control-system/Assignment 6 - Tuning PID

Improved Particle Swarm Optimization and Ziegler-Nicols 1 on PID Tuning

This dir is belong to Control System class contains with Tuning PID with ZN1 and IPSO on motor system.

Software

This program ran in Matlab

IPSO Method

Variables

s = tf('s'); defines s as 'frequency domain' for transfer function and will be used further.

J = 0.01;
b = 0.1;
K = 0.01;
R = 1;
L = 0.5;

Those variable comes from BLDC control system.

c1=2; c2=2; w_max = 1; w_min = 0.1; particles=50; iterations=100;
var=3; e_max = 1; e_min=0.1;

% Search limit
lim_min = 0;
lim_max = 2500;

Variable above is the constant for PSO tuning.

Testing

ITAE Cost Function

Step Response

Ramp Response

Impulse Response

Acceleration Response

Results

Elapsed time is 18.701024 seconds.

Before PSO-PID

        RiseTime: 1.0161
    SettlingTime: 1.8471
     SettlingMin: 0.0819
     SettlingMax: 0.0907
       Overshoot: 0
      Undershoot: 0
            Peak: 0.0907
        PeakTime: 3.0168
         SSError: 0.9095

After PSO-PID

Kp = 853.3161

Ki = 74.1078

Kd = 2.4810e+03

        RiseTime: 9.5287e-04
    SettlingTime: 0.0012
     SettlingMin: 0.9949
     SettlingMax: 0.9976
       Overshoot: 0
      Undershoot: 0
            Peak: 0.9976
        PeakTime: 0.0036
         SSError: 0.0024
       DelayTime: 0.000595

ZN1 Method

Variables

s = tf('s'); defines s as 'frequency domain' for transfer function and will be used further.

J = 0.01;
b = 0.1;
K = 0.01;
R = 1;
L = 0.5;

Those variable comes from BLDC control system.

tic
timeVal=tic;
[y,t] = step(motor);
h = mean(diff(t));
dy = gradient(y, h);                                            % Numerical Derivative
[~,idx] = max(dy);                                              % Index Of Maximum
b = [t([idx-1,idx+1]) ones(2,1)] \ y([idx-1,idx+1]);            % Regression Line Around Maximum Derivative
tv = [-b(2)/b(1); (1-b(2))/b(1)];                               % Independent Variable Range For Tangent Line Plot
f = [tv ones(2,1)] * b;                                         % Calculate Tangent Line

L = tv(1);
T = tv(2);

figure(1)
plot(t, y)
hold on
plot(tv, f, '-r')                                               % Tangent Line
plot(t(idx), y(idx), '.r')
title('Mencari tangent line plant ')% Maximum Vertical
hold off
grid

Process above is to find tangent line and L and T constant

After L and T constant is obtained, the values is used to obtained Kp, Ki, and Kd constant

control = tf(zeros(1,1,5));
sys=tf(zeros(1,1,5));
complete=tf(zeros(1,1,5));

% sistem dengan P
kp = T/L
control(:,:,1)= tf([0 kp 0],[1 0]);

% sistem dengan PI
kp = 0.9*T/L
Ti= L/0.3;
ki = kp/Ti
control(:,:,2)= tf([0 kp ki],[1 0]);

% sistem dengan PID
kp = 1.2*T/L
Ti= 2*L;
ki = kp/Ti
Td = 0.5*L;
kd = kp*Td
control(:,:,3)= tf([kd kp ki],[1 0]);

Testing

Step Response

Ramp Response

Impulse Response

Acceleration Response

Results

Elapsed time is 0.065802 - 0.455767 seconds.

Before ZN1-PID

        RiseTime: 1.0161
    SettlingTime: 1.8471
     SettlingMin: 0.0819
     SettlingMax: 0.0907
       Overshoot: 0
      Undershoot: 0
            Peak: 0.0907
        PeakTime: 3.0168
         SSError: 0.9095

After ZN1-PID

Control P: Kp = 140.9417 Control PI: Kp = 126.8475 ; Ki = 711.9513 Control PID: Kp = 169.13; Ki = 1.5821e+03; Kd = 4.5201

        RiseTime: 0.0676
    SettlingTime: 0.8486
     SettlingMin: 0.8129
     SettlingMax: 1.4349
       Overshoot: 43.4944
      Undershoot: 0
            Peak: 1.4349
        PeakTime: 0.17391
         SSError: -0.0021
       DelayTime: 0.0444

Notes

Contact nanda.r.d@mail.ugm.ac.id for more information

Links

You can access the source code here github.com/nandard/control-system.git