Effect of Zeros and Poles

* Transfer Function
, wn=2, jeta=1/2

1. Additonal Zeros


[code matlab]
clear, cla                       % initialize
wn=2; je=1/2;
a=[0.5, 1, 5, 10, 100];         % Zero Position
den=[1 2*je*wn wn^2];
for i=1:5
    num(i,:)=wn^2*[1 a(i)*je]/(a(i)*je);
    sys=tf(num(i,:),den);       % Transfer Function
    step(sys)                   % Step Response
    hold on
end
grid on
legend(‘a=0.5′,’a=1′,’a=5′,’a=10′,’a=100’)
[/code]
2. Additonal Poles


[code matlab]
clear, cla
wn=2; je=1/2;
a=[1 2 5 10 100];
num=wn^2;
for i=1:5
    den(i,:)=conv([1 2*je*wn wn^2],[1 a(i)*je]);
    sys=tf(num*a(i)*je,den(i,:));
    step(sys);
    hold on
end
grid on
den=[1 2*je*wn wn^2];
sys=tf(num,den);
step(sys)
legend(‘a=1′,’a=2′,’a=5′,’a=10′,’a=100′,’Original’)
[/code]