Time Delay Effects on the Frequency Domain Description of a Discrete Linear Heating System

M. Sarhan (USA)


Heating System With Time Delay, Frequency Response, Fourier Series, Distributed Parameter Systems, Transfer Function, The Heat Equation and Laplace Transform.


This paper presents two models of a heating system with control input and a distributed output. In the first system, there is no time delay and in the second, there is a time delay. Applying Fourier series expansion, we obtain the transfer function of each system. Truncating Fourier series to N terms, gives an approximate system representing the input output relation. We show that the error due to approximation goes to zero when the number of terms becomes very large. Because of the advantages in analyzing discrete systems, we obtain the discrete system transfer function then present and analyze the frequency response in each case. We study the effects of the delay on the frequency response. We present the simulation to show the results of our analysis. Finally, we present our conclusions and discuss possible future work.

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