Maybe a mistake in the documentation of function ''robgain''

Please refer to this documentation: robgain

as well as this system:

In the example "Robust Performance of Closed-Loop System", it says that "Create a model of the controller, and build the closed-loop sensitivity function, S. The sensitivity measures the closed-loop response at the plant output to a disturbance at the plant input."

The corresponding codes are:

k = ureal('k',10,'Percent',40);
delta = ultidyn('delta',[1 1]); 
G = tf(18,[1 1.8 k]) * (1 + 0.5*delta);
C = pid(2.3,3,0.38,0.001);
S = feedback(1,G*C);
tf(S)

ans =
 
  s^4 + 1002 s^3 + 1810 s^2 + 1e04 s + 4.337e-15
  -----------------------------------------------
  s^4 + 1002 s^3 + 8691 s^2 + 5.145e04 s + 5.4e04
 
Continuous-time transfer function.

However, when I refer to the documentation of feedback, it seems that the code feedback(1,G*C) actually refers to the closed-loop response at the plant input, instead of that at the plant output. I use the function connect to prove this:

G.InputName = 'e2';
G.OutputName = 'y';
C.InputName = 'e1';
C.OutputName = 'u';
S1 = sumblk("e1 = r - y");
S2 = sumblk("e2 = u + d");
inputs = {'d'};
outputs = {'e2'};
S = connect(G,C,S1,S2,inputs,outputs);

Warning: The following block inputs are not used: r.

tf(S)

ans =
 
  From input "d" to output "e2":
        s^4 + 1002 s^3 + 1810 s^2 + 1e04 s
  -----------------------------------------------
  s^4 + 1002 s^3 + 8691 s^2 + 5.145e04 s + 5.4e04
 
Continuous-time transfer function.

The preceding two results are the same, which prove my assumption.

To measure the closed-loop response at the plant output to a disturbance at the plant input, the codes should be:

S = feedback(G,C);
tf(S)

ans =
 
  From input "e2" to output "y":
                 18 s^2 + 18000 s
  -----------------------------------------------
  s^4 + 1002 s^3 + 8691 s^2 + 5.145e04 s + 5.4e04
 
Continuous-time transfer function.

or in the "connect" version

G.InputName = 'e2';
G.OutputName = 'y';
C.InputName = 'e1';
C.OutputName = 'u';
S1 = sumblk("e1 = r - y");
S2 = sumblk("e2 = u + d");
inputs = {'d'};
outputs = {'y'};
S = connect(G,C,S1,S2,inputs,outputs);

Warning: The following block inputs are not used: r.

tf(S)

ans =
 
  From input "d" to output "y":
                 18 s^2 + 18000 s
  -----------------------------------------------
  s^4 + 1002 s^3 + 8691 s^2 + 5.145e04 s + 5.4e04
 
Continuous-time transfer function.

Please check other documentatins which also use this sensitivity function.

Best regards.

Answer 1

[Paul]

Hi Hongrui,

I agree that the statement on the doc page for that example is incorrect. At the bottom of the page you can click on one of the stars to rate the page, and then (I think) a dialog box will pop up where you can type in some feedback.

Keep in mind that, for this example, the command

feedback(1,G*C)

yields the closed loop transfer function from d to e2 AND from r to e1 (referring to your diagram) as those transfer functions are the same. So the example could be viewed as the sensitivity function at the plant input (in response to a disturbance at the plant input) OR the sensitivity function at the plant output (in response to a disturbance at the plant output).

k = ureal('k',10,'Percent',40);
delta = ultidyn('delta',[1 1]); 
G = tf(18,[1 1.8 k]) * (1 + 0.5*delta);
C = pid(2.3,3,0.38,0.001);
S = feedback(1,G*C);
G.InputName = 'e2';
G.OutputName = 'y';
C.InputName = 'e1';
C.OutputName = 'u';
S1 = sumblk("e1 = r - y");
S2 = sumblk("e2 = u + d");
inputs = {'d','r'};
outputs = {'e2','e1'};
S = connect(G,C,S1,S2,inputs,outputs);
tf(S(1,1))

ans =
 
  From input "d" to output "e2":
        s^4 + 1002 s^3 + 1810 s^2 + 1e04 s
  -----------------------------------------------
  s^4 + 1002 s^3 + 8691 s^2 + 5.145e04 s + 5.4e04
 
Continuous-time transfer function.

tf(S(2,2))

ans =
 
  From input "r" to output "e1":
  s^4 + 1002 s^3 + 1810 s^2 + 1e04 s + 4.337e-15
  -----------------------------------------------
  s^4 + 1002 s^3 + 8691 s^2 + 5.145e04 s + 5.4e04
 
Continuous-time transfer function.

[Cris LaPierre]

To provide feedback directly to MathWorks, please Contct Support: https://www.mathworks.com/support/contact_us.html

[Hongrui]

Thank you!

[Cris LaPierre]

Keep in mind feedback provided through the link I shared gets looked at within 24 hours and routed to the appropriate team. Feedback provided directly on the webpage in not automatically routed through support, so it will be longer before it is seen.

[Paul]

Hi Chris,

That's an interesting comment. I don't see a link on the "contact_us" page that seems explicitly appropriate for comments on documenation, which I think is the only issue at hand. Which one would you suggest? Any idea how much longer it takes if going through the doc page rating?

[Steven Lord]

To report a bug in the documentation to the Support staff using the link Cris posted select the Product Usage area (as it is an "Errors or performance issues" with the documentation.)