International Journal of applied mathematics and computer science

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Paper details

Number 4 - December 2018
Volume 28 - 2018

A memory-efficient noninteger-order discrete–time state–space model of a heat transfer process

Krzysztof Oprzędkiewicz, Wojciech Mitkowski

A new, state space, discrete-time, and memory-efficient model of a one-dimensional heat transfer process is proposed. The model is derived directly from a time-continuous, state-space semigroup one. Its discrete version is obtained via a continuous fraction expansion method applied to the solution of the state equation. Fundamental properties of the proposed model, such as decomposition, stability, accuracy and convergence, are also discussed. Results of experiments show that the model yields good accuracy in the sense of the mean square error, and its size is significantly smaller than that of the model employing the well-known power series expansion approximation.

noninteger-order systems, heat transfer equation, infinite dimensional systems, continuous fraction expansion, stability