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Routh table 1 + GD = 0 ,
is then given by
1
2
1
2k 1+ k+1
2k
Routh table is then given by s+2
s2 + s 1 ✓
◆
k
1+
=0
s , s3 + 2s2 + (k + 1)s + 2k = 0.
s3 + 2s2 + (k + 1)s + 2k = 0. 1 k+1
2
2k
1
So the closedloop system is stable iff k > 0 .
2k
So the closedloop system is r to e :=
.
27. Find the transfer function from stable iff kr> 0 y for the following feedback system, where
27. Find the transfer function from r to e := r y for the following feedback system, where a
1
10
D(s) = + b,
G( s ) =
,
H (s) = 10 .
a
1
s
D(s) = + b,
G( s ) s + 1 ,
=
H (s) = s + 10
.
s s+1 s + 10 We will consider this feedback system for the next six problems.
We will consider this feedback system for the next six problems.
w
r y
D(s)
− x u G(s)
v H(s) Solution: Since we are interested in the transfer function with input r, set all the other inputs in the Solution: Since we are interestedvin 0). By deﬁnition of e, we see that E/R =,1setYall .the other inputs in the
block diagram to be zero (w = = the transfer fun...
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This note was uploaded on 01/27/2014 for the course MAE 171A taught by Professor Idan during the Winter '09 term at UCLA.
 Winter '09
 IDAN

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