Adding noise to a PID signal

Hi everyone, As the title says I have created a PID system, and am attempting to add random noise over the created signal, but am unsure how to create the noise in this instance as it is not a normal function. Any advice or tips on how do add noise in this domain is greatly appreiated. Code is shown below

clear % housekeeping

clc % housekeeping

num= [1] % num of transfer function

denom= [1 3 1] % denom of transfer function

gp= tf(num, denom) % transfer function

h= [1] ; % feedback

m_nocontroller=feedback(gp, h)

step(m_nocontroller)

hold on

kp=3;

ki=0;

kd=0;

gc=pid(kp, ki, kd)

mc=feedback(gc*gp, h)

step(mc)

grid on

Answer 1

[Pat Gipper]

Hi Nathan,

You can use the lsim command to get a general response of your controller. I think you want to see the response when there is noise added to the input command. The code snippet below will do this for you.

t=(0:.001:7)';% time vector

u=ones(size(t));% input vector

n=randn(size(t));% Normal distributed samples

y=lsim(mc,u+n,t);% System response to step + random noise

% Plot PID response to unit step with added noise

figure;plot(t,y);grid

Sometimes the noise is added in at a separate point in the system as a disturbance. For example, it might be a disturbance that is added after the PID controller. But you would need to re-create your system object with the second input to do this.

[Sam Chak]

Hi @Pat Gipper,

Thank you for the suggested solution to plot the noise-contaminated system output.

Since the output measurement is contaminated by noise, it will affect the PID controller output signal as well. Would you advise @Nathan Ross on how to plot the noise-contaminated PID control signal for a linear system as well?