EE370 Old Exams2
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Transcript of EE370 Old Exams2
1
EE370/01 Examination No. 2 Fall 2006/07
Kuwait University
Electrical Engineering Department
Name : ………………………………………
Student I. D. : …………………………………….…
Signature : …………………………………….…
Problem No. Grade
1 25
2 25
3 25
4 25
Total
100
Problem 1 (25 points):
A) (10 points) Sketch the root locus for the unity negative feedback system with the open
loop transfer function ( 4)
( )( 2)( 4)
k sG s
s s
B) (10 points) Find the breakaway point and/or the break in point
C) (5 points) Find the point where the root locus crosses the jw-axis
2
Problem 2 (25 points): Use the following root locus for a unity negative feedback system
to answer the following questions.
A) (5 points) Find the range of k for which the system is stable?
B) (5 points) Can you find the value of k that will yield zero steady state error
for a step input (yes or no)? Why?
C) (5 points) Show the point on the root locus where the steady state error due to a ramp
input is minimum?
D) (5 points) can you find the value of k so that the peak time of the system is 0.1 sec
(yes or no)? Why?
E) (5 points) choose the simplest type of controller to yield 4 sec settling time? Do not
design the controller.
Problem 3 (25 points): Use the root locus technique to design a PID controller for the unity
negative feedback system with open loop transfer function 1
( )( 2)( 4)
G ss s
to yield:
Zero steady state error due to a step input
0.6 settling time
10% overshoot.
Show all the design steps.
Problem 4 (25 points): Given ( 2)
( )( 4)( 1)
sG s
s s
, use asymptotic approximations to
A. (10 points) Sketch the Bode plot of the magnitude
B. (10 points) Sketch the Bode plot of the phase
C. (5 points) Consider ( )kG s , find the value of k so that the phase margin of the closed loop
system is zero.
Root Locus
Real Axis
Imag
inar
y A
xis
-10 -8 -6 -4 -2 0 2 4-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
EE370/01 Examination No. 2 Fall 2008/09
(50 minutes)
Kuwait University
Electrical Engineering Department
Name : ………………………………………
Student I. D. : …………………………………….…
Signature : …………………………………….…
Problem 1 (25 points): Sketch the root locus of the unity negative feedback system with the open
loop transfer function 2 2 2
( )( 4)( 5)
s sG s
s s
. Find the jw -axis crossing and the gain 0k at the
crossing.
Problem
No.
Grade
1
/ 25
2
/ 25
3
/ 25
4
/ 25
Total
/ 100
4
Problem 2 (25 points): Use the asymptotic approximation technique to sketch the Bode plots of
)5()1(
3)(
sss
ssG . Show on the plots: the slope of each line, the gain margin, and the phase
margin of the feedback system?
Problem 3 (25 points): Given the open loop transfer function 1
( )( 4) ( 5) ( 23)
G ss s s
. Use the
root locus technique to design a controller that yields 0.05 steady-state error?
Problem 4 (25 points): Given the open loop transfer function )8)(5(
1)(
ssssG . Use the root
locus technique to design a lead controller to yield 20% overshoot and 0.8 sec peak time?
-70 -60 -50 -40 -30 -20 -10 0 10 20-50
-40
-30
-20
-10
0
10
20
30
40
50
System: sysGain: 6.84e+003
Pole: 0.0546 + 15.1iDamping: -0.00362Overshoot (%): 101
Frequency (rad/sec): 15.1
Root Locus
Real Axis
Imagin
ary
Axis
5
EE370/51 Examination No. 2 Spring 2009
(50 minutes)
Kuwait University
Electrical Engineering Department
Name (Arabic) : ………………………………………
Student I. D. : …………………………………….…
Signature : …………………………………….…
Problem 1 (35 points): For the unity negative feedback system with the open loop transfer function
.
a) (20 points) Sketch the root locus
b) (5 points) Use the root locus to tell if the feedback system is stable or not when ?
Why?
c) (5 points) Find the breakaway and/or break-in points
d) (5 points) Find the angles (in degree) of departure from poles
Problem
No.
Grade
1
/ 35
2
/ 30
3
/ 35
Total
/ 100
6
Problem 2 (30 points): For the unity negative feedback system with open-loop transfer function
. Use the root locus technique to design a lead controller
that
will yield a settling time 1.5 seconds and a peak time 0.6 second. Assume the value of ?
Problem 3 (35 points): Given the Bode plots for a plant in a unity negative feedback system.
Answer the following:
a) (5 points): Is the feedback system stable? Why?
b) (15 points): Find the gain margin, the phase margin, and the plant bandwidth?
c) (5 points): Find the output (of the feedback system at steady state) when the reference signal
is sin(10 )t ?
d) (5 points): Estimate the damping ratio?
e) (5 points): What is the maximum gain you can multiply the plant and still keep the feedback
system stable?
-60
-50
-40
-30
-20
-10
0
10
Magnitude (
dB
)
10-1
100
101
-270
-225
-180
-135
-90
-45
0
Phase (
deg)
Bode Diagram
Frequency (rad/sec)
