Transfer function with time delay, transcendental transfer function

Question: How to define the transfer function

in Matlab?

where

s: is the laplace variable

z: is a spatial variable (also a constant here)

k1,k2,w: are constants

Answer 1

[MA]

clear all
close all
clc;
k1=1;k2=1;w=.5;z=2;
s=tf('s');
H = (-(((s^2)+(k1+k2)*s)/(w*(s+k2)))*z);
bode(H)
grid on

[August]

there is the "exp" missing like:

H = exp(-(((s^2)+(k1+k2)*s)/(w*(s+k2)))*z);

but then matlab answers:

??? Error using ==> tf.exp at 31 The input argument of the "lti/exp" command must be a transfer function of the form -M*s.

Answer 2

[milad karimshoushtari]

I have the same problem, did you find any answer?

[August]

unfortunately not until now

Answer 3

[milad karimshoushtari]

I found a solution for a similar problem, you can not define this transfer function in matlab or simulink. use the time domain equation with derivatives that resulted to this transfer function, then use finite deference method to approximate the derivative of spatial variable then you can write a recursive code in matlab or in s-func simulink to solve it, it is not easy! search for finite deference method to solve spatial dependent differential equations then you will figure out the rest.

[August]

Thanks for your idea, do you have an example of your proposal or a link with example code?