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41)
a)
Imaginary Axis
Nyquist Diagram
=0,GH=K
=0.89,
GH=1.66K
Real Axis
b)
Imaginary Axis
Nyquist Diagram
=2.3
GH=6K
Real Axis
42)a) The bode plot with
margin is
is shown in figure. The phase margin is
and the gain
Bode Diagram
9989
:
31)
a) Whenever you have a pole between two zeros on the real axis, then the root locus must lie
on the real axis between the pole and one of the zeros for either positive or negative feedback gain. Thus,
the only option to stabilize
9989
21)
a) For
:
, we have:
The response to a unit step with zero initial conditions will be
. To determine
the amount of time it take to settle to within of its final value, we want to find the time
such that
. Thus, we obtain
The 1090% r
9089
11) a) Begin by combining and
at the node between and
:
into an equivalent impedance
. Sum the currents
1
_1
1
1
1
1
1
1
1
1
1
This transfer function is an important result. When we find the equivalent impedance, the circuit becomes a
v
9089
89/10/18 :
12:00
:
51) For the following system,
R
s 10
+
K (s)

C
s ( s 2 4 s 5)
a) Consider
, find values for to have
.
b) Find steady state error to unit ramp.
c) Repeat part (b) with
and explain the effect of this controller.
52
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89/10/1 :
:
41) For the following systems plot the Nyquist diagram and find the stability region for .
a)
b)
42) Consider the following system
R
+
2 e sT
s
2( s 5)

Y
2
s2
a) Plot the Bode diagram and determine the gain margin and ph
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89/8/22 :
:
31) a) Use a Root Locus argument to show that any system having a pole on the positive real axis with a
positive real zero on either side, requires an unstable controller to stabilize it.
b) A plant has a nominal model give
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88/8/5 :
:
21) Consider the system:
Driven with a unit step from zero initial conditions.
a) For
derive expressions for the 1090% rise time and the settling time ,
where the settling is to within an error
from the final value of 1. Ho
9089
89/7/21 :
11)
:
Consider the circuit shown in figure below:
R1
R2
Vi
a)
Vo
C
Calculate the transfer function
b) For the values
3 ,
12 and
10 , find the pole and zero of the system
c) For the value
0 find the time response of
when
is a