Question

The transfer function of a linear time invariant system is given by

\(\rm H(s) = 2s^4 − 5s^3 + 5s +2\)

The number of zeros in the right half of the s-plane is ________.

Answer 1

Given \({\rm{H}}\left( {\rm{s}} \right) = 2{{\rm{s}}^4} - 5{{\rm{s}}^3} + 5{\rm{s}} +2\)

Obtain RH criteria we get

s4	2	0	-2
s3	-5	5
s2	2	+2
s1	10	0
s0	2

Auxiliary Equation AE:

\(2{{\rm{s}}^2}{\rm{\;}}+{\rm{\;}}2{\rm{\;}} = {\rm{\;}}0\)

\({\rm{\;and\;}}\frac{{{\rm{d(AE)}}}}{{{\rm{ds}}}} = 4\)

∴ No. of sign changes in first columns = 2

∴ No. of roots in Right Half of s – plane = 2