Effects of time delay on the frequency domain description of a heating system

In this paper, we present 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 with increasing number of terms N. We present and analyze the frequency response in each case. We follow by simulation examples to show the results of our analysis. Finally, we present our conclusions and discuss possible future work.