T. Hagglund . (1995) PID controllers: theory, design, and tuning.
19. 19)
  - W.K. Ho , Y. Hong , A. Hansson , H. Hjalmarsson , J.W. Deng . Relay auto-tuning of PID controllers using iterative feedback tuning. Automatica , 149 - 157
20. 20)
  - W.K. Ho , W. Xu . PID tuning for unstable processes based on gain and phase margin specifications. IEE Proc. Control Theory Appl. , 5 , 392 - 396
21. 21)
  - Y.H. Lee , J.S. Lee , S.W. Park . PID controller tuning for integrating and unstable process with time delay. Chem. Eng. Sci. , 3481 - 3493

Genuine feasible stability margin region for integrating unstable processes with PD control

Genuine feasible stability margin region for integrating unstable processes with PD control

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