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Bilinear Method for Dynamic System Simulation

Untuk mensimulasikan sistem dinamik menggunakan metode bilinier, langkahlangkahnya adalah sama seperti pada backward difference, bedanya adalah variabel penggantinya, yaitu

 s=(2/dt)*((1-z^-1)/(1+z^-1)):

1. Masih dengan permisalan yang sama yaitu akan mensimulasikan sistem seperti gambar sebagai berikut.

 2. Mensubstitusi variabel s dengan (2/dt)*((1-z^-1)/(1+z^-1)).

 3. Menuliskan kode berikut pada m-file matlab editor.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                                                              Mensimulasikan sistem dinamik                                                   %%
%%                                                                menggunakan metode bilinear                                                     %%
%%                                                                     yaitu mensubstitusikan                                                          %%
%%                                                                     s=(2/dt)(1-z^-1)/(1+z^-1)                                                         %%
%%                                                                   misalkan fungsi alih adalah                                                       %%
%%                                                                      1/(s^2+5) dengan dt=0.1                                                        %%
%%                                                                 sehingga persamaan menjadi                                                      %%
%%                                             y(k)=(7.9/4.05)y(k-1)-y(k-2)+0.01u(k)+0.02u(k-1)+0.01u(k-2)                               %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear;
x=linspace(0,10,100);
u(1)=0;
u(2)=0;
y(1)=0;
y(2)=0;
for k=3:100
u(k)=1;
y(k)=(7.9/4.05)*y(k-1)-y(k-2)+0.01*u(k)+0.02*u(k-1)+0.01*u(k-2);
end
plot(x,y);
title('Simulasi Sistem Dinamik Menggunakan Bilinear');
xlabel('detik');
ylabel('magnitude');
axis([0 10 -0.5 2]);
 

Hasil simulasinya adalah sebagai berikut

Download file Matlab

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