Skip to main content
SpringerLink
Log in

Improved PID controller tuning rules for performance degradation/robustness increase trade-off

  • Original Paper
  • Published:
Electrical Engineering Aims and scope Submit manuscript

Abstract

Definitely, robustness is an important feature that any control system must take into account, especially considering that the design is usually based on low-order linear models that represent the whole controlled process. The problem is that to include such characteristic implies a degradation in the system’s performance. With regard to the previous statement, this paper is concerned with the design of the closed-loop control system, to take into account the system performance to load-disturbance and to set-point changes and its robustness to variation of the controlled process characteristics. The aim is to achieve a good balance between the multiple trade-offs. Here, a PID control design is provided that looks for a robustness increase, allowing some degradation in the system’s combined performance. The proposed approach is complementary to the work presented by Arrieta and Vilanova (Simple PID tuning rules with guaranteed \(M_s\) robustness achievement, in 18th IFAC world congress, 2011; Ind Eng Chem Res 51(6):2666–2674, 2012. doi:10.1021/ie201655c); Arrieta et al. (Performance Degradation Driven PID controller design, in PID12, IFAC conference on advances in PID control, 2012).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Alfaro VM (2006) Low-order models identification from process reaction curve. Cienc Tecnol (Costa Rica) 24(2):197–216 (in Spanish)

    MathSciNet  Google Scholar 

  2. Arrieta O, Alfaro VM (2003) PI and PID controller tuning using IAE and ITAE integral criteria. Ingeniería (Costa Rica) 13(1–2):31–39 (in Spanish)

    Google Scholar 

  3. Arrieta O, Vilanova R (2010) Performance degradation analysis of controller tuning modes: application to an optimal PID tuning. Int J Innov Comput Inf Control 6(10):4719–4729

    Google Scholar 

  4. Arrieta O, Vilanova R (2011) Simple PID tuning rules with guaranteed \(M_s\) robustness achievement. In: 18th IFAC world congress, August 28–September 2, Milano-Italy

  5. Arrieta O, Vilanova R (2012) Simple servo/regulation proportional-integral-derivative (PID) tuning rules for arbitrary \(M_s\)-based robustness achievement. Ind Eng Chem Res 51(6):2666–2674. doi:10.1021/ie201655c

    Article  Google Scholar 

  6. Arrieta O, Vilanova R, Alfaro VM (2012) Performance Degradation Driven PID controller design. In: PID12, IFAC conference on advances in PID control, March 28–30, Brescia-Italy

  7. Arrieta O, Vilanova R, Alfaro VM, Moreno R (2008) Considerations on PID controller operation: application to a continuous stirred tank reactor. In: 13th IEEE international conference on emerging technologies and factory automation (ETFA08), September 15–18, Hamburg-Germany

  8. Arrieta O, Vilanova R, Visioli A (2011) Proportional-integral-derivative tuning for servo/regulation control operation for unstable and integrating processes. Ind Eng Chem Res. doi:10.1021/ie101012z

    Google Scholar 

  9. Arrieta O, Visioli A, Vilanova R (2010) PID autotuning for weighted servo/regulation control operation. J Process Control 20(4):472–480

    Article  Google Scholar 

  10. Åström K, Hägglund T (1984) Automatic tuning of simple regulators with with specifications on phase and amplitude margin. Automatica 20:645–651

    Article  MathSciNet  MATH  Google Scholar 

  11. Åström K, Hägglund T (1995) PID controllers: theory, design, and tuning. Instrument of Society of America, Research Triangle Park, North Carolina

  12. Åström K, Hägglund T (2000) Benchmark systems for PID control. In: IFAC digital control: past, present and future of PID control. Terrassa, Spain

  13. Åström K, Hägglund T (2001) The future of PID control. Control Eng Pract 9:1163–1175

    Article  Google Scholar 

  14. Åström K, Hägglund T (2004) Revisiting the Ziegler–Nichols step response method for PID control. J Process Control 14:635–650

    Article  Google Scholar 

  15. Åström K, Hägglund T (2006) Advanced PID control. ISA—The Instrumentation, Systems, and Automation Society

  16. Babb M (1990) Pneumatic instruments gave birth to automatic control. Control Eng 37(12):20–22

    Google Scholar 

  17. Bennett S (2000) The past of PID controllers. In: IFAC digital control: past, present and future of PID control. Terrassa, Spain

  18. Chen D, Seborg D (2002) PI/PID controller design based on direct synthesis and disturbance rejection. Ind Eng Chem Res 41(19):4807–4822

    Article  Google Scholar 

  19. Cohen GH, Coon GA (1953) Theoretical considerations of retarded control. ASME Trans 75:827–834

    Google Scholar 

  20. Fung H, Wang Q, Lee T (1998) PI Tuning in terms of gain and phase margins. Automatica 34:1145–1149

    Article  MATH  Google Scholar 

  21. Ho WK, Hang CC, Cao LS (1995) Tuning PID controllers based on gain and phase margin specifications. Automatica 31(3):497–502

    Article  MathSciNet  MATH  Google Scholar 

  22. Ho WK, Lim KL, Hang CC, Ni LY (1999) Getting more phase margin and performance out of PID controllers. Automatica 35:1579–1585

    Article  MATH  Google Scholar 

  23. Ingimundarson A, Hägglund T, Åström KJ (2004) Criteria for desing of PID controllers. ESAII, Universitat Politecnica de Catalunya, Technical report

  24. Kravaris C, Daoutidis P (1990) Nonlinear state feedback control of second order nonminimum-phase nonlinear systems. Comput Chem Eng 14(4–5):439–449

    Article  Google Scholar 

  25. Kristiansson B, Lennartson B (2006) Evaluation and simple tuning of PID controllers with high-frequency robustness. J Process Control 16:91–102

    Article  Google Scholar 

  26. López AM, Miller JA, Smith CL, Murrill PW (1967) Tuning controllers with error-integral criteria. Instrum Technol 14:57–62

    Google Scholar 

  27. Martin J, Smith CL, Corripio AB (1975) Controller tuning from simple process models. Instrum Technol 22(12):39–44

    Google Scholar 

  28. O’Dwyer A (2003) Handbook of PI and PID controller tuning rules. Imperial College Press, London

    Book  MATH  Google Scholar 

  29. Rivera DE, Morari M, Skogestad S (1986) Internal model control 4. PID controller design. Ind Eng Chem Res 25:252–265

    Google Scholar 

  30. Rovira A, Murrill PW, Smith CL (1969) Tuning controllers for setpoint changes. Instrum Control Syst 42:67–69

    Google Scholar 

  31. Skogestad S (2003) Simple analytic rules for model reduction and PID controller tuning. J Process Control 13:291–309

    Article  Google Scholar 

  32. Tan W, Liu J, Chen T, Marquez HJ (2006) Comparison of some well-known PID tuning formulas. Comput Chem Eng 30:1416–1423

    Article  Google Scholar 

  33. Van de Vusse JG (1964) Plug-flow type reactor versus tank reactor. Chem Eng Sci 19:964

    Google Scholar 

  34. Vilanova R (2008) IMC based robust PID design: tuning guidelines and automatic tuning. J Process Control 18:61–70

    Article  Google Scholar 

  35. Yaniv O, Nagurka M (2004) Design of PID controllers satisfying gain margin and sensitivity constrains on a set of plants. Automatica 40:111–116

    Article  MathSciNet  MATH  Google Scholar 

  36. Zhuang M, Atherton D (1993) Automatic tuning of optimum PID controllers. IEE Proc Part D 140(3):216–224

    Article  MATH  Google Scholar 

  37. Ziegler J, Nichols N (1942) Optimum settings for automatic controllers. ASME Trans 64:759–768

    Google Scholar 

Download references

Acknowledgments

The financial support from the University of Costa Rica, under the Grants 731-B4-213 and 322-B4-218, is greatly appreciated. Also, this work has received financial support from the Spanish CICYT program under Grant DPI2013-47825-C3-1-R.

Author information

Authors and Affiliations

  1. Instituto de Investigaciones en Ingeniería, Facultad de Ingeniería, Universidad de Costa Rica, San José, 11501-2060, Costa Rica

    O. Arrieta

  2. Departamento de Automática, Escuela de Ingeniería Eléctrica, Universidad de Costa Rica, San José, 11501-2060, Costa Rica

    O. Arrieta & J. D. Rojas

  3. Departament de Telecomunicació i d’Enginyeria de Sistemes, Escola d’Enginyeria, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain

    R. Vilanova & M. Meneses

Authors
  1. O. Arrieta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Vilanova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. D. Rojas
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Meneses
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. Arrieta.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arrieta, O., Vilanova, R., Rojas, J.D. et al. Improved PID controller tuning rules for performance degradation/robustness increase trade-off. Electr Eng 98, 233–243 (2016). https://doi.org/10.1007/s00202-016-0361-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00202-016-0361-x

Keywords

Search

Navigation