Can't see any effect of NoiseVariance with idpoly and lsim

I'm trying to simulate this system with an output disturbance.

With or without NoiseVariance specified I cannot see any difference in the output.

% Plant model
A = [1 -0.8];
B = 0.4;
d = 2;
C = 1;
D = conv(A,[1 -1]);
nT = 8;
Ts = 1;
Vq = 1;
sys = idpoly(A,B,C,D,1,Vq,Ts,'IODelay',d)
t = [0:nT]'*Ts;
u = ones(nT+1,1);
 
% Simulation
y = lsim(sys,u,t);
sim_data = table(t, u, y, ...
    'VariableNames', {'t','u','y'})
 
figure
subplot(2,1,1)
plot(sim_data.t, sim_data.y, 'o-')
grid on
legend('y(k)')
subplot(2,1,2)
stairs(sim_data.t, sim_data.u, 'LineWidth',2)
grid on
legend('u(k)')
xlabel('t')

sim_data =

9×3 table

t u y

_ _ ______

0 1 0

1 1 0

2 1 0.4

3 1 0.72

4 1 0.976

5 1 1.1808

6 1 1.3446

7 1 1.4757

8 1 1.5806

I've read the documentation, tried looking for examples, ...

sys = idpoly(A,B,C,D,F,NoiseVariance,Ts)

What am I doing wrong?

Answer 1

[Bill Tubbs]

Maybe lsim is not the right function to use. I solved the problem by using sim instead, which has options including to add noise:

% Simulation
opt = simOptions('AddNoise',true);
y = sim(sys,u,opt);

I didn't know about sim. According to the documentation, the differences between the two functions are:

y = sim(sys,udata) returns the simulated response of an identified model using the input data, udata.

whereas:

y = lsim(sys,u,t) simulates the (time) response of continuous or discrete linear systems to arbitrary inputs.

Not sure I understand the differences...