Given a transfer function Hs s 2ss2 750s 14 calculate th

Given a transfer function: H(s) = s + 2/s(s^2 + 7.50s + 14), calculate the number and location of all poles and zeros. Recall that the poles are the squareroots of the denominator polynomial and the zeros are the squareroots of the numerator polynomial. Given a transfer function: H(s) = 26/s(s^2 + 2s + 26), calculate the number and locations of all poles and zeros.

Solution

(a)

There are 3 poles and 1 zero

The zeros are -2

The poles are 0 -4 -5

The roots of poles and zeros in MATLAB are as follows:

>> n1=[1 2];
>> roots(n1)

ans =

    -2

>> d1=[1 7.5 14 0];
>> roots(d1)

ans =

         0
   -4.0000
   -3.5000

(b)

There are 3 poles and no zeros

The poles are 0 -1 + 5i and -1 - 5i

The roots of poles in MATLAB are as follows:

>> d2=[1 2 26 0];
>> roots(d2)

ans =

        0         
-1.0000 + 5.0000i
-1.0000 - 5.0000i