Exponential terms in numerator and denominator in a Transfer Function

Question

Jacob John 2019-7-16

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https://ww2.mathworks.cn/matlabcentral/answers/472031-exponential-terms-in-numerator-and-denominator-in-a-transfer-function

回答： Jesús Zambrano 2020-2-6

Transfer Function.PNG

I have the LTI system in the attachement and written below. Though, I am having difficulties typing it into Matlab. Is this possible with the exponentials?

num=exp(sqrt(s/alpha)*H)+exp(sqrt(s/alpha)*H)

den=A*R*(k*sqrt(s/alpha)+h_surface)*(exp(sqrt(s/alpha)*H)-exp(-sqrt(s/alpha)*H)

Please see the attachement for a clearer figure.

Thank you

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Answer 1

Jesús Zambrano 2020-2-6

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Hi Jacob,

First please check that the transfer function is linear and time invariant. Most likely is not linear. For a system to be linear means that changing the input in a linear way will change the output in the same linear way. So if the input x1(t) produces the output y1(t) and the input x2(t) produces the output y2(t), then linear combinations of those inputs will produce linear combinations of those outputs.