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HW6Problem2

# HW6Problem2 - clc clear all close all num=[0 0.6042 0...

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clc; clear all ; close all ; num=[0 0.6042 0 4.1572 0 6.1591]; den=[1 3.4630 7.1704 10.2787 8.6926 6.1591]; %% Part a lambda2=roots(den) % S domain roots lam=roots(num) % S domain zeros %% Part b figure() trf=tf(num,den); bode(trf); %% part c figure() %LT=2.*(z-1).*z./(3.*z-1); for r=0.8:0.05:1 p=1; for th=0:pi/36:2*pi z=r*exp(sqrt(-1)*th); LT(p)=(2.*(z-1).*z)./(3.*z-1); p=p+1; end hold all ; plot(real(LT),imag(LT)) end for th=0:pi/36:2*pi p=1; for r=0.8:0.05:1 z=r*exp(sqrt(-1)*th); LT(p)=2.*(z-1).*z./(3.*z-1); p=p+1;

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end hold all ; plot(real(LT),imag(LT)) end title( 'LambdaT plot' ) Xlabel( 'real axis' ) ylabel( 'Imaginary axis' ) %% Part d T1=0.7; % absolutely unstable T2=0.1; % relatively stable and absolutely stable T3=0.42; % relatively unstable and absolutely stable T=[T1,T2,T3] for j=1:1:3 figure() for r=0.8:0.1:1 p=1; for th=0:pi/36:2*pi z=r*exp(sqrt(-1)*th); LT(p)=2.*(z-1).*z./(3.*z-1); p=p+1; end hold all ; plot(real(LT),imag(LT)) end for th=0:pi/36:2*pi p=1; for r=0.8:0.05:1 z=r*exp(sqrt(-1)*th); LT(p)=2.*(z-1).*z./(3.*z-1); p=p+1; end hold all ;
plot(real(LT),imag(LT)) end title( 'LambdaT plot and poles of the system for

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