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Fractional Order State Space Models of the One-Dimensional Heat Transfer Process

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Fractional Dynamical Systems: Methods, Algorithms and Applications

Abstract

The chapter presents the fractional order, state space models of the one dimensional heat transfer process. The proposed models are based on a known semigroup state space model of a parabolic system with distributed control and observation. The first model presented is the time continuous model using the Caputo definition of the fractional derivative over time and the Riesz definition to express the spatial fractional derivative. The second proposed model is the discrete time model, employing the discrete Grünwald-Letnikov operator. The last discrete time fractional order model uses a new, memory-effective method, proposed by the authors as a method of solution for the discrete fractional state equation. The proposed method uses the CFE approximant to express the fractional derivative. Elementary properties (stability, convergence and accuracy) for each proposed model are analysed and results are verified using real experimental data.

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Acknowledgements

This chapter is sponsored by AGH project no 16.16.120.773.

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Correspondence to Krzysztof Oprzȩdkiewicz .

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Oprzȩdkiewicz, K., Mitkowski, W. (2022). Fractional Order State Space Models of the One-Dimensional Heat Transfer Process. In: Kulczycki, P., Korbicz, J., Kacprzyk, J. (eds) Fractional Dynamical Systems: Methods, Algorithms and Applications. Studies in Systems, Decision and Control, vol 402. Springer, Cham. https://doi.org/10.1007/978-3-030-89972-1_13

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