for simulation of pid controller what should I use N filter coefficient value 1 or 100?

for simulation of pid controller what should I use N filter coefficient value 1 or 100?

Im tuning PID Controller for buck converter voltage regulation, can I use N value 1 or 100? or 1000? 5000?

Answer 1

[Sam Chak]

Hi @SASANK DAS,

I don't know your Buck Converter model. However, in this example, the filter divisor N is 751. Generally, the value for N is high. Since you asked about the value for N, then I guess you designed yours using the ideal form:

If your theoretical ideal gives a good performance on paper, then you should make this term in the denominator of the derivative filter relatively small, because

% Buck Converter Transfer Function
V  = 100;
C  = 1e-6;
L  = 2.2e-3;
R  = 500;
Gp = tf(V/(C*L), [1 1/(R*C) 1/(C*L)])

Gp =
 
         4.545e10
  -----------------------
  s^2 + 2000 s + 4.545e08
 
Continuous-time transfer function.

margin(Gp)      % Stable but Phase margin is very small, oscillatory response is expected

step(Gp)        % as confirmed by the step response

% standard-form PID with 1st-order derivative filter
Kp = 0.03;          % proportional gain
Ti = 3.6e-6;        % integral time
Td = 0.0006;        % derivative time
N  = 751;           % filter divisor
Gc = pidstd(Kp, Ti, Td, N)

Gc =
 
             1      1              s      
  Kp * (1 + ---- * --- + Td * ------------)
             Ti     s          (Td/N)*s+1 

  with Kp = 0.03, Ti = 3.6e-06, Td = 0.0006, N = 751
 
Continuous-time PIDF controller in standard form

margin(Gc*Gp)       % Phase margin is improved to approximately 60 deg

% closed-loop system and check if no RHP poles
Gcl = zpk(feedback(Gc*Gp, 1))

Gcl =
 
           1.0255e12 (s^2 + 2034s + 4.623e08)
  -----------------------------------------------------
  (s^2 + 2024s + 4.624e08) (s^2 + 1.252e06s + 1.025e12)
 
Continuous-time zero/pole/gain model.

tau = 4e-5;
[u, t] = gensig('square', tau, 2*tau, tau/2^10);
lsim(Gcl, u, t), ylim([-1 2]), grid on

S = stepinfo(Gcl)

S = struct with fields:
         RiseTime: 1.8759e-06
    TransientTime: 5.9018e-06
     SettlingTime: 5.9018e-06
      SettlingMin: 0.9168
      SettlingMax: 1.0846
        Overshoot: 8.4647
       Undershoot: 0
             Peak: 1.0846
         PeakTime: 3.9736e-06