How to do integration in mfile just like in Simulink in matlab?

Question

I am not sure why this code is not working:

if true
  %% PID Test file
% Start the script
clear
clc
kp = 180;
kI = 3200;
kD = 1;
start_time = 0;
step_time = 1;
end_time = 2;
Ts = 0.1;% Sample Time
step_value = 1;
initial_value = 0;
Fn = 50;
  W = 2*pi*Fn;
  Phase = 0;
  Amp = 1;
steps = 1;
if steps
[t,y] = step_fun(start_time,step_time,end_time,Ts,step_value,initial_value);
sim('PID_Test_sim.mdl')
else
  t = start_time:Ts:end_time;
  y = sin(W*t);
  sim('PID_Test_sim.mdl')
end
x_min = start_time;
x_max = end_time;
y_min = initial_value - 1;
y_max = step_value + 1;
figure();
subplot(2,1,1);
stairs(t,y);grid on;hold on; stairs(ScopeData.time,ScopeData.signals(1,2).values,'--r');hold off;%y([y_min y_max]);xlim([x_min x_max]);
subplot(2,1,2);
plot(t,y);grid on;hold on; plot(ScopeData.time,ScopeData.signals(1,2).values,'--r');hold off;%y([y_min y_max]);xlim([x_min x_max]);
Input = y;
time = t;
dt = diff(time);
D = [0,diff(Input.*kD) ./ dt]';
I = [cumtrapz(time,(Input.*kI))]';
%I = [0;(I(1:end-1)+I(2))];
I_test = I;
I_test(I_test>0) = (I(find(I>0,1,'first'))) + I(I>0);
I_test = [0,I_test(1:end-1)];
P = [Input*kp]';
Compare = ScopeData1;
figure();
subplot(3,1,1);
stairs(time,P);grid on;hold on; stairs(Compare.time,Compare.signals(1,1).values,'--r');hold off
subplot(3,1,2);
plot(time,I);grid on;hold on; plot(Compare.time,Compare.signals(1,2).values,'--r');hold off
subplot(3,1,3);
plot(time,D);grid on;hold on; plot(Compare.time,Compare.signals(1,3).values,'--r');hold off
Test = [I ScopeData1.signals(1,2).values time'];
[time,Output] = PID_fun(kp,kI,kD,Input,time,ScopeData1);
figure();
subplot(2,1,1);
stairs(t,y);grid on;hold on; stairs(ScopeData.time,ScopeData.signals(1,2).values,'--r');hold off;
subplot(2,1,2);
plot(time,Output);grid on;hold on; plot(ScopeData.time,ScopeData.signals(1,1).values,'--r');hold off;
Test = [I ScopeData1.signals(1,2).values I_test P ScopeData1.signals(1,1).values D ScopeData1.signals(1,3).values time' Output ScopeData.signals(1,1).values];

It is a very simple code that generate a step signal (in step_fun) and sfterword run the simulation mdl which is a PID controller with step function as input. and then i am running my PID function which is explained later by variables (P,I,D) and in the integration i am becomming different results between simulation and mfile? can you help me with this? ther results are:

     % code
% My integration results of the input signal when kI = 3200;
mfile    simulation
0   0
0   0
0   0
0   0
0   0
0   0
0   0
0   0
0   0
0   0
160 0
480 320
800 640
1120    960
1440    1280
1760    1600
2080  1920
2400  2240
2720  2560
3040  2880
3360  3200

here is some figures with the results:

Best Regards and thx in advance

Answer 1

so finally i did answer my own question :)

the simulation takes the integration on the point beofer the current one t(i-1) yet the cumtrapz takes the integration for the current point t(i) and that is the differents.

as a results i have changes my cumtrapz to cumtrapzt where i calculated the diff(t) till t(i-1) of the given data set (t(end-1))

thx for the help anyway

Answer 2

It's difficult to tell without seeing the Simulink model, but I suspect that in Simulink you are using a variable-step solver, which is able to take much smaller time steps than in your MATLAB file, giving you more accurate results.

If you have the Control System Toolbox, I would suggest that you use the pid command to create the PID in MATLAB and then the step or lsim command to compute the step response, rather than your manual attempt. My guess is that the results will be much closer.