written 8.2 years ago by | • modified 8.2 years ago |
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: