for PI feedback controller with un-unity feedback, final values is off

I have a second-order transfer function, and I am using integral control, but the final value will not settle at the input level (step).

My attempt is below

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s = tf('s');

G = tf(1, [1, 1.4, 1]);

>> ki=1; % I-gain

Dc=ki/s; % I-control with integral gain ki

step(feedback(Dc*G,0.5,-1)); % the 0.5 is what I have in the feedback path and G*Dc is the gain in the forward path.

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The output will not settle at 1. Any suggestions

Answer 1

[Sam Chak]

Hi @Abdulaziz Abutunis

You can fix the issue by scaling the step input to match the gain in the feedback path (H) in order to eliminate the steady-state error.

s   = tf('s');
Gp  = tf(1, [1, 1.4, 1]);
ki  = 1;
Gc  = ki/s;
H   = 0.5;
Gcl = feedback(Gc*Gp, H)

Gcl =
 
             1
  -----------------------
  s^3 + 1.4 s^2 + s + 0.5
 
Continuous-time transfer function.

scaledIn = H;  % scale the step input to match H
tFinal   = 30;
step(scaledIn*Gcl, tFinal)

[Abdulaziz Abutunis]

Thank yo Sam for your response.

I thought there will be some command used to account for that rather than simply scaliing the input.

Thank you again

Aziz

[Sam Chak]

You are welcome, @Abdulaziz Abutunis. Don't forget to 'click-accept' the answer, and feel free to post new questions related to transfer function design problems.