# Step Response of Transfer Function is Different Than Response of State Space

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Gee on 30 Mar 2022
Commented: Gee on 30 Mar 2022
Hello everyone,
I am working on linearization of my nonlinear model (6DOF aircraft model) and I used the Linear Analysis Tool to generate the state space model and produce a step response. Which is shown below: However, when I take my state space model to the MATLAB Workspace, and I find the transfer function by extracting the A, B, C, and D matrices, then I generate a step response of the transfer function, I do not get the same response from the Linear Analysis Tool. See the code and output below:
A= linsys1.A;
B= linsys1.B;
C= linsys1.C;
D= linsys1.D;
[num, den]= ss2tf(A,B,C,D);
G=tf(num,den);
step(G)
step(linsys1) When I try to use step(linsys1) instead, I get the same plot as in the Linear Analysis Tool. What is the reason that the step response of the Transfer Function not matching the one of the state space?
##### 2 CommentsShowHide 1 older comment
Paul on 30 Mar 2022
The iu defaults to one if not specified.

Paul on 30 Mar 2022
Is linsys1 a discrete-time or continuous-time, i.e., what is the output of
linsys.Ts
If the result of that command is not zero, then try
G = tf(num,den,linsys.Ts)
Or the simpler
G = tf(linsys);
step(G)
If tf(linsys) doesn't do the trick, then there may be other aspects to investigate. In general, if you already have an ss object, that's what should be used.
Gee on 30 Mar 2022
Hi Paul. Thanks for the answer. Yes, Linsys1 is a discrete-time (Ts=1/30 s). I modified the Ts of the transfer function but it still does not give me the correct response. I also tried your last suggestion and it didn't work as well. Looks like I will stick to the ss object and use it to plot step response.