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For a particular unity feedback system G(S)=242(S+5)S(S+1)(S2+5S+121)
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Arranging the above equation in time constant form,

G(S)H(S)=242x5(1+S/5)S(1+S)(1+5121S+S21121121

=10(1+S/5)S(1+S)(1+0.041S+S21121)

System consists of quadratic pole

Comparing the denominator (S2+5S+121) with the denominator of standard equation

S2+2ξwnS+w2n,

w2n=121

wn=11 rad/sec

2ξwn=5

ξ=5(2x11)

ξ=0.2

The factors are:

Constant k=10

1 pole at the origin, 1S,

Simple pole, 1(1+S) wc1=1 rad/sec

Simple pole, 1(1+(S/5) wc2=5 rad/sec

Quadratic pole, 1(1+0.041S+S2/121) wc3=11 rad/sec

Magnetic plot.

K=10, 2logk=20dB

Correction factor, -20log2ξ=-20log(2 x 0.2)

=+7.95dB

For phase angle plot,

G(jw)H(jw)=10(1+jw5)jw(1+jw)(1+0.041jw+(j2w2)121)

=10(1+j(w5)(jw(1+jw)(1+0.041jw(w2121))j2=-1

< G(jw)H(jw)=<10+j0<(1+j(w5))(<jw<1+jw<(1+0.041jw(w2121))

<10+j0=0,

<1+jw5=+tan(1)

w5

< 1jw=-90

<1(1+jw)=-tan(1)w

<1/(1+0.041jw-(w^2/121))=tan(1)(0.041w(1(w2/121))

Phase angle table:

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