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Order Functions Selection in the Variable-, Fractional-Order PID Controller

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Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 320))

Abstract

In the paper a variable-, fractional-order PID (VFOPID) controller microprocessor realization problems are discussed. In such controllers the variable-, fractional-orders backward differences and sums (VFOBD/S) are used to perform closed-loop system error discrete-time differentiation and integration. In practice all digitally differentiated and integrated signals are noised so there is a necessity of a digital signal pre-filtering. This additionally loads the DSP system. A solution of this problem is proposed. Also the possibilities of the VFOPID controller DSP realizations are presented and compared with the computer simulation results.

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References

  1. As̈trom̈, K.J., Hägglund, T.: PID controllers: Theory, design and tuning. Instrument Society of America (1995)

    Google Scholar 

  2. Chen, Y.Q., Petras, I., Xue, D.: Fractional Order Control - A Tutorial. In: 2009 American Control Conference Hyatt Regency Riverfront. St. Louis, MO (2009)

    Google Scholar 

  3. Gene, F.: Digital signal processor trends, pp. 52–55. Texas Instruments (2000)

    Google Scholar 

  4. Franklin, G.F., Powell, J.D., Ememi-Naeini, A.: Feedback Control of Dynamic Systems. Prentice Hall, Upper Saddle River (2002)

    Google Scholar 

  5. Hussain, Z.M., Sadik, A.Z., Shea, P.: Digital signal Processing. An Introduction with MATLAB and Applications. Springer, Berlin (2011)

    Google Scholar 

  6. Ifeachor, E.C., Jervis, B.W.: Digital Signal Processing. Addison- Wesley, Harlow (1998)

    Google Scholar 

  7. Jacquot, R.G.: Modern Digital Control Systems. Marcel Dekker, Inc., New York (1994)

    Google Scholar 

  8. Karam, L.J., AlKamal, I., Gatherer, A., Frantz, G.A., Anderson, D.V., Evans, B.L.: Trends in Multicore DSP Platforms. IEEE Signal Provessing Magazine (38), 28–49 (2009)

    Google Scholar 

  9. Monje, C.A., Chen, Y., Vinagre, B., Xue, D., Feliu, V.: Fractional-order Systems and Controls Fundamentals and Applications. Advances in Industrial Control. Springer London Limited (2010)

    Google Scholar 

  10. Monje, C.A., Vinagre, B.M., Chen, Y.Q., Feliu, V., Lanusse, P., Sabatier, J.: Proposals for fractional PIλD μ tuning. In: Proceedings of Fractional Differentiation and its Applications, Bordeaux, France (2004)

    Google Scholar 

  11. Ogata, K.: Discrete-Time Control Systems. Prentice Hall International Editions, Englewood Cliffs (1987)

    Google Scholar 

  12. Ostalczyk, P.: Fractional-order backward difference equivalent forms. In: Le Mehaute, Tenreiro Machado, J.A., Trigeassou, J.C., Sabatier, J. (eds.) Fractional differentiation and its Applications. Systems Analysis, Implementation and Simulation, System Identification and Control, pp. 545–556. Ubooks Verlag, Neusä Germany (1995)

    Google Scholar 

  13. Ostalczyk, P.: A note on the Grünwald-Letnikov fractional-order backward difference. Physica Scripta (T136), 1–5 (2009)

    Google Scholar 

  14. Podlubny, I.: Fractional-order Systems and Fractional-order Controllers. Slovak Academy of Sciences Institute of Experimental Physics, UEF SAV Kosice (1994)

    Google Scholar 

  15. Gene, F.: Digital signal processor trends. Texas Instruments, pp. 5–52 (2000)

    Google Scholar 

  16. Podlubny, I.: Fractional Differential Equations. Academic Press, London (1999)

    MATH  Google Scholar 

  17. Podlubny, I.: Fractional-Order Systems and controllers. IEEE Transactions on Automatic Control 44(1), 208–214 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  18. Weeks, M.: Digital Signal Processing. Jones and Bartlett Publishers, Boston (2011)

    MATH  Google Scholar 

  19. Sankowski, D., Kucharski, J., Łobodziński, W.: Auto-tuning Temperature Control Using Identification by MBS. IEE Proc. Control Theory Appl. 144(3), 233–240 (1997)

    Article  MATH  Google Scholar 

  20. Shenga, H., Sunb, H., Coopmansc, C., Chenc, Y.Q., Bohannanc, G.: Physical Experimental Study of Variable-order Fractional Integrator and Differentiator. In: Podlubny, I., Vinagre Jara, B.M., Chen, Y., Feliu Batlle, V., Tejado Balsera, I. (eds.) Proceedings of FDA10. The 4th IFAC Workshop Fractional Differentiation and its Applications, Badajoz, Spain, October 18-20 (2010)

    Google Scholar 

  21. Silva, M.F., Tenreiro Machado, J.A.: Fractional Order PD-Joint Control of Legged Robots. Journal of Vibration and Control 12(12), 1483–1501 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  22. Vilanova, R., Visioli, A. (eds.): PID Control in the Third Millennium. Advances in Industrial ControlLimited. Springer, London (2012)

    Google Scholar 

  23. Xue, D., Chen, Y.: A Comparative Introduction of Four Fractional Order Controllers. In: Proceedings of the 4th World Congress on Intelligent Control and Automation, Shanghai, P.R.China, June 10-14 (2002)

    Google Scholar 

  24. Xue, D., Zhao, C., Chen, Y.: Fractional Order PID Control of A DC-Motor with Elastic Shaft: A Case Study. In: Proceedings of the 2006 American Control Conference Minneapolis, Minnesota, USA, June 14-16 (2006)

    Google Scholar 

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Correspondence to Piotr W. Ostalczyk .

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Ostalczyk, P.W., Duch, P., Brzeziński, D.W., Sankowski, D. (2015). Order Functions Selection in the Variable-, Fractional-Order PID Controller. In: Latawiec, K., Łukaniszyn, M., Stanisławski, R. (eds) Advances in Modelling and Control of Non-integer-Order Systems. Lecture Notes in Electrical Engineering, vol 320. Springer, Cham. https://doi.org/10.1007/978-3-319-09900-2_15

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  • DOI: https://doi.org/10.1007/978-3-319-09900-2_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09899-9

  • Online ISBN: 978-3-319-09900-2

  • eBook Packages: EngineeringEngineering (R0)

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