Analysis and Controller Design of a Distributed Parameters Heating System with Time Delay

M. Sarhan (USA)


Systems with time delay, Fourier series, distributed parameter systems, transfer function, the heat equation and Laplace transform.


In this paper, we present a heating system, modeled by the heat equation with time delay control input and distributed output. Applying Fourier series expansion, we obtain the transfer function of the system. Truncating Fourier series, gives an approximate system representing the input output relation. We derive the error bound due to Fourier approximation. We design a controller for the system and present examples to show the response in each case. Finally, we present our conclusions.

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