Abstract
In the paper new, discrete, transfer function models of non integer order inertial plant are proposed. These models can be employed to digital modeling of high order dynamic systems, for example heat transfer systems. Models under consideration use Charef approximation and generating functions expressed by schemes given by Euler, Tustin and Al-Aloui. The practical stability and accuracy for all presented models is analysed also. Results are by simulations depicted.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Al-Alaoui, M.A.: Al-Alaoui operator and the \(\alpha \) -approximation for discretization of analog systems. Facta Univ. (Nis)Ser. Electron. Energ. 19(1), 143–146 (2006)
Caponetto, R., Dongola, G., Fortuna, I., Petras, I.: Fractional Order Systems Modeling and Control Applications. World Scientific Series on Nonlinear Science, vol. 72. World Scientific Publishing, New Jersey (2010)
Charef, A., Sun, H.H., Tsao, Y.Y., Onaral, B.: Fractional system as represented by singularity function. IEEE Trans. Autom. Control 37(9), 1465–1470 (1992)
Chen, Y.Q.: Oustaloup Recursive Approximation for Fractional Order Differentiators, MathWorks Inc., Matlab Central File Exchange (2003)
Das, S.: Functional Fractional Calculus for System Identification and Controls. Springer, Berlin (2008)
Das, S., Pan, I.: Fractional Order Signal Processing. SpringerBriefs in Applied Sciences and Technology. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-23117-9-2
Dlugosz, M., Skruch, P.: The application of fractional-order models for thermal process modelling inside buildings. J. Build. Phys. 39, 1–13 (2015)
Djouambi, A., Charef, A., BesançOn, A.: Optimal approximation, simulation and analog realization of the fundamental fractional order transfer function. Int. J. Appl. Math. Comput. Sci. 17(4), 455–462 (2007)
Dzielinski, A., Sierociuk, D., Sarwas, G.: Some applications of fractional order calculus. Bull. Pol. Acad. Sci. Techn. Sci. 58(4), 583–592 (2010)
Garrappa, R., Maione, G.: Fractional Prabhakar derivative and applications in anomalous dielectrics: a numerical approach. In: Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M. (eds.) Theory and Applications of Non-integer Order Systems. LNEE, vol. 407, pp. 429–439. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-45474-0_38
Kaczorek, T.: Practical stability of positive fractional discrete-time systems. Bull. Pol. Acad. Sci. Tech. Sci. 56(4), 313–317 (2008)
Kaczorek, T.: Selected Problems in Fractional Systems Theory. Springer, Heidelberg (2011)
Kaczorek, T., Rogowski, K.: Fractional Linear Systems and Electrical Circuits. Bialystok University of Technology, Bialystok (2014)
Maione, G.: High-speed digital realizations of fractional operators in the delta domain. IEEE Trans. Autom. Control 56(3), 697–702 (2011)
Mitkowski, W., Skruch, P.: Fractional-order models of the supercapacitors in the form of RC ladder networks. Bull. Pol. Acad. Sci. Tech. Sci. 61(3), 581–587 (2013)
Obraczka, A., Mitkowski, W.: The comparison of parameter identification methods for fractional partial differential equation. Solid State Phenom. 210, 265–270 (2014)
Oprzedkiewicz, K., Mitkowski, W., Gawin, E.: Parameter identification for non integer order, state space models of heat plant. In: MMAR 2016: 21th International Conference on Methods and Models in Automation and Robotics, 29 August–01 September 2016, pp. 184–188. Miedzyzdroje, Poland (2016). ISBN:978-1-5090-1866-6, 978-837518-791-5
Oprzędkiewicz, K., Kołacz, T.: A non integer order model of frequency speed control in AC motor. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds.) Challenges in Automation, Robotics and Measurement Techniques. AISC, vol. 440, pp. 287–298. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29357-8_26
Ostalczyk, P.: Discrete Fractional Calculus. Applications in control and image processing. Series in Computer Vision, vol. 4. World Scientific Publishing, Singapore (2016)
Oustaloup, A., Levron, F., Mathieu, B., Nanot, F.M.: Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Trans. Circ. Syst. I Fundam. Theor. Appl. I 47(1), 25–39 (2000)
Stanislawski, R., Latawiec, K.J., Lukaniszyn, M.: A comparative analysis of Laguerre-based approximators to the Grunwald-Letnikov fractional-order difference. Math. Probl. Eng. 2015, 10 (2015). Article ID 512104
Acknowledgements
This paper was sponsored partially by AGH UST grant no. 11.11.120.815.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Oprzędkiewicz, K. (2018). Discrete Transfer Function Models for Non Integer Order Inertial System. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Automation 2018. AUTOMATION 2018. Advances in Intelligent Systems and Computing, vol 743. Springer, Cham. https://doi.org/10.1007/978-3-319-77179-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-77179-3_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-77178-6
Online ISBN: 978-3-319-77179-3
eBook Packages: EngineeringEngineering (R0)