1. Given the transfer function H(s) = a/ s+a, evaluate settling time and rise ti

Question

1. Given the transfer function H(s) = a/ s+a, evaluate settling time and rise time for the following values of a: 1, 5, and 6. Also, plot the poles. (Hint; Use the step() function to obtain values asked) 2. Given the transfer function G(s) = s + b/s^2+as+b; a. Evaluate percent overshoot, settling time, peak time, and rise time for the following values: a = 4; b = 25. Also, plot the poles and zeros. b. Evaluate percent overshoot, settling time, peak time, and rise time for the following values: a = 2; b = 7. Also, plot the poles and zeros. 3. Discuss the effects of pole location upon the time response for both first- and second-order systems. Discuss any discrepancies between your calculated and experimental values.

Explanation / Answer

count=1;
% Q1
for a=[1,5,6]
h=tf(a,[1 a]);
figure(count)
subplot(2,1,1)
step(h)
x=['step response for a=',num2str(a)];
title(x)
grid on
subplot(2,1,2)
zplane([-a],[]);

y=['zero pole plot for a=',num2str(a)];
title(y)
grid on
count=count+1;
stepinfo(h) % this will provide settling time and rise time

end

%Q2.a
clear all
clc
a=4;
b=25;
g=tf([1 b],[1 a b]);
subplot(2,1,1)
step(g)
stepinfo(g)
subplot(2,1,2)
c=roots([1 a b]);

zplane(c,[-b]);

%%Q2.b

clear all
clc
a=2;
b=7;
g=tf([1 b],[1 a b]);
subplot(2,1,1)
step(g)
stepinfo(g)
subplot(2,1,2)
c=roots([1 a b]);

zplane(c,[-b]);

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