How to implement PID anti-windup in my m-file (i.e., without using Simulink)

Hi everyone,

I'm working on my own MATLAB PID code that should be initiated within an external algorithm coded as a function in another m-file.

The PID part (without anti-windup) looks like this one:

%% Initialization stage
clc
clear

s = tf('s');
t = (0:0.05:30)';
opt = stepDataOptions('InputOffset', Offset, 'StepAmplitude', 1); 

OLTF = 1/(1.2 * s + 1); % open-loop

%% Defining "closed-loop":
Gm = 1/(0.1*s + 1); 
Kp = 3.71580598721178; % proportional gain
Ki = 3.30711176584135; % integral gain
Kd = 1.80393204651312; % derivative gain
TauD = 0.0; % derivative low-pass filter time constant
Gc = Kp + Ki/s + Kd*s / (TauD * s + 1); % controller transfer function
CLTF = feedback(Gc * OLTF, Gm); % closed-loop 

%% Defining system responses
y = step(CLTF, t, opt);

I'm struggling to implement anti-windup in this m-file code.

I think there is one approach by thinking of it as a parallel transfer function, but I don't have any clue!

Any help is highly appreciated .. Thank you so much

Answer 1

[Sam Chak]

Hi @Ali

Not sure if you are still interested. If the output of is within the range of the actuator, then the anti-windup is probably not needed. Instead of letting , assign a positive value should do the trick. The selected PID gains remain unchanged. is assigned.

The response looks pretty fast when compared to the previous . If the range of the actuator is within , then no saturation occurs.

%% Initialization stage
s    = tf('s');
t    = (0:0.05:5)';
% opt = stepDataOptions('InputOffset', Offset, 'StepAmplitude', 1); 
OLTF = 1/(1.2 * s + 1);                 % open-loop

%% Defining "closed-loop":
Gm   = 1/(0.1*s + 1); 
Kp   = 3.71580598721178;                % proportional gain
Ki   = 3.30711176584135;                % integral gain
Kd   = 1.80393204651312;                % derivative gain
TauD = 1e2;                             % derivative low-pass filter time constant
Gc   = Kp + Ki/s + Kd*s/(TauD*s + 1)    % controller transfer function

Gc =
 
  373.4 s^2 + 334.4 s + 3.307
  ---------------------------
          100 s^2 + s
 
Continuous-time transfer function.

CLTF = minreal(feedback(Gc*OLTF, Gm))   % closed-loop 

CLTF =
 
      3.112 s^3 + 33.9 s^2 + 27.9 s + 0.2756
  ----------------------------------------------
  s^4 + 10.84 s^3 + 39.56 s^2 + 27.95 s + 0.2756
 
Continuous-time transfer function.

%% Defining system responses
% y = step(CLTF, t, opt);
step(CLTF, t)

S    = stepinfo(CLTF)

S = struct with fields:
         RiseTime: 0.4323
    TransientTime: 0.6408
     SettlingTime: 0.6408
      SettlingMin: 0.9059
      SettlingMax: 1.0123
        Overshoot: 1.2305
       Undershoot: 0
             Peak: 1.0123
         PeakTime: 1.0297

Gu = minreal(feedback(Gc, OLTF*Gm))

Gu =
 
  3.734 s^4 + 43.79 s^3 + 67.38 s^2 + 28.23 s + 0.2756
  ----------------------------------------------------
     s^4 + 10.84 s^3 + 39.56 s^2 + 27.95 s + 0.2756
 
Continuous-time transfer function.

step(Gu, t)