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);
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?

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Accepted Answer

Paul on 30 Mar 2022
Is linsys1 a discrete-time or continuous-time, i.e., what is the output of
If the result of that command is not zero, then try
G = tf(num,den,linsys.Ts)
Or the simpler
G = tf(linsys);
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.
  1 Comment
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.

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