How to find kp ki values by having pm and gcf in matlab ?

transfer function

Answer 1

[Sam Chak]

Hi @Basava

I guess you are not looking for the analytical formulas for and because you asked in this forum.

So, when the phase margin and the gain crossover frequency are given, you can try numerically designing something like the following example. For more info, look up the documentation of the commands used in this example.

If you find the example helpful, please consider accepting ✔ and voting 👍 on the answer. Thanks a bunch! 🙏

G    = tf(1, [1 2 1])               % plant transfer function

G =
 
        1
  -------------
  s^2 + 2 s + 1
 
Continuous-time transfer function.

wc   = 1;                           % desired gain crossover frequency (rad/s)
opts = pidtuneOptions('PhaseMargin', 45, 'DesignFocus', 'reference-tracking');  % tuning options
C    = pidtune(G, 'PI', wc, opts)   % tuning algorithm

C =
 
             1 
  Kp + Ki * ---
             s 

  with Kp = 1.41, Ki = 1.41
 
Continuous-time PI controller in parallel form.

Gcl  = feedback(C*G, 1)             % closed-loop TF

Gcl =
 
         1.414 s + 1.414
  -----------------------------
  s^3 + 2 s^2 + 2.414 s + 1.414
 
Continuous-time transfer function.

margin(C*G)                         % check if the requirements are met

step(Gcl)                           % step response