The Fractional Order PID Control of the Forced Air Heating System

eng Article in English DOI: 10.14313/PAR_231/5

send Krzysztof Oprzędkiewicz , Maciej Podsiadło AGH Akademia Górniczo-Hutnicza, Wydział Elektrotechniki, Automatyki, Informatyki i Inżynierii Biomedycznej

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Abstract

The paper presents the implementation of the Fractional Order PID controller to control the temperature in the isothermal room applied in a pharmaceutical factory. The formula of the controller dedicated to transfer function model of the temperature is proposed, the stability analysis using the Matignon Theorem is also presented. Results of simulations show that the proposed controller is able to assure the better control quality than PID controller tuned with the use of auto-tuning function.

Keywords

forced heating system, Fractional Order PID controller, ORA approximation, stability

Sterowanie PID ułamkowego rzędu układem ogrzewania powietrza

Streszczenie

Artykuł prezentuje implementację regulator PID ułamkowego rzędu (FOPID) do sterowania temperaturą w pomieszczeniu izotermicznym stosowanym w fabryce farmaceutycznej. Zaproponowano formułę regulatora dla modelu obiektu opisanego transmitancją oraz analizę stabilności z wykorzystaniem Tw. Matignona. Wyniki badań symulacyjnych wskazują, że proponowany regulator zapewnia lepszą jakość regulacji, niż typowy regulator PID dostrojony zużyciem autotuningu.

Słowa kluczowe

aproksymacja ORA, stabilność, system ogrzewania powietrza, ułamkowy regulator PID

Bibliography

  1. Caponetto R., Dongola G., Fortuna L., Petras I., Fractional order systems: Modeling and Control Applications. [in:] Chua L.O., editor, World Scientific Series on Nonlinear Science, 1–178. University of California, Berkeley, 2010.
  2. Das S., Functional Fractional Calculus for System Identification and Control. Springer, Berlin 2010.
  3. Faieghi M.R., Nemati A., On fractional-order PID design. [in:] Michalowski T., editor, Applications of MATLAB in Science and Engineering, 273–292. InTech, Rijeka Croatia, 2011.
  4. Kaczorek T., Singular fractional linear systems and electrical circuits. “International Journal of Applied Mathematics and Computer Science”, Vol. 21, No. 2, 2011, 379–384.
  5. Kaczorek T., Rogowski K., Fractional Linear Systems and Electrical Circuits. Bialystok University of Technology, Bialystok, 2014.
  6. Matignon D., Stability results for fractional differential equations with applications to control processing. [in:] IMACS-SMC Proceedings, Lille, France, July 1996, 963–968.
  7. Merrikh-Bayat F., Mirebrahimi N., Khalili M.R., Discrete-time fractional-order PID controller: Definition, tuning, digital realization and some applications. “International Journal of Control, Automation, and Systems”, Vol. 13, No. 1, 2015, 81–90.
  8. Edet E., Katebi R., On Fractional-Order PID Controllers, Fractional order systems: Modeling and Control Applications. [in:] Preprints of the 3rd IFAC Conference on Advances in Proportional-Integral-Derivative Control, Ghent, Belgium, May 9–11, 2018, 739–744.
  9. Oustaloup A., Levron F., Mathieu B., Nanot F., Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Transactions on Circuits and Systems I: Fundamental Theory Applications, Vol. 47, No. 1, 2000, 25–39, DOI: 10.1109/81.817385.
  10. Petras I., Fractional – Order feedback control of a DC motor. “Journal of Electrical Engineering”, Vol. 60, No. 3, 2009, 117–128.
  11. Podlubny I., Fractional Differential Equations. Academic Press, San Diego 1999.
  12. Ranganayakulu R., Babu G.U.B., Rao A.S., Patle D.S., A comparative study of fractional order PIλ/PIλDμ tuning rules for stable first order plus time delay processes. “Resource-Efficient Technologies”, Vol. 2, No. 1, 2016, 136–152.
  13. Teplakov A., Fractional-order Modeling and Control of Dynamic Systems. PhD thesis, Tallin Unviersity of Technology, Estonia, Tallin 2015.
  14. Valerio D., Costa J., Tuning rules for fractional PID controllers. [in:] Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and its Applications Porto, Portugal, July 19–21, 2006, 1–6.