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Backward Difference Method for Dynamic System Simulation

Untuk mensimulasikan sistem dinamik menggunakan metode backward difference, maka langkah-langkah yang dilakukan adalah:

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

    2. Mensubstitusikan variabel S dengan (1-Z^-1)/dt.

    3. Menuliskan program dalam Matlab M-file berikut.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                                mensimulasikan                                                               %%
%%                                                 sistem dinamik                                                                %%
%%                                                   y/u=1/(s^2+5)                                                                %%
%%                                     dengan mensubstitusi s=(1-z^-1)/dt                                               %%
%%                                               persamaan menjadi                                                           %%
%%                                        y/u=dt^2/(1+5dt^2-2z^-1+z^-2)                                                    %%
%%                                    y(k)=(2y(k-1)-y(k-2)+(dt^2)u(k))/(1+5dt^2)                                        %%
%%                                                                                                                                       %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear;
x=linspace(0,10,1000);
y(1)=0; %nilai awal=0
y(2)=0; %
dt=0.01;
for i=3:1000
     u(i)=1; %input step satuan
     y(i)=(2*y(i-1)-y(i-2)+(dt^2)*u(i))/(1+5*dt^2);
end
plot(x,y);
title('Simulasi Sistem Dinamik Menggunakan Bacward Differensi');
xlabel('Detik');
ylabel('Magnitude')
 

Hasil simulasinya adalah sebagai berikut

Download file Matlab

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