CONTROL THEORY
HOMEWORK 3
SOLVED BY:
MAHMOOD HAKKI ISMAEEL
, Q1)
512 ( s +3 )
G ( s )=
s ( s + 16 s+ 256 )
3
G ( s )=
512 ( 3s +1)
1 1
s ( s 2 +16 s +1 )
256 16
3 s
2.097152× 10 ( +1)
3
G ( s )= 2
s (s + 16 s+ 1)
Converting s to w
w
2.097152× 103 ( +1)
3
G ( s )=
w(w 2+ 16 w+1)
mag=20 log 10 ( 2.097152 ×10 ) +20 log 10( √0.333 w +1 ¿ )−20 log 10 ( √ w +256 w +65536 w ) ¿
3 2 2 6 4 2
ph=tan−1 ( 0.333 w ) −90−3 tan−1 (16 w¿)¿
W mag ph
0.01 58.267 -97.341
0.05 44.289 -92.442
0.1 38.272 -90
0.5 24.402 -82.351
1 18.707 -74.401
5 9.612 -52.338
10 7.207 -64.716
50 -11.526 -165.917
100 -23.227 -172.109
1000 -63.11 -177.391
10000 -103.118 -179.720
HOMEWORK 3
SOLVED BY:
MAHMOOD HAKKI ISMAEEL
, Q1)
512 ( s +3 )
G ( s )=
s ( s + 16 s+ 256 )
3
G ( s )=
512 ( 3s +1)
1 1
s ( s 2 +16 s +1 )
256 16
3 s
2.097152× 10 ( +1)
3
G ( s )= 2
s (s + 16 s+ 1)
Converting s to w
w
2.097152× 103 ( +1)
3
G ( s )=
w(w 2+ 16 w+1)
mag=20 log 10 ( 2.097152 ×10 ) +20 log 10( √0.333 w +1 ¿ )−20 log 10 ( √ w +256 w +65536 w ) ¿
3 2 2 6 4 2
ph=tan−1 ( 0.333 w ) −90−3 tan−1 (16 w¿)¿
W mag ph
0.01 58.267 -97.341
0.05 44.289 -92.442
0.1 38.272 -90
0.5 24.402 -82.351
1 18.707 -74.401
5 9.612 -52.338
10 7.207 -64.716
50 -11.526 -165.917
100 -23.227 -172.109
1000 -63.11 -177.391
10000 -103.118 -179.720
