Control System Tuner always selects maximum value

Hey,

I am new to the Matlab Control System Toolbox and want to try out the Control System Tuner but I am facing a weird problem.

This is my control loop:

And I want to tune the PI controller to achieve a stable response. So I have specified the following Step Tracking Goal:

However, the Control System Tuner just gives me the maximum possible gain:

Does someone of you has an idea if I have to adjust the settings somehow or what else could be the reason for this behaviour?

Thanks

Answer 1

[Sam Chak]

Hi @Cedric

The algorithm in Control System Tuner will find the best combination of PI gains that produces the smallest steady-state error.

In your case, by selecting the maximum allowable gain for , the smallest steady-state error is achieved.

However, if a Proportional Controller is placed at the feedback path, and set , the desired response is achieved PERFECTLY!

Gp  = tf(1, [1 -1])

Gp =
 
    1
  -----
  s - 1
 
Continuous-time transfer function.

Gc  = pid(1000);
Gcl = feedback(Gc*Gp, 1)

Gcl =
 
   1000
  -------
  s + 999
 
Continuous-time transfer function.

sse = abs(dcgain(Gcl) - 1)

sse = 0.0010

Alternative solution:

[Cedric]

Thank you for your response.

I am not searching for the solution to this specific control loop but more asking how i can make the CST to find the solution that fits best to the desired response . From my point of view this would be .

[Sam Chak]

Hi @Cedric

Inside the Control System Tuner, there are rules that prevent it from using an unstable zero to cancel out an unstable pole.

Gp  = tf(1, [1 -1])

Gp =
 
    1
  -----
  s - 1
 
Continuous-time transfer function.

Gc  = pid(1, -1)

Gc =
 
             1 
  Kp + Ki * ---
             s 

  with Kp = 1, Ki = -1
 
Continuous-time PI controller in parallel form.

Gcl = feedback(Gc*Gp, 1)

Gcl =
 
   s - 1
  -------
  s^2 - 1
 
Continuous-time transfer function.

ToF = isstable(Gcl)     % 0 means False

ToF = logical
   0

step(Gcl, 40), grid on