First-Order Plus Dead Time Model
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Following this Mathworks example I'm getting the expected output using the example of
with this code:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/210779/image.png)
num = 5;
den = [1 1];
P = tf(num,den,'InputDelay',3.4)
figure()
step(P)
But how would I plot this by first solving the transfer function analytically, i.e., if I apply a step input to
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/210780/image.png)
which gives me ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/210781/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/210781/image.png)
then perform inverse Lapace transform on![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/210782/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/210782/image.png)
which gives me ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/210783/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/210783/image.png)
but how do I apply the dead time part of
?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/210784/image.png)
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Answers (1)
Muhammad Aseer Khan
on 12 Feb 2021
for exp(-a*s)F(s) the Laplace inverse will be f(t-a)U(t-a). Then find inverse laplace of first 5/(s(s+a)) and then put (t-a) instead of t.
In Programming, Run a loop for no. of times you want to get samples. Say, I want to get 10 samples:
S12=[]; % It is am empty matrix in which I want to store my elements of all step response
for i=1:10
S12=[S12;5-5*exp(-0.2*(i-1.4))];
end
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