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

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?

[Mathieu NOE]

hello

maybe there is an error in this line

[num, den]= ss2tf(A,B,C,D);

because the input number is not defined

doc says :

[NUM,DEN] = ss2tf(A,B,C,D,iu) calculates the transfer function from the iu'th input

[Paul]

The iu defaults to one if not specified.

Answer 1

[Paul]

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]

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.