simulation discrete-time model

I'm studying the linear model of a DC motor. In state-space form, the governing equations above can be expressed by choosing the rotational speed and electric current as the state variables.

So:

Ac = [-b/J k/J; -k/L -R/L];
Bc = [0; 1/L];
Cc = eye(2);
Dc = zeros(2,1);

I expressed all in discrete -time:

sys_TC = ss(Ac,Bc,Cc,Dc);
sys_TD = c2d(sys_TC,Ts);
[A,B,C,D] = ssdata(sys_TD);

Now I shuould simulate the model (TD). In this sense, I simulate the input signal with the function rand. How can I obtain the results of the output and collect them in a matrix?

Answer 1

[Star Strider]

To simulate your system with the appropriate input, use the lsim function. You will need to create a time vector as well as the input signal vector. (You have a single-input system, so this is straightforward. For multiple-input systems, the number of columns in the input signal must match the number of columns of the B matrix.)

[massimiliano frasca]

Thanks for your help, I tried to do how you suggest. How can you see from my question, the output should be a vector with two rows and one column, but when I use the lsim function I obtain a vector with one rows and one column. Did I make a mistake or is is this the output form of lsim function?

[Star Strider]

As always, my pleasure!

No, the output should be a matrix of N rows and two columns.

This code:

[u,t] = gensig('square',1,10,Ts);
y = lsim(sys_TD, u, t);

returns a (10001x2) output matrix in ‘y’ when I run it, as it should. If you are not using the gensig function, be sure to create ‘u’ and ‘t’ as column vectors.