Unformatted text preview: ction with input r
/R Hence, we start
block diagramdown the equation for= 0). follows:
writing to be zero (w = v Y as By deﬁnition of e, we see that E/R = 1 Y /R. Hence, we start
writing down the equation for Y as follows:
Y = GU = GD(R Y = GU = GD(R H Y ). H Y ).
7 7 Solving for the ratio Y /R, we have
Y (s)
GD
=
.
R (s)
1 + GDH
The transfer function from r to e is
Q(s) := GD
s(s2 + (11 b)s + 10 a)
=3
1 + GDH
s + 11s2 + 10(b + 1)s + 10a E (s)
=1
R (s) 28. Find the condition on the parameters a and b such that the closedloop system is stable.
Solution: Routh table is given by
1
11
c
10a 10(b + 1)
10a where
c = 110(b + 1) 10a. The system is stable iff c > 0 and 10a > 0 hold, or equivalently,
0 < a < 11(b + 1)
29. What is the system type for tracking? Assume stability and a 6= 0.
Solution: When a 6= 10, the transfer function Q(s) has one zero at the origin, and hence it is Type 1
When a = 10 and b 6= 11, there are two zeros at the origin and Q(s) is Type 2 If a = 10 and b = 11, then there are three zeros at the origin...
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 Winter '09
 IDAN
 Steady State

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