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MEEN 364 Exam 2 Spring 2014
Texas A&M University
Department of Mechanical Engineering
MEEN 364 Dynamic Systems and Controls
Exam 2 Apr. 3, 2014, 7 PM to 9 PM, CHEM Rm100 Name : Please
circle your section below: Section (Lab Time): 501 (M 1:50-4:40 PM)
502 (T 8:00-10:50 AM) 503 (T 2:20-5:10 PM)
504 (W 1:50-4:40 PM) 505 (R 11:10-2:00 PM) 506 (W 8:00-10:50
AM)
507 (T 11:10-2:00 PM) 508 (R 2:20-5:10 AM)
NOTE: NO CALCULATORS, BOOKS, NOTES OR MOBILE PHONES "On my
honor, as an Aggie, I have neither given nor received unauthorized
aid on this academic
work."
Signature: ________________________________________
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MEEN 364 Exam 2 Spring 2014
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MEEN 364 Exam 2 Spring 2014
Problem 1 [20 points] A) Find the Laplace transform of the
following signal:
() = () +
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MEEN 364 Exam 2 Spring 2014
B) Use the Laplace Transform to find the solution () to the
following differential equation:
() () + () = with initial conditions (0) = 0 and (0) = 1.
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MEEN 364 Exam 2 Spring 2014
Problem 2 [20 points] Consider the following block diagram:
A) Determine the transfer function between the input disturbance
() and the output (). B) Determine the transfer function between
the reference () and the output (). C) For the transfer function
from part B, if = 3, determine the location of the poles and
zeroes.
D) Using the transfer function from part B, if = 3, determine
the final value, if any, of the system output for a unit step
reference input?
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MEEN 364 Exam 2 Spring 2014
Problem 2 (continued)
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Problem 2 (continued)
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MEEN 364 Exam 2 Spring 2014
Problem 2 (continued)
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MEEN 364 Exam 2 Spring 2014
Problem 3 [20 Points] Consider the following mass-slider-bar
system:
A slider of mass m, is shown connected to the walls by two
springs of stiffness k, on either side. The sliders initial
position is the static equilibrium position. Viscous friction
between the slider and the ground is modeled by the coefficient b.
Attached to the center of the block at a pivot point is a slender,
uniform bar of mass m, and length l. There is viscous damping at
the pivot point as well modeled by the coefficient, c. Assume the
moment of inertia for the bar about its mass center to be IG. The
equations of motion are given by the following equations: Slider: 2
+ 12 cos 2 sin + + 2 = 0 Bar:
+ 142 + 12 cos + + 12 sin = 0 A) Determine the equilibrium
position(s) of the system.
B) Select one of the equilibrium position(s) of the system, and
linearize the system about this
point.
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MEEN 364 Exam 2 Spring 2014
Problem 3 (continued)
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Problem 3 (continued)
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MEEN 364 Exam 2 Spring 2014
Problem 3 (continued)
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MEEN 364 Exam 2 Spring 2014
Problem 4 [20 Points] Consider the block diagram shown
below:
It is desired to place the dominant poles of the closed loop
system at the locations shown below:
sin(30) = 12 cos(30) = 32
Assume second order dominance, with the third pole of the
closed-loop system placed at a distance 10 times the distance of
the dominant poles from the imaginary axis. A) Determine the values
of the constants, Kp, Kd and KI to place the poles as desired. B)
Neglecting the effect of the closed loop zeroes, determine the
percent overshoot and the
approximate settling time assuming a unit step input. C)
Determine the final value of (), if one exists, assuming a unit
step input. 13
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MEEN 364 Exam 2 Spring 2014
Problem 4 (continued)
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Problem 4 (continued)
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Problem 4 (continued)
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MEEN 364 Exam 2 Spring 2014
Problem 5 [20 Points] Consider the open loop transfer function
is given as:
() = 49( 2)(0.05 + 1)240()( + 0.1)(2 7 + 49) For this transfer
function:
A) Required: Sketch the combined magnitude plot for the transfer
function (). Clearly label the break point frequencies and the
slope of the asymptotes.
Optional: Sketch the individual magnitude plots in the plot
spaces provided for each term of
the transfer function (). Note: These individual plots are only
to assist in awarding partial credit, if necessary.
B) In the table provided, list the phase contribution of each
term of () as 0 and , and then provide the total phase at these
frequencies. A phase plot of () is NOT required.
C) Is this system stable? Is this system minimum-phase? Briefly
justify your answers.
x log 10 (x) x log 10 (x) x log 10 (x) x log 10 (x) x log 10
(x)0.1 -1.000 2.1 0.322 4.1 0.613 6.1 0.785 8.1 0.9080.2 -0.699 2.2
0.342 4.2 0.623 6.2 0.792 8.2 0.9140.3 -0.523 2.3 0.362 4.3 0.633
6.3 0.799 8.3 0.9190.4 -0.398 2.4 0.380 4.4 0.643 6.4 0.806 8.4
0.9240.5 -0.301 2.5 0.398 4.5 0.653 6.5 0.813 8.5 0.9290.6 -0.222
2.6 0.415 4.6 0.663 6.6 0.820 8.6 0.9340.7 -0.155 2.7 0.431 4.7
0.672 6.7 0.826 8.7 0.9400.8 -0.097 2.8 0.447 4.8 0.681 6.8 0.833
8.8 0.9440.9 -0.046 2.9 0.462 4.9 0.690 6.9 0.839 8.9 0.9491.0
0.000 3.0 0.477 5.0 0.699 7.0 0.845 9.0 0.9541.1 0.041 3.1 0.491
5.1 0.708 7.1 0.851 9.1 0.9591.2 0.079 3.2 0.505 5.2 0.716 7.2
0.857 9.2 0.9641.3 0.114 3.3 0.519 5.3 0.724 7.3 0.863 9.3 0.9681.4
0.146 3.4 0.531 5.4 0.732 7.4 0.869 9.4 0.9731.5 0.176 3.5 0.544
5.5 0.740 7.5 0.875 9.5 0.9781.6 0.204 3.6 0.556 5.6 0.748 7.6
0.881 9.6 0.9821.7 0.230 3.7 0.568 5.7 0.756 7.7 0.886 9.7 0.9871.8
0.255 3.8 0.580 5.8 0.763 7.8 0.892 9.8 0.9911.9 0.279 3.9 0.591
5.9 0.771 7.9 0.898 9.9 0.9962.0 0.301 4.0 0.602 6.0 0.778 8.0
0.903 10.0 1.000
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MEEN 364 Exam 2 Spring 2014
Problem 5 (continued)
A) Required: Plot of |()|
Optional: Individual Magnitude Plots for each term of ()
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Problem 5 (continued)
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MEEN 364 Exam 2 Spring 2014
Problem 5 (continued)
B) Required: Table of ()
Term Phase for Phase for
Total
C) Is this system stable? Is this system minimum-phase? Briefly
justify your answers.
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Problem 1 (20 points) __________ Problem 2 (20 points)
__________ Problem 3 (20 points) __________ Problem 4 (20 points)
__________ Problem 5 (20 points) __________ Total (100 points)
__________
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