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MECH0023 Dynamics and Control Coursework
创建日期：2024-06-07 17:47:25
所属分类：物理Physical
标签： MECH0023
Dynamics and Control Coursework

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MECH0023 Dynamics and Control Coursework

PLEASE REMEMBER TO PUT YOUR CANDIDATE NUMBER (NOT YOUR NAME)
ON YOUR WORK WHEN YOU SUBMIT IT
Estimated time required
for completion
The expected time required to complete this work is
approximately [16 hours].
This is a rough indication of how long the work should
take you if you have attended the course, have read
through and are familiar with the material in advance. It
is intended only as a guide. It does not indicate the
time available to complete the assignment which will
always be considerably longer than the estimated time
to complete the work.
Supplementary material
provided (if any) NONE (Refer to course handouts and online material)
Minimum requirements
to complete assessment
For completion of this assessment we assume that
students have access to Moodle, Microsoft Word,
Microsoft Excel, MATLAB, pen, paper and ruler, and a
means of document scanning if required.
Word limit
Where relevant, any word limits have been indicated in
the assessment. Any overlength pieces of work will be
subject to penalties for exceeding word counts and, in
some cases, the additional material may not be marked.
Presentation
No marks are allocated to presentation but for markers
to understand your work it is important to make the
presentation clear and logically.
Referencing and
citations
You must reference material that is not your own. There
is no need to cite material taken directly from class
notes. Lists of references are excluded from word limit.
Marking criteria
A breakdown of marks awarded to each question is
provided and a comprehensive set of marking criteria
and key points to be raised is given on pages 3-4.
UCL AI Category:
Category 2: “AI tools can be used in an assistive role”.
Students are permitted to use AI tools to assist with
phrasing of text, creation and formatting of figures, but
the design and technical content is the student’s
responsibility and must be their individual contribution.
Page 2
Submission
 Please upload your work as a single file via the submission link on Moodle. Hard
copy submissions will not be accepted
 All text passages must be typed. Handwriting is only acceptable for figures, labels
or mathematical expressions.
 If you do have to include any elements that are not typed/computer generated (e.g.
figures, diagrams, equations etc.), please follow the advice for submitting handwritten
answers for any submission that requires scanning documents (the webpage refers
to 24-hour timed exams but is applicable to all online submissions). It is the student’s
responsibility to ensure that these are legible and of satisfactory resolution.
 If for any reason you are not able to use the app recommended by ISD at the link
above, you can consult the following resources for advice about preparing your
submission:
o Submitting handwritten assignments to Moodle using mobile or tablet Devices
- Device Camera
o Submitting handwritten assignments to Moodle using mobile or tablet devices
- MS One Drive App
 Please DOUBLE CHECK that the file you are uploading is the correct one and is
complete (with all pages visible).
 All coursework marking is anonymous, so please do not include your name on your
submission.
 If you are unable to submit via Moodle please send a screenshot to the Teaching and
Learning Team at: [email protected].
 Details on late submission penalties, which will be applied to any work submitted
after the deadline without a SoRA or approved EC, can be found here in the UCL
Academic Manual: Late Submission Penalties
Page 3
Assessment Criteria
Mark range Expected standard
32-40
(80-100%)
Outstanding submission demonstrating a deep understanding of a wider
range of topics. All calculations are accurate and values provided to an
appropriate level of precision. Parameters and examples are chosen with
great insight and fully justified. Presentation is impeccable, of publishable
standard: phrasing is concise and precise and figures are perfectly
formatted and labelled, providing information efficiently and in full detail
with descriptive informative legends and with cross reference to the text.
28-31
(70-79%)
Excellent work, subjected to a rigorous quality assessment that
addresses main concepts and theories. All calculations are accurate and
justification is given for choices of parameters and/or assumptions made.
Wider knowledge and understanding of the meaning of the work is
demonstrated; discussions are thoughtful and conclusions are
appropriate and fully justified. Text is concise and precise and figures are
clear, fully and accurately labelled and described in the text and legends.
24-27
(60-69%)
Good quality work with some exceptions for example a few minor
mistakes in calculations or weak justification for some of the chosen
parameters or examples. Values are provided to an appropriate level of
precision, final answers are clearly distinguishable and working is shown,
with some attempt at reasoning or justification included. Figures are
useful and correct though may benefit from some additional labelling,
formatting and/or more-specific description.
20-23
(50-59%)
Acceptable submission where the majority of the goals of the assignment
have been understood and tackled, demonstrating that some key
engineering principles have been applied correctly. Some calculations
show minor mistakes, lack of explanation, or are attempted using
incorrect methods. Justifications may be weak or missing in the
descriptions of engineering decisions, methods, conclusions.
12-19
(30-49%)
Submission showing attempts at answering the assignment but with
many gaps in knowledge and only limited understanding being
demonstrated through text, figures and calculations. Sections of the
assignment may be left unanswered. Many calculations exhibit major
mistakes, many methods are incorrect or missing.
0-11
(0-29%)
A submission demonstrating major gaps in understanding the
assignment, failing to meet the majority of the assignment’s goals.
Solutions are largely incomplete and show major mistakes and/or lack of
the required knowledge.
Please turn over for guidance on each question:
Page 4
Specific guidance:
Q1: Describe your methods clearly and specifically. Choose examples of nonlinear effects
carefully and ensure you describe -specifically- how they affect this particular relationship.
Q2: Take care to write your methods and results clearly, especially highlighting the most
important concepts and specific values in your comparisons.
Q3: Ensure you include as much detail and description as is necessary in your plots and
descriptions.
Q4: a) Your decisions and reasoning should relate to this specific example. c) Choose an
appropriate example which you can describe specifically and clearly.
Q5: a) Describe your reason for your choice clearly justified by referring to the relevant
formulation. b) Clearly show derivation of the necessary equations and your calculations.
Q6: Demonstrate how you obtained the equivalent stiffness and damping values. Your plot
should follow the high standard in the marking scheme. You should clearly identify
differences between two graphs and state the reasons behind it.
Page 5
Control Section (20 Marks in total)
ఏ೘(௦)
௏ೌ (௦)
= ௄೐
௦ൣ(௃௦ା௕)(௅ೌ௦ାோೌ)ା௄೐మ൧
[Eqn.1]
Use the values for these parameters you obtained
in the Control Lab, or if you were unable to
attend, use the following parameter values:
Ke = 0.036; J = 2.17 x 10-5; b = 0;
La = 0.85 x 10-3; Ra = 6.3
Figure 1: Schematic diagram (plan view) of a d.c. motor with an arm, indicating shaft angle
(t) and arm-end position d(t).
1) The motor and arm shown in Figure 1 are used to make small ajustments to a position,
d(t). Its normal central operating point is: (t) = 30º, and d(t) = 35mm.
a) Find an approximate linear relationship around the operating point which relates
small changes in (t) to small changes in d(t).
b) Describe any two further non-linear effects that could affect the relationship
between the control voltage input to the motor, V(t), and the arm-end position, d(t).
[Word limit: 150 words total for b)]
[4 marks]
2) In the case of this specific motor, perform the following steps using MATLAB to
investigate whether it is reasonable to assume the coil inductance, La, is negligible:
a) Create two versions of the open loop transfer function (OLTF), one including coil
inductance, La, and the other neglecting it (assuming La = 0).
b) Create a closed loop transfer function (CLTF) for each case using K = 1 for “unity
feedback”. Use these CLTFs to plot a step response for each case and compare the
modelled responses, e.g. looking at the time to first peak of each.
Overlaying the two responses on the same axes is recommended to enable clear
comparison, with any differences labelled and described.
c) The inductance, La, appears in a 1st-order lag component of the OLTF: 1/(Las + Ra).
Calculate the time constant of this lag in seconds.
d) Discuss whether the coil inductance is negligible in practice, referring specifically to
your analysis above and the system shown in Figure 1. [Word limit: 150 words]
[6 marks]
(t)
d(t)
Page 6
3) Referring to Eqn. 1, the open loop transfer function model G(s):
a) Given that the OLTF, G(s), is marginally stable, describe what would happen if the
input V(s) was switched from 0 to a constant 1 Volt. [Word limit: 50 words]
Important: Assume La = 0 for parts b) and c).
b) Investigate the performance of a closed loop system with unity feedback:
i) Plot a root locus diagram of G(s) using MATLAB or sketching by hand.
ii) Label areas on the root locus plot to show the following performance criteria:
damping ratio is at least 0.8 and natural frequency is at least 50 rad/s.
iii) Hence describe whether proportional feedback control could result in a system
which meets both the performance criteria. [Word limit: 100 words]
c) A Proportional Derivative (PD) controller is added in the forward path, having the
transfer function:
() = ஽ + ௉ = 0.5 + 20
i) Plot the root locus for the OLTF with controller, C(s)G(s), using MATLAB or
sketching by hand.
ii) Label areas on your root locus plot to show the following performance criteria:
damping ratio is at least 0.8 and natural frequency is at least 50 rad/s.
iii) Hence identify the range of values of k for which the system can achieve both
the performance criteria? [Word limit: 100 words]
[6 marks]
Page 7
4) The control lab demonstrated an inverted pendulum, as shown in Figure 2:
Figure 2: Schematic diagram (isometric view) of an inverted pendulum. The angle of the
pendulum from vertical, (t), is controlled by a d.c. motor with shaft angle (t).
a) Evaluate whether the following assumptions would be appropriate, providing a
YES/NO answer and reasoning in each case:
i) sin()  .
ii) (t)  0.
iii) Air resistance to movement is negligible.
iv) The pendulum is a uniform cylinder with mass equally distributed along its
length.
v) This nonlinear system can be approximated with linear models.
vi) (t) and (t) are not coupled and can be controlled independently.
b) Describe another example of inherently unstable behaviour in any other system;
mention why it is unstable and describe the behaviour without a controller. [Word
limit: 150 words]

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MAS316/414 ACCT2522 MSIN0181 ATMS 201 COMP3425 MATH7861 SOLA2060 MA 325 7CCEMCTH ECON 432 INFT2051 SOLA 2060 ECOS2002 Stats141XP BIOA02H3 S2022 MA4601 K5 COMP5329 EG 284 IB3A70 WECO1020 COMP3027 Energy ACS61011 MAST20026 STAT 533 MATA31 ENVS257 BEM2031 EC 486 COMP0172 CS3214 EECE5644 IB2B20 COSC2536 COSC1147 COMP6214 5CCM242A COMP0130 AMME2000 MTMG50: EG238 ACF6006 QBUS2810 COSC2391 ECON7560 MATH377 STA305 CS 486 COMP1117B EL648 ELEC3909 ECON 241 COMP 4901W BUSI4428 ENEN20002 ENGN4524 ELEC3115 CSC 413 PSYC 100B ECON1002 MATH256 ANSC20005 MTHS2008 MATH40082 COSC 2406 FIT3174 STA 238 CMT202 Differential Equations MTHM017 GARCH 101 MATH2069 CSC336S ACSC12 ETF2121 CEME 2001 DB B474F ARHT1001 EECS 3311 3220 STATS 786 CS 484 COMP20008 MATH4091 ECE 455 CSCI 204 BUS B200F BA 875 BU5562 COSC 1147 X11 GEOG 101 IMM250F CSE 584A MATH38172 LAB 4 ELEC5882M FINS5523 EE 430 COMP 465 6CCS3PRE 7CCSMNSE FINANCE ACMB02H3 ENGG2112 ELEC5616 SCM B371 CHEM3120 CS22 ECMT2130 MAST30011 ADSPBF706 CENG0013 ACCOUNTING BUSS1040 CHEM 181 MAT136H1 GY 6183 COMP3170 AGRI90089 PHYSICS 1002 ECON10003 IEOR E4004 ACS61012 MATH 40550 MKTG2113 TELE4653 ENSC1004 ECE 232E MK726 MTRX2700 SHEET 3 CSCA08 COMP30027 Math 2XX3 statistic MMAN3200 BISM7213 ECMM109 ECON 2022 FNCE 20005 GR5067 CSCB09 ME 3017 CS 5100 PHYS 2903 COMS 4771 COMP222 COMP 1046 CSC148H1 ISYS2038 FINS2615 OT5206 COMP2048 A6 MECH5770M MA826/20 CMPT 726 STA457 INFS6071 INFS588 integral ECON 216 IRDR 0017 MA323 PA 15213 PSYC2001 ENV222 Statistics ACCT5930 ACCT12 LAND2121 ME 5405 COMM1180 TELE3113 A7 ECE 568 ACCT2019 INFS1200 ENGG1340 CS 1400 ASST3 FINM7409 SWEN30006 INFO2222 FIN20150 SOSS1000 CSSE7231 FINS5513 COMS3200 CECN 702 ECON4060H MN3515 HW2 PSYA02H3 ECON 2112 COMP90051 CS 1652 MA30059 AF1605 MKTG7501 ECO-6003B COM4521 CTM ECON3350 COMP 3804 ELEC9762 BISM 7255 ST22 MATH20014 MNE3122 COMP343 MATH5165 ELE7029 ENGR30002 SEEM3500 ECON7350 RISK5002 FINM7405 COMP90059 MOS 3320B STAT 431 BISM7221 MATH3014 MTH783P EBA 35302 ACS133 BUS2206 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