How do you extract the state space model from ssest()?

How do you extract the state space model from ssest()? Please see the below code :

%% Construct SISO System with input u
A           = -1;
B           = 1;
C           = 1;
D           = 0;
time        = [0:0.001:10]';
sysTrue     = ss(A,B,C,D);
u           = ones(length(time),1);

%% Generate output data y
[y]         = lsim(sysTrue,u,time);

%% Use ssest() to identify the SISO system
id=iddata(y,u,mean(diff(time)));
A0 = 0;
B0 = 0;
C0 = 1;
D0 = 0;
m = idss(A0,B0,C0,D0);
S=m.Structure;
S.C.Free=false;
S.D.Free=false;
m.Structure=S;
opt = ssestOptions;
opt.EnforceStability=true;
sys1 = ssest(id,m,opt);

%% Extract the A, B, C, and D matricies from sys1 to to put the state space model in a ss class
sys2 = ss(sys1.A,sys1.B,sys1.C,sys1.D);

%% Simulate sys1 and sys2 and compare results to y:
out1 = lsim(sys1,u,time);
out2 = lsim(sys2,u,time);
plot(time,y,time,out1,time,out2)
legend({'y','sys1','sys2'})
xlabel('time (s)')
ylabel('y')

The produces the following plot:

Why do I get different results for sys1 and sys2? Am I not extracting the state space model correctly?

Thanks!

[Rajiv Singh]

You can directly do sys2 = ss(sys1);

[eddie ball]

That works too! Thanks for the tip!

Answer 1

[M]

sys1 is a discrete-time state space model.

If you want to compare the results with sys2, replace your code with:

%% Extract the A, B, C, and D matricies from sys1 to to put the state space model in a ss class
sys2 = ss(sys1.A,sys1.B,sys1.C,sys1.D,sys1.Ts);

You should obtain similar plots for both sys1 and sys2.

[eddie ball]

That was my issue, thanks M.!