2. Using MATLAB, find the root locus plot of the following loop transfer functio

Question

2. Using MATLAB, find the root locus plot of the following loop transfer functions. Submit the code as well as the root locus plots. (10 points) (10 points) a)T(s) = (s2+4) (s2+s+16) Analog Filters We can use MATLAB tools to find the poles and transfer functions of standard filters: Butterworth Filter This program creates a second order butter worth filter. Run this code and see what it gives you. W-0.01:0.01:1e2: [z, p, k-buttap (2) %% second order Butterworth [num, den]=tfdata (zpk ( z , p ,k), 'v') %%numerator and denominator of %%transfer function %%transfer function sys-tf (num, den) H-freqresp (sys, w) H-permute (H, [3 1 2]) abs_H-abs (H(:,1)) axes ('FontSize',20) plot (log1o (w),20 log10 (abs_H))

Explanation / Answer

% program for root locus
num1=1;
den1=conv([1 0 4],[1 1 16]);
a=tf(num1,den1);

num2=[ 1 -3];
den2=conv([1 5 4],[1 6]);
b=tf(num2,den2);

figure(1)
rlocus(a);
grid on;

figure(2)
rlocus(b)
grid on;

respose plots

(a)

(b)

analog filter

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