First-Order Plus Dead Time Model

Question

Vinci 2019-3-28

回答： Muhammad Aseer Khan 2021-2-12

Following this Mathworks example I'm getting the expected output using the example of

with this code:

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

which gives me

then perform inverse Lapace transform on

which gives me

but how do I apply the dead time part of

?

Answer 1

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