M3H624735 American Academy of English Eng material Control Systems Paper - Science
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F/QAP/021/004
College of Engineering
Alternative Assessment - Course Work.2
Name of the programme BEng CAME / BEng MT / BEng EPE / BEng EIE
Name of Course with Code Control Systems / M3H624735
Level/Semester & AY Level 3 / Semester B & AY 2019-20
Name of the Course Team Associate Professor G. R. Rameshkumar /
Coordinator/Course Team Associate Professor R. Amuthakkannan
Members Mrs. B.M. Sangeetha
Ms. Jawaher Rashid Ahmed Al Yaarubi
Ms. Huda Salim Nasser Al Harthi
Ms. Halima Mohammed Said Al Gafri
Course Work Type Alternative CW2 (Online test + Assignment)
Assessment weightage 50\% (Online test, 10\% + Assignment, 40\%)
Type and Date of submission
Online submission – 04.06.2020 (Task 2-5)
The aim of this module is to provide students, a
foundation in control systems theory. This includes
studying the fundamental concepts, analysis tools,
mathematical techniques and applications of control
systems in modern engineering.
Learning Outcomes On completion of this course work the student should be
able to:
1. Define poles and zeros of a system and determine
these from either the system differential equation or
from the transfer function.
2. Describe the concept of stability and analyse
various classes of stability.
3. Design and Analyse frequency response in
Nyquist/Polar diagrams and Bode plots.
4. Analyse the concept of system error, error
coefficients and determine these from transfer
functions.
5. Explain the concepts of controllers used in
engineering - P, I and D combinations
Aim
Expected Task
This alternative assessment course work 2 is to assess the students understanding on system
errors and error coefficients, stability concept, stability analysis, frequency domain analysis, and
controllers.
This coursework 2 consists of FIVE tasks which you have to address each of them in a form of
developing, simplification, analysis and estimation of frequency response of control systems and
controllers. This task is an individual task, but the assignments are distinct to each student so
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that each student is faced with tasks that meet his or her individual needs. This means each
student will get unique set of values for the parameters given and one common online test with
20 multiple choice questions.
The report should clearly demonstrate the use of suitable methods to determine the expected
outcomes. The report should be typed one in case of figures and long derivation may be
inserted as hand written scanned copy in the report with a maximum word limit of 1000 words.
Assessment Marking Scheme
Coursework 2 – Task 1, 20 multiple choice questions with 1 marks each.
Coursework 2 – Task 2 - 5 will be marked accordingly to the following grading rubrics.
Serial
No.
Component Description
Weightage
1
Identification and problem formulation
100*0.20\%
2
Mathematical modeling and Development
100*0.40\%
3
Analysis of modeling and evaluation
100*0.40\%
Total
100\%
Instructions
1. Plagiarism is a serious offence. In case of any plagiarism detected, penalty will be imposed
leading to zero mark. Policy and guidelines for dealing with plagiarism and malpractice in
examination can be viewed by clicking:
http://coeportal.nu.edu.om/member/contentdetails.aspx?id=490
2. For online submission of course work, a word or pdf file with appropriate cover page (in the
given template) mentioning name of student, and student number should be uploaded using
the submission link created (NU-CoE Learn (blackboard)) and made available by the course
coordinator.
Referencing
Harvard Referencing (CCE Style) First Edition 2013 should be followed for both in-text and
listing references. This downloadable document can be found in our COE portal at:
http://coeportal.nu.edu.om/member/contentdetails.aspx?cid=628
Name and Signature of Course Team Coordinator
Associate Professor Dr. G.R. Rameshkumar
Date: 29.04.2020
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Task: 1 (20 Marks)
This online test consists of 20 multiple-choice questions. It’s important to thoroughly read the
chapter’s systems response (second order), steady state errors, stability analysis, frequency
response analysis and controllers.
Only one Attempt - You will have only one attempt and you should complete in one sit.
Timing – Students must complete the 20 (equal distribution of questions from all
chapters that are mentioned above) multiple choice questions within the 30 minutes time
frame allotted for the exam. Students must not stop the session and then return to it.
This is especially important in the online environment where the system will time-out
and not allow the student to reenter the exam site.
Answers - You may review your answer-choices and compare them to the correct
answers after your final attempt.
(Online test will be conducted during the last week of May 2020, detailed instructions will
be provided before the test)
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Task: 2 (20 marks)
The engine, body, and tires of a racing vehicle affect the acceleration and speed attainable. The
speed control of the car is represented by the model shown in Figure 1.
R(s) +
+
K1
-
+
+
𝟏𝟎
𝒔+𝟏
𝟏
𝟐𝒔 + 𝟎. 𝟓
C(s)
-
K2
Figure 1
(i). Develop the closed loop transfer function of the racing vehicle.
(ii). Design the control system by selecting gains K 1 and K2 such that it has a damping
ratio (ξ) and settling time (Ts) seconds.
Note: Refer the attached Table for damping ratio (ξ) and settling time (T s)
seconds.
(iii). Estimate the rise time and peak time.
(iv). Write a general MATLAB codes to reduce the block diagram into a single feedback
control system, to calculate transfer function and to obtain unit step response and
impulse response.
(v). Determine the poles and zeros of the designed closed loop transfer function and show
their positions on s-plane.
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Task: 3 (15 Marks)
The engine, body, and tires of a racing vehicle affect the acceleration and speed attainable. The
speed control of the car is represented by the model shown in Figure 2.
R(s)
E(s)
+
_
𝐾(𝑠 + 𝐴)
𝑠(𝑠 + 𝐵)(𝑠 + 𝐶)(𝑠 + 𝐷)
C(s)
Figure 2
(i).
Determine the steady-state error of the system with unity gain and explain with
suitable justification about the system type.
Note: Refer the attached Table for A, B, C, and D values.
(ii). Determine the static error coefficient associated with the system.
(iii). Assume the steady state error to be 10\%. What will be the value of the controller
gain, K?
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Task: 4 (20 marks)
a) A ship steering system is bound with the following Equation.
1+𝐾
𝑠3
+
𝑄
=0
+ 5𝑠 + 2
4𝑠 2
(i). Identify the characteristic equation.
(ii). Identify the range of K value to make the steering system stable.
Note: For the above task take:
𝑄=
𝑌𝑜𝑢𝑟 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑛𝑢𝑚𝑏𝑒𝑟 ∗ 0.5
𝑌𝑜𝑢𝑟 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑛𝑢𝑚𝑏𝑒𝑟 − 100000
b) The characteristic equation of a control system is given by:
Q(s) = PS5 + 2PS4 + 2PS3 + 4PS2 + 11S + 10 = 0
Note: For the above task, take
𝑃=
2 ∗ 0.25 ∗ 𝑍 2
, 𝑤ℎ𝑒𝑟𝑒 𝑍 = 𝑌𝑜𝑢𝑟 𝑠𝑡𝑢𝑑𝑒𝑛𝑡 𝑛𝑢𝑚𝑏𝑒𝑟
4 ∗ 𝑍 ∗ 2 ∗ 0.125 ∗ 0.5 ∗ 𝑍
(i).
Identify the stability of the system using Routh Hurwitz Algorithm.
(ii).
Comment about the Roots location.
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Task: 5 (25 Marks)
a) Discus the Time Response Analysis and the Frequency Response Analysis.
b) Discuss the Bode plot and Nyquist (Polar) plot to estimate the system stability and comment
on Gain Margin (GM) and Phase Margin (PM).
c) The unity feedback control system is represented in Figure 3. In order to improve the
performance, a PD controller is introduced in the forward path in series with the plant as
shown in Figure 4.
Plant
R(s)
+
E(s)
_
𝐸
𝑠(𝑠 + 50)
C(s)
Figure 3.
Plant
PD Controller
+
+
1
R(s) +
+
𝐸
𝑠(𝑠 + 50)
C(s)
+
sKd
Figure 4.
(i).
Evaluate the damping ratio, un-damped natural frequency and percentage
overshoot without introducing controller.
Note: Refer the attached Table for E value.
(ii).
Estimate the value of Kd, if the damping ratio to be improved by 25\% and thus
compare the change in percentage overshoot.
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Table: The values of ξ, Ts, A, B, C, D and E
Sl.
No.
Student
Number
1
Task 2
Task 3
Task 5
Damping ratio
(ξ)
Settling time
(Ts) seconds
A
B
C
D
E
111076
0.015
5
5
6
7
8
1000
2
120316
0.055
6
8
6
9
10
1005
3
120645
0.052
3
3
4
7
5
1010
4
140490
0.054
2
7
8
9
10
1015
5
140734
0.053
4
10
12
13
14
1020
6
140782
0.056
7
5
11
14
20
1025
7
140824
0.047
5
3
5
8
12
1030
8
150136
0.028
8
11
14
18
10
1035
9
150215
0.039
5
2
5
8
9
1040
10
150304
0.015
7
7
4
11
16
1045
11
150754
0.100
3
13
17
21
22
1050
12
150781
0.102
9
2
15
8
9
1055
13
160040
0.103
2
6
9
11
19
1060
14
160053
0.104
4
7
14
18
13
1065
15
160073
0.105
6
12
5
10
16
1070
16
160083
0.106
5
4
21
3
21
1075
17
160086
0.107
8
6
22
2
21
1080
18
160090
0.108
9
23
23
8
23
1085
19
160094
0.109
3
24
24
7
24
1090
20
160098
0.203
2
12
25
5
25
1095
21
160101
0.251
5
7
26
9
26
1100
22
160107
0.205
6
4
27
3
27
1105
23
160121
0.201
8
9
28
10
21
1110
24
160139
0.202
4
8
29
12
23
1115
25
160142
0.203
5
7
23
15
22
1120
26
160143
0.204
6
2
25
14
26
1125
27
160182
0.125
2
11
21
18
24
1130
28
160187
0.134
5
16
20
19
26
1135
Rev: 00 Template B 9th July 2017
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F/QAP/021/004
29
160188
0.152
9
17
20
7
14
1140
30
160253
0.126
7
15
17
14
32
1145
31
160263
0.129
8
4
12
25
8
1150
32
160423
0.129
4
5
2
16
18
1155
33
160424
0.131
3
6
24
5
9
1160
34
160428
0.132
6
7
23
16
12
1165
35
170101
0.133
2
8
16
19
14
1170
36
170178
0.141
7
12
26
5
13
1175
37
170208
0.142
9
14
24
6
21
1180
38
170253
0.143
4
13
12
4
17
1185
39
170277
0.144
6
21
11
10
8
1190
40
170292
0.145
7
22
13
9
6
1195
41
170344
0.146
9
25
14
5
4
1200
42
170352
0.153
10
24
15
6
5
1205
43
170409
0.165
11
26
15
7
3
1210
44
170440
0.176
12
16
13
8
7
1215
45
170453
0.186
13
17
13
9
8
1220
46
180031
0.195
14
18
16
11
9
1225
47
180312
0.205
15
23
8
10
12
1230
48
190018
0.225
16
24
8
16
21
1235
49
190023
0.220
10.5
25
3
16
23
1240
50
190071
0.300
11.5
26
5
18
2
1245
UCW/RESIT Students
Sl.
No.
Student
Number
1
Task 2
Task 3
Task 5
Damping ratio
(ξ)
Settling time
(Ts) seconds
A
B
C
D
E
120441
0.300
7
15
16
4
18
1250
2
120653
0.310
4
12
8
3
21
1255
3
160150
0.320
3
11
9
4
19
1260
4
160378
0.330
8
10
15
5
17
1265
5
160439
0.340
10
9
3
6
16
1270
6
170229
0.350
12
8
17
7
8
1275
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7
170366
0.360
6
7
15
8
4
1280
8
180259
0.370
5
13
8
9
15
1285
9
180286
0.380
7
14
12
10
13
1290
10
180297
0.390
12
16
3
11
18
1295
11
190011
0.345
10
17
4
12
14
1300
12
190037
0.355
12
18
6
14
12
1305
13
190038
0.375
13
19
5
7
19
1310
14
190041
0.385
14
20
7
4
9
1315
15
190064
0.405
15
21
8
3
8
1320
16
09134
0.415
8
22
3
6
4
1325
17
09680
0.425
4
23
2
9
9
1330
Stay Home Stay Safe
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