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

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Abdulaziz Abutunis
Abdulaziz Abutunis 2023-10-17
评论： Sam Chak 2023-10-19
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
--------------------------------------------------
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.
------------------------------------------------------------
The output will not settle at 1. Any suggestions

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Sam Chak
Sam Chak 2023-10-18
Ran in:
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)
  2 个评论
Abdulaziz Abutunis
Abdulaziz Abutunis 2023-10-18
移动：Sam Chak 2023-10-19
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
Sam Chak 2023-10-19
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.

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