Question

Problem 1: (10 pts) Let Y(S) = 4:0251712s+10 Use Matlab's "tf2zpk" and "residue" commands to: k (s-- (-2) a) (5 pts) Convert y(s) into pole-zero form, 1.e -p -p,Xs-p.)(-p) "polei zero are com en If pole/zero are complex, combine conjugate pairs into 2nd order terms with real coefficients. b) (5 pts) Find the inverse Laplace transform y(t). Please combine conjugate complex parts so that y(t) is real (not complex).

Answer 1

a) matlab code:

clc;

clear all;

close all;

s=tf('s');

num=[2 12 10];

den=[1 9 30 52 48];

[Z,P,K]=tf2zpk(num,den)

The values of Z P and k are given below

Z =

0
0
-5
-1

P =

-4.0000 + 0.0000i
-3.0000 + 0.0000i
-1.0000 + 1.7321i
-1.0000 - 1.7321i

K =

2

b)

clc;

clear all;

close all;

syms s

g=(2*s^2+12*s+10)/(s^4+9*s^3+30*s^2+52*s+48);

ilaplace(g)

ans =

exp(-4*t)/2 - (8*exp(-3*t))/7 + (9*exp(-t)*(cos(3^(1/2)*t) + (17*3^(1/2)*sin(3^(1/2)*t))/27))/14