Transcribed Text
x1(t)
x2(1)
1 N/m
f(t)
1 kg
1 Ns/m
1 kg
1
Frictionless
Figure 218
1) Find the transfer function, X2/F, for the network shown in Figure 218
R
L
+
vi(t)
C

Figure 46
2) Find the value of R and C in Figure 46, where L = 1H so that a unit step voltage input will cause
a
20%
overshoot and a 1 ms settling time in the voltage across the capacitor.
Amp
Motor
R(s)
E(s)
K1
25
C(s)
s(s + 1)
K2S
Tachometer
Figure 512
3) Find the value of K1 and K2 for the system in Figure 512 which yields a 16% overshoot and a 200 ms settling
time for a unit step input.
4) If a Routh table has two sign changes above the even polynomial and five sign changes
4)
below the even polynomial, how may RHP poles does the system have?
5) What is the percent overshoot of a system with the transfer function H(s) = 2
?
s²+2s+6
5)
6) What is the 1% settling time of a system with the transfer function 2s+1
s²+2s+6
6)
7) What is the natural frequency of a system with the transfer function H(s)= 2s+1
?
s2+2s+6
7)
8) A system has a characteristic equation: q(s)=33+2032+58490. How many roots are in the
8)
RHP?
R(s)
55 + 254 + 45³ + 52 + 4
((s)
+ s² + 5
Figure 211
9) What is the differential equation for the system shown if Figure 211?
9)
I
+
vi(t)
+
1H
1

vo(t)
Figure 212
10) Find the transfer function, Vo/Vi, for the network shown in figure 212
1
1 H
0000
+
vi(1)
+
1

1 F
vo(i)
Figure 213
11) Find the transfer function, Vo/Vi, for the network shown in figure 213 
G2
+
+
+
R o
G1
E
oy

Figure 31(a)
12) What is the transfer function for the system shown in Figure 31(a)
R(s) +
E(s)
38343
C(s)
s(s + 200)

Figure 511
13) Find the settling time for the system in Figure 5 11
the MULTIPLE answers CHOICE. are correct, Choose write the one alternative that best completes the statement or answers the question. If none
"None" in the space provided. (Worth 1 pts each)
of
14) If F(s) (s5)(s6) (s+4)e6s what is f(t)?
14)
A) Ju(t6)
C)
B)
D)
15) Which system is stable, given the follosing characteristic equations?
A) q(s)=s4+6s²+25
15)
B) q(s)=s++8s³+32s²+80s+100
C) Both systems are stable
D) Neither system is stable
Controller
Process
Signal 1
Signal 2
Signal 3
Signal 4
Measurement
Signal 5
Figure 11
16) Many luxury automobiles have thermostatically controlled airconditioning systems for the
comfort of the passengers. Figure 11 can be used to represent such a system where the driver sets
16)
the desired temperature using a dashboard panel. Which element is the process?
A) The measured temperature
B) The driver
C) The automobile cabin
D) The temperature sensor
17) Many luxury automobiles have thermostatically controlled airconditioning systems for the
comfort of the passengers. Figure 11 can be used to represent such a system where the driver sets
17)
the desired temperature using a dashboard panel. Which element is the Signal 3?
A) The measured temperature
C) The error signal
B) The automobile cabin temperature
D) The desired temperature set by the driver
18) Many luxury automobiles have thermostatically controlled airconditioning systems for the
comfort of the passengers. Figure 11 can be used to represent such a system where the driver sets
18)
the desired temperature using a dashboard panel. Which element is the controller?
A) The driver
C) The measured temperature
B) The temperature sensor
D) The automobile cabin
19) A laser is controlled by an input current to yield the power output. A microprocessor compares
the desired power level with a measured signal proportional to the laser power output obtained
19)
from a power sensor. The microprocessor generates the input current to the laser based upon this
comparison. Using the diagram in Figure 11, which element is the controller?
A) The microprocessor
B) The power sensor
C) The measured signal
D) The laser
+
R(s)
3
1
Y(S)
S + 7
S
2
+
Figure 23
Y(s)
20) What is the transfer function, for the system shown in Figure 23?
20)
R(s)
A) T(s)= 2s+3
3
B) T(s)=
C) 2s+3
D) 3
s2+13s+3
s2+13s+3
s²+7s+3
s²+7s+3
9
1
1
S + 6
S + 5
/
R
920 Y
4

I
Figure 24
21) What is the cofactor for path P1 from R to Y for the signal flow graph shown in Figure24°
21)
A) 41=1  15 1
B) A1=129
s+6
D) Both A and C are correct
3
e 26
22) What is the transfer function from R to Y for the signal flow graph shown in Figure 26?
kGaGbGc
kGaGbGc
A)
13Ga3Gb2Gc+6GaGc+6GbGc
B)
13Ga3GaGb2Gc+6GaGc+6GaGbGc
kGaGbGc
kGaGbGc
C)
1+3Ga3GaGb2Gc6GaGc+6GaGbGc 
D)
1+3Ga3Gb2Gs6GaGc+6GbGc 
K
1
Go
Gb
Gc
Gd
Ro
o
Y
3
2
2
Figure 27
23) What is the transfer function from R to Y for the signal flow graph shown in Figure 27?
2
GaGbGcGd
GaGbGcGd+kGa
A)
B)
13Gak(2Gb2Gc)+6GaGc
13Gak(2Gb2Gc)
GaGbGcGd+kGa(1+2Gc
GaGbGcGd+kGa(12Gc)
D)
+3Ga+2Gb+2Gc+6GaGc
13Ga2Gb2Gc+6GaGo
TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. (Worth 1 pts each)
24) A control system is an interconnection of components that will provide a desired system response.
24)
25) The transfer function reprents the ratio of the time based output to the time based input.
25)
26) A second order system is characterized by two values, the natuarl frequency and the damping
26)
ratio.
27) An underdampled system will not oscillate.
27)
28) An openloop actuator control to obtain system uses a controller to compare the output to the input. The result is
28)
fed to an the desired response.
29) A second order system is characterized by two values, the natuarl frequency and the damping
29)
ratio.
30) In order to develop the differential equations for a system, the engineer must first understand the
30)
physical laws associated with the system.
31)
31) A first order system reaches 37% of its final value in one time constant.
32)
32) A system with impulse response h(t) is BIBO (bounded input bounded output) stable if and only if
80
s /h(T) dT=0.
00
33)
33) A necessary condition for stability is that all the coeficients of the characteristic polynomial be
positive.
R(s) +
E(s)
C(s)
G(s)

Figure 71
1) What is the %O.S., settling time, and steadystate error to a unit step input for the system in Figure 71  if
5000
s(s+75)
2) Design the values of n,K, & a for the system in Figure 71 where
K
G(s)=
to meet the following requirements: 1) Kz=110; and 2) %O.S. = 12%.
sn(s+a)
R(s)
+
K
((s)
s(s + 1)
1Os
K
Figure 73
3) Design the value of K for the system in Figure 73 so that an input of u(t) will have a steadystate error of 0.1.
Current Compensator
[s + 5)
F
C
G
C(s) =
1.42e+003
X
(s + 15.2)
H

FS
Closed
X
Root Locus
Pole Values:
5.06
13.2 + 1.88i
OK
*
System Data
83
System Name:
untitled
Plant Model: untitledG
Zeros:
Poles:
1
10
20
<none>
8
6
4
I
2
Figure 910
4) Design a lag compensator for the system in Figure 910 that will improve the steady  state error by a factor of
5.
</none>Current Compensator
219
F
C
G
Q(s) =
H
FS
Closed
X
Root Locus
Pole Values:
13.1
OK
System Data
x
System Name:
untitled
Plant Model: untitledG
Zeros:
Poles:
<none>
5
5
10
11
5
Figure 912
5) Design a lead compensator for the system in Figure 912 that will place the dominant secondorder  ro
4.61+j7.634..
</none>6) What is the static acceleration error constant for a unity feedback control system whose
e
forward transfer function is G(s)
?
S3(st7)(s+14)(s+19)
R(s) +
E(s)
C(s)
G(s)

Figure 71
7) What is the steadystate  error for the system in Figure 71  if G(s)=
15(s+2)(s+8)
and
7)
(2(s+8)(s2+5s+15
r(t)=tu(t)?
8) Find the value of a which will yield Kz=5,000 for the system in Figure 71  if
8)
G(s)=
100500(s+5)(s+14)(s+23)
s(s+27)(s+a)(s+33)
9) What value of K will yield a steadystate  error of 0.08 for the system in Figure 71 if
9)
and r(t) =
27tu(t)?
s(s+6)(s+9)(s+22)
10) What is the static velocity error constant for the system in Figure 71  if G(s)=
10)
250(s+1)(s+5)
?
s(s+2)(s²+5s+10)
X
X
Figure 811
11) Using figure 811, sketch the general shape of the root locus for the polezero  plot shown.
11)
R(s)
+
((s)
G(s)

Figure 813
12) Sketch the root locus for the system shown in figure 813  when G(s)= K(s+10)(s+20)
12)
(s+30)(s²20s+200
13) Sketch the root locus for the system shown in figure 813 when G(s)
K(s+8)
(s+2)(s+4) (s+6)
13)
Current Compensator
(s+5)
1.42e+003
F
C
G
C(s) =
X
(s + 15.2)
H
FS
Closed
x
Root Locus
Pole Values:
5.06
13.2 + 1.88i
1.9 + 3.29i
OK
*
System Data
@
83
System Name:
untitled
Plant Model: untitledG
Zeros:
Poles:
I
<none>
8
10
20
6
4
2
igure 910
14) What is thedamping ratio for the system shown in Figure 910? 
</none>Current Compensator
(s + 0.1)
F
C
G
C(s) =
5.84
X
S
H
x
FS
Closed
a
X3
Root Locus
Pole Values:
0.0612
OK
System Data
x
System Name:
untitled
Plant Model: untitledG
Zeros:
Poles:
<none>
4
1
1
1
gure 914
15) What is the error constant for the system shown in Figure 914?
</none>MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. If none of
the answers are correct, write "None" in the space provided. (Worth 1 pts each)
16) How can you determine where the root locus crosses the imaginary axis?
16)
A)
Search
along the imaginary axis for points that have odd multiples of 180° angles to the
openloop poles and zeros.
B) Apply RouthHurwitz to the openloop transfer function's characteristic equation.
C) Apply RouthHurwitz to the closedloop transfer function's characteristic equation
D) Search along the imaginary axis for points that have odd multiples of 180° angles to the
closedloop poles and zeros.
E) Both A & Care correct.
17) Which compensator represents a lag controller?
17)
A) Gd(s)Sto.05
B)
s+0.01
C)
D) Gds)=5+5
S
18) A unity feedback control system whose forward transfer function is
18)
S3(st7)(s+14)(++19)
is what type system?
A) Type 3
B) Type 2
C) Type 0
D) Type 1
19) Which rules for plotting the root locus change depending upon whether the system is a
19)
positivefeedback or a negativefeedback system?
A) Realaxis segments.
B) Symmetry.
C) Number of branches.
D) Starting and ending points.
R(s) +
E(s)
C(s)
G(s)

Figure 71
20) What is the system type for the system in Figure 71  if
20)
G(s)_K(S2+65+6),
(s+5) 2 (s+3)
A) Type 2
B) Type 1
C) Type 3
D) Type 0
"RUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. (Worth 1 pts each)
21) The Type number of a system is the same regardless whether you look at it relative to a control
21)
input or a disturbance input.
22) The poles and zeros of a system change as the gain of the system changes.
22)
23) A PID compensator requires a PD compensator cascaded with a PI compensator.
23)
24) Steady state error is only relevant for stable systems
24)
25) The angle from a point on the root locus to all the zeros of the openloop transfer function minus
25)
the angle to all the poles of the openloop transfer function is equal to an odd multiple of 180°.
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