Skip to main content
SpringerLink
Log in

PID Controller for Non-stationary Plants of Relative Second Order

  • Conference paper
  • First Online:
Recent Research in Control Engineering and Decision Making (ICIT 2020)

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 337))

  • 492 Accesses

Abstract

PID controllers are widely used in industry. These controllers provide good control quality for most industrial applications when set up correctly. One of the possible approaches to the typical controllers’ calculation for non-stationary objects of a relative second order is presented in this paper. Here we consider the modified structure of the controller where its proportional and differential components are put in feedback. As a result, two control loops are formed. Such an implementation is relevant for stabilization systems since it allows us to reduce control throws when the set point changes. This is due to the fact that the inner loop is less sensitive to a change in the set point value than the outer. The large coefficients method is used as the theoretical basis for studying the system properties. It is shown that in this case the processes of the system correspond to the second-order transfer function with constant coefficients. The characteristic equation of this transfer function is recommended to be formed using a modal approach according to the requirements for the quality of the processes. At the same time, this equation is the basis for determining the parameters of the PID controller. In this way, we form the desired distribution of the roots and ensure the system robustness with respect to the variable parameters of the plant. The results of numerical simulation of an example in MatLab are presented. They illustrate the PID control properties if the controller is calculated according to the proposed method as well as confirm the system robustness when the plant coefficients vary widely.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Visioli, A.: Practical PID Control. Springer, London (2006)

    MATH  Google Scholar 

  2. O’Dwyer, A.: Handbook of PI and PID Controller Tuning Rules, 3rd edn. Imperial College Press, London (2009)

    Google Scholar 

  3. Atherton, D.: PID controller tuning. Comput. Control Eng. J. 2(10), 44–50 (1999)

    Article  Google Scholar 

  4. Skogestad, S.: Simple analytic rules for model reduction and PID controller tuning. J. Process Control 13(4), 291–309 (2003)

    Article  MathSciNet  Google Scholar 

  5. Schei, T.S.: Automatic tuning of PID controllers based on transfer function estimation. Automatica 30(12), 1983–1989 (1994)

    Article  Google Scholar 

  6. Wang, Q.-G., Zhang, Z., Astrom, K.J., Chek, L.S.: Guaranteed dominant pole placement with PID controllers. J. Process Control 2(19), 349–352 (2009)

    Article  Google Scholar 

  7. Ang, K.H., Chong, G., Li, Y.: PID control system analysis, design, and technology. IEEE Trans. Control Syst. Technol. 4(13), 559–576 (2005)

    Google Scholar 

  8. Moradi, M.H.: New techniques for PID controller design. In: Proceedings of the IEEE Conference on Control Applications, vol. 2, pp. 903–908 (2003)

    Google Scholar 

  9. Astrom, K.J., Hagglund, T.: The future of PID control. Control Eng. Pract. 9, 1163–1175 (2001)

    Article  Google Scholar 

  10. Denisenko, V.V.: PID controller: principles of construction and modification. STA 4, 66–74 (2006)

    Google Scholar 

  11. Rotach, V.Ya.: Automatic Control Theory, 5th edn. Publishing House MEI, Moscow (2008)

    Google Scholar 

  12. Vostrikov, A.S., Frantsuzova, G.A.: Synthesis of PID-controllers for nonlinear nonstationary plants. J. Optoelectron. Instrum. Data Process. 5(51), 471–477 (2015)

    Article  Google Scholar 

  13. Aridome, H., Nakamoto, M., Wakitani, S., Yamamoto, T.: Design of an I-PD control system with low-pass filter and its application. IEEJ Trans. Electron. Inf. Syst. 4(138), 313–318 (2018)

    Google Scholar 

  14. Silva, G.J., Datta, A., Bhattacharyya, S.P.: On the stability and controller robustness of some popular PID tuning rules. IEEE Trans. Autom. Control 9(48), 1638–1641 (2003)

    Article  MathSciNet  Google Scholar 

  15. Ho, M.-T., Lin, C.-Y.: PID controller design for robust performance. IEEE Trans. Autom. Control 8(48), 1404–1409 (2003)

    Google Scholar 

  16. Alfaro, V., Vilanova, R.: Model-Reference Robust Tuning of PID Controllers. Springer, Switzerland (2016)

    Google Scholar 

  17. Obika, M., Yamamoto, T.: An evolutionary design of robust PID controllers. In: IEEE International Conference on Mechatronics and Automation, vol. 1, pp. 101–106 (2005)

    Google Scholar 

  18. Chang, W.-D., Yan, J.-J.: Optimum setting of PID controllers based on using evolutionary programming algorithm. J. Chin. Inst. Eng. 3(27), 439–442 (2004)

    Article  Google Scholar 

  19. Micic, A.D., Matausek, M.R.: Optimization of PID controller with higher-order noise filter. J. Process Control 5(24), 694–700 (2014)

    Article  Google Scholar 

  20. Divya, N., Nirmalkumar, A.: A survey on tuning of PID controller for industrial process using soft computing techniques. Int. J. Pure Appl. Math. 11(118), 663–667 (2018)

    Google Scholar 

  21. Zhmud, V.A., Pyakillya, B.I., Liapidevskii, A.V.: Numerical optimization of PID-regulator for object with distributed parameters. J. Telecommun. Electron. Comput. Eng. 2(9), 9–14 (2017)

    Google Scholar 

  22. Frantsuzova, G.A.: PI2D-controllers synthesis for nonlinear non-stationary plants. In: 14th International Scientific-Technical Conference APEIE, vol. 1, pp. 212–216. NSTU, Novosibirsk (2018)

    Google Scholar 

  23. Frantsuzova, G., Zhmud, V., Vostrikov, A.: Possibilities of typical controllers for low order non-linear non-stationary plants. Stud. Syst. Decis. Control 199, 527–539 (2019)

    Article  Google Scholar 

  24. Chen, Y.Q., Bhaskaran, T., Xue, D.: Practical tuning rule development for fractional order proportional and integral controllers. J. Comput. Nonlinear Dyn. 3(2), 8 (2008)

    Google Scholar 

  25. Zhmud, V.A., Zavoryn, A.N.: Fractional-exponent PID-controllers and ways of their simplification with increasing control efficiency. Autom. Softw. Eng. 1, 30–36 (2013)

    Google Scholar 

  26. Shaha, P., Agashe, S.: Review of fractional PID controller. Mechatronics 38, 29–41 (2016)

    Article  Google Scholar 

  27. Yurkevich, V.D.: Calculation and tuning of controllers for nonlinear systems with different-rate processes. Optoelectron. Instrum. Data Process. 5(48), 447–453 (2012)

    Article  Google Scholar 

  28. Meerov, M.V.: Synthesis of Structures of High Accuracy Automatic Control Systems. Science, Moscow (1967)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Novosibirsk State Technical University, Karl Marx Ave. 20, 630092, Novosibirsk, Russia

    Galina Frantsuzova & Anatoly Vostrikov

Authors
  1. Galina Frantsuzova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anatoly Vostrikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Galina Frantsuzova .

Editor information

Editors and Affiliations

  1. Yury Gagarin State Technical University of Saratov, Saratov, Russia

    Olga Dolinina

  2. ITMO University, Saint Petersburg, Russia

    Igor Bessmertny

  3. Yury Gagarin State Technical University of Saratov, Saratov, Russia

    Alexander Brovko

  4. University of Texas at El Paso, El Paso, USA

    Vladik Kreinovich

  5. Yury Gagarin State Technical University of Saratov, Saratov, Russia

    Vitaly Pechenkin

  6. Yury Gagarin State Technical University of Saratov, Saratov, Russia

    Alexey Lvov

  7. Novosibirsk State Technical University, Novosibirsk, Russia

    Vadim Zhmud

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Frantsuzova, G., Vostrikov, A. (2021). PID Controller for Non-stationary Plants of Relative Second Order. In: Dolinina, O., et al. Recent Research in Control Engineering and Decision Making. ICIT 2020. Studies in Systems, Decision and Control, vol 337. Springer, Cham. https://doi.org/10.1007/978-3-030-65283-8_4

Download citation

Publish with us

Policies and ethics

Search

Navigation