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Euler Integration Method for Dynamic System Simulation

Seperti pada metode backward difference, untuk mensimulasikan sistem dinamik menggunakan metode integrasi euler, maka langkah-langkah yang dilakukan adalah:

    1. Misalkan sistem yang akan disimulasikan adalah seperti gambar sebagai berikut.

    2. Mengubah persamaan fungsi alih dengan persamaan state space.

    3. Menerapkan metode integrasi euler ke tiap persamaan statusnya.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                                       mensimulasikan                                                        %%
%%                                                        sistem dinamik                                                         %%
%%                                                         y/u=1/(s^2+5)                                                          %%
%%                                dengan menggunakan metode integrasi euler                                      %%
%%                                           dengan mengubah ke persamaan                                            %%
%%                                                 state spacenya menjadi                                                   %%
%%                                                             dx1/dt=x2                                                           %%
%%                                                          dx2/dt=-5x1+u                                                        %%
%%                                                                  y=x1                                                             %%
%%                                        maka dengan menerapkan metode euler                                     %%
%%                                                          persamaan menjadi                                                %%
%%                                                       x1(k)=x1(k-1)+dt*x2(k-1)                                            %%
%%                                                 x2(k)=x2(k-1)+dt*(-5*x1(k-1)+u(k-1))                                  %%
%%                                                                y(k)=x1(k)                                                        %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear;
x=linspace(0,10,1000);
x1(1)=0; %nilai awal=0
x2(1)=0; %
u(1)=0;
dt=0.01;
for i=2:1000
u(i)=1; %input step satuan
x2(i)=x2(i-1)+dt*(-5*x1(i-1)+u(i-1));
x1(i)=x1(i-1)+dt*x2(i-1);
y(i)=x1(i);
end
plot(x,x1);
title('Simulasi Sistem Dinamik Menggunakan Integrasi Euler');
xlabel('Detik');
ylabel('Magnitude')
 

Hasil simulasinya adalah sebagai berikut

Download file Matlab

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