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EEL 4652C Control Systems 1 (Spring 2024) Homework 1
Study the “EEL 4652C Midterm E
xam” given in Fall 202
3. The exam’s questions and their solutions are posted for your convenience in the Canvas module “Spring 2024 Homework Assignments”
and in Canvas Assignments. For each of the three problems there are new tasks given in this homework assignment. Each of the problems (and sub-problems) requires some analytical solution and explanations along with MATLAB and/or Simulink verification or analysis. Both parts of each sub-problem are equally weighted. Problem 1: Transient Response In the exam
the unit step response of G(s) is shown. G(s) has poles at {s = -1, s = -6.1, s = -2 ± j30, s = -20} and zero at s = -6. The 5
th
order G(s) system can be nicely approximated by a first order model G(s)
reduced
= 1/(s+1). 1.1
Use MATLAB Control Systems Toolbox (CST) to compare the step response of G(s) to G(s)
reduced
. Show both step responses on the same LTIVIEW screen. [Comment: In more recent versions of MATLAB the “
ltiview
”
command has been replaced by “
LinearSystemAnalyzer
”
working exactly the same as “
ltiview
”
. Since we are interested only in the step response, you may also use the “
step
”
command.] 1.2
How many time constants does it take for the step response of G(s) to reach 90% of its steady-state value? 1.3
Remove the pole at s = -1 from G(s). Replace it with a complex pole so that: (i) The new complex pole is dominant (that is, the 6
th
order G(s)
new
can be approximated by the new system G(s)
new-reduced
that has the complex pole that you chose, (ii) Peak Overshoot of the step response is 7% and (iii) The 5% Settling Time of G(s)
new
is around 4 [sec]. Problem 2: Closed Loop Stability and Tracking In the given unity feedback loop the process is P(s) = 8/s(s+1).
2.1 Demonstrate the argument between Engineer A and B in parts 2.2 and 2.3 of the exam problem. Use CST. 2.2 Demonstrate in Simulink the solution offered by Engineer C (in part 2.4 of the exam). Observe the ramp input r(t), the output y(t) and the error signal e(t). [Observe r(t) and y(t) on the same scale, and observe e(t) on a separate scope]. 2.3 Process P(s) is replaced by an unstable process P
new
(s) = 8/s(1-s).
The specifications are: (i) Stabilize the loop, and (ii) Zero steady-state error to step input. Engineer D claims that P and PI controls are no longer acceptable. A PD controller C(s) = K
P
+ K
D
s is suggested. Is she right? Demonstrate your analytic solution in Simulink or CST.
Problem 3 DC Motor Control: In the exam we considered a permanent magnet DC motor that has the following parameters: 2
{
4.2[
],
0.04[
],
0.25[
/
],
0.25[
/
/ ],
0.002[
]}
a
a
T
E
m
L
R
L
H
K
N m
A
K
V
rad
s
J
J
Kg m
=
=
=
=
=
=
Let’s call this Case A. The load inertia and the motor inertia were matched L
m
J
J
=
and the connection between the two inertias was by direct drive. The electromechanical time constant was much larger than the electrical time constant: m
e
. In the following block diagram G(s) stands for the simplified armature voltage to speed transfer function
1
( )
( )
1
E
a
m
s
K
U
s
s
=
+
(in speed control problems, either open-loop or closed-loop).
Your preview ends here
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Related Questions
please help solve A-F. thank you
You are an engineer working on a project and your prototype has failed prematurely. You question whether or not a key component of the prototype was manufactured with the correct material. There are two way to check for the material properties. The first way is to have a material certification done to confirm the exact material composition. This will take some time. The second method to confirm the material properties is to make an ASTM test sample and test for the material properties. This tensile test was completed on a test sample with an initial diameter of .501” and an initial length of 2”. The Load-Deflection data for this tensile test is below. Use this data to answer the first set of questions on the Final Exam in eLearning. A. Determine the Ultimate Tensile Strength B. Determine the 0.2% Offset Yield Strength C. Determine the value of the Proportional Limit D. Determine the Modulus of Elasticity E. Determine the Strain at Yield F. Calculate %…
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Cost (Price/Hec)
100
200
Net Profit (Price/Hec)
Variety
Wheat
Barley
Man-days/Hec
50
10
120
30
The farmer has a budget of US$10,000 and availability of 1,200 man-days during
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fft, pdes, etc.;
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Problem Description (CCOs #1, 2, 3, 4, 5, 6, 7, 8, 11, 12)
A water tank of radius R = 1.8m with two outlet pipes of radius r₁ = 0.05m and r2 installed at heights h₁ = 0.13m
and h₂ = 1m, is mounted in an elevator moving up and down causing a time dependent acceleration g(t) that must be
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g(t) = go+a1 cos(2π f₁t) + b₁ sin(2π f₁t) + a2 cos(2π f₂t) + b₂ sin(2π f₂t),
(1)
Figure 1: Water tank inside an elevator
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aiso required to add a Handwritten integrity Statement. Pieose follow the below steps:
1 Write on a blank poper your AUM student ID, full name, course code, section and date
2 Write the following integrity statement and sign:
"7 offirm that I have neither given nor received any help on this assessment and that personally compieted it
on my own."
3. Write your onswer to the obove question as required
4. Put your Original Civil ID card or AUM ID card on the poper
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www
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Scientific Abilities
Is able to construct a
force diagram
Missing
No representation is
constructed.
Inadequate
FD is constructed but
contains major errors such
as incorrect mislabeled or
not labeled force vectors,
length of vectors, wrong
direction, extra incorrect
vectors are added, or
vectors are missing.
Needs Improvement
FD contains no errors in
vectors but lacks a key
feature such as labels of
forces with two subscripts or
vectors are not drawn from
single point, or axes are
missing.
Adequate
The diagram contains no
errors and each force is
labeled so that it is clearly
understood what each force
represents.
Explain whether or not this…
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To use transformation equations to calculate the plane state of stress in a rotated coordinate system.
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positive direction for the rotation is also shown in the second figure.
The stresses in the rotated coordinate system are given by the following equations:
στ
σy
+
cos 20+Try sin 20
2
2
σετ συ
=
σy'
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is its moment of inertia.
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it is free to rotate the vertical plane without friction.
You are to find the angular acceleration of the seesaw when it is set in motion from the
horizontal position. In all cases, assume that m₁ > m₂, and that counterclockwise is
considered the positive rotational direction.
Figure
m₁
O
m₂
1 of 3
Part A
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Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY