Need help writing code for this problem: Problem #1: Consider a system with tran

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Need help writing code for this problem:

Problem #1: Consider a system with transfer function G(s) = Y(s) U(s) s +2os+ (a) Let o,- rad/s, 0.6 and the input be a unit step function. Then Y(s) can be written as Y(s) = s(s2 +1.2s +) Find and plot y(t), the inverse Laplace transform of Y(s), using MATLAB. time of the four time responses. time responses. (b) Repeat (a) for ? = l, ç= 1.4, and ? = 0.2, and compare the rise time, overshoot, and settling (c) Repeat (a) for a, = 2 rad/s and compare the rise time, overshoot, and settling time of the two

Explanation / Answer

Answer for a

syms s x
f=1/(s*(s^2+1.2*s+1)
h=ilaplace(f)
ezplot(matlabFunction(h), [1,1000])
Answer for b

syms s x
f=1/(s^2+2*s+1)
h=ilaplace(f)
ezplot(matlabFunction(h), [1,1000])

sys = tf([1],[1 2 1]); step(sys)

syms s x

f=1/(s*(s^2+2.8*s+1))

h=ilaplace(f)

ezplot(matlabFunction(h), [1,1000])

sys = tf([1],[1 2.8 1]); step(sys)

syms s x

f=1/(s*(s^2+0.4*s+1))

h=ilaplace(f)

ezplot(matlabFunction(h), [1,1000])

sys = tf([1],[1 0.4 1]); step(sys)

Answer for c

syms s x

f=4/(s*(s^2+4*s+4))

h=ilaplace(f)

ezplot(matlabFunction(h), [1,1000])

sys = tf([4],[1 4 4]); step(sys)

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