Applying white noise to PID model in matlab

Question

I'd like to exclusively apply a white noise signal to a PID model in matlab. I know how to both generate this signal and how to add white noise to the other signals, but I have no idea how to apply only the white noise.

I tried to use lsim function but this one needs signals in time domain and in my white noise signal I have only values and samples. Below is how I created white noise (X):

L=100000; %Sample length for the random signal
mu=0;
sigma=2;
X=sigma*randn(L,1)+mu;

Answer 1

The solution depends on where you want to add the noise:

• Noise on the input

  lsim(sys, u+X, t);
  

• Noise on the output

  Y = lsim(sys, u, t) + X;
  

• Additive process noise: in this case you need to use sim, which is an extension of lsim

  Useful links:

  • Overview of the simulated model
  • Example