# How to define the transfer function with exp

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milad karimshoushtari on 4 May 2015
Answered: Meet Doshi on 10 Oct 2017
I cannot make this transfer function either in matlab or in simulink, It has a wierd delay! can anyone help me please?! exp means a delay?! T(z,s) is output temperature and Tin(s) is input temperature.
s: is the laplace variable z,v,k1,k2,m(z) are constant
if gives this error ??? Error using ==> tf.exp at 31 The input argument of the "lti/exp" command must be a transfer function of the form -M*s.

Sriram Narayanan on 6 May 2015
Edited: Sriram Narayanan on 6 May 2015
It is not possible to specify an exponential delay in the transfer function other than the form exp(-M*s) when using the laplace variable. However, this delay could be specified by seperating the terms as exp(-(z/v)*s))*exp(m/(s + k2))*exp(-(k1*z/v)) where the last two terms are constant gains for the transfer function.
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Sriram Narayanan on 6 May 2015
One suggestion I have is to calculate the 1st order or higher-order approximation using Taylor expansion, similar to performing a Pade approximation for exp(-M*s) which is (1 - M*s/2)/(1 + M*s/2) for 1st order.

Meet Doshi on 10 Oct 2017
hd = exp(tf([-2 0],1))