Unformatted text preview: n of the damping ratio ⇣ . Since
A hassais 2
smaller ⇣ than
Routh table + then given by B, we have MA > MB where MA is the percent overshoot of A, and MB is
k
G(s) = 2 similarly. For (s) = 1order .systems with the same denominator (characteristic polynomial),
D second +
deﬁned s 1 ,
1 ks+ +
1
s
2 the percent overshoot is larger with a zero than without a zero, so MC > MA . Hence, the system with
2k
1 the of k percent overshoot is C .
Find the rangelargestin which the closedloop system is stable.
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.
6
w
r y
D(s)
− x u G(s)
v H(s) Solution: Since we are interested in the transfer function with input r, s...
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 Winter '09
 IDAN
 Steady State, system S, following systems

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