ACS133 Physical Systems
Assignment 3, 2021-22
Lingzhong Guo, Anton Selivanov

Assignment weighting
10%
Assignment released
Week 8, Spring Semester, 31 March 2022
Assignment due
Week 10, Spring Semester (Blackboard online submission deadline 23:59pm, 5 May
2022). You may submit your work before the submission deadline (the deadline is not a target!).
Do not leave it to the last minute in case you encounter problems. For full information see the
assignment briefing below.

Penalties for late submission
Late submissions will incur the usual penalties of a 5% reduction in the mark for every working day
(or part thereof) that the assignment is late and a mark of zero for submission more than 5 working
days late. See https://www.sheffield.ac.uk/ssid/assessment/grades-results/submission-marking
for more information.

Feedback
No later than 2-3 weeks after the submission deadline. This will include the overall mark, individual
component marks and comments on performance on the assignment. Note that marks may be
subject to change as a result of unfair means.

Unfair means
Work must be completed as individuals. Submitted work must be your own. All submitted work will
be checked. Suspected unfair means will be investigated and may lead to penalties.
See: http://www.shef.ac.uk/ssid/exams/plagiarism for guidance.


Special circumstances
If you have medical or personal circumstances which cause you to be unable to submit this
assignment on time or that may have affected your performance, please complete and submit a
special circumstances form along with documentary evidence of the circumstances. Please see:
https://www.sheffield.ac.uk/ssid/unfair-means/index for guidance as to which form is appropriate
for your circumstances, and what, if any, supporting documentation is required.

Help
This assignment briefing, the lecture notes, and the laboratory handouts (all available on
Blackboard) provide all the information that is required to complete this assignment. It is not
expected that you should need to ask further questions. Remember that you need to decide on
what is the most appropriate approach to carry out the simulations and present your results. This is
also part of what you are being assessed on and will assess your knowledge and understanding of
the taught material for ACS133.

Assignment briefing
x This assignment/report will assess your fundamental understanding of physical systems,
including use of MATLAB/Simulink relevant to the AC133 module. The assignment is a case
study of the modelling and simulation of a thermal system that you have studied in the
Spring semester.
x Your answers must consist of MATLAB code and Simulink model(s) used to solve the
assignment questions shown below together with any supporting output results
(plots/figures etc.) and any other relevant evidence to justify your solution.
x In the report you need to address the questions directly, include your working methodology,
justifications/assumptions, as well as include brief discussion of the results as appropriate.
x MATLAB code must have comments that include the title, author, date, the purpose of the
code and help details as shown in the MATLAB laboratory sessions.
x In doing the assignment, you should be prepared to use the MATLAB help system and do
some personal study to learn about functions or features you may need.


Submitting your work
You must submit a report document and all your relevant MATLAB/Simulink files.
x Report document You must submit the completed assignment report to the ACS133
Blackboard page, via Turnitin, as a single document. You must include your University
registration number at the top of every page (header). Your report should be word
processed, using minimum size font 11, minimum 2.5cm margins all around,
x MATLAB/Simulink files In addition to the report submission, you must also submit ʹ via
Turnitin - a single zip file (*.zip, *.7z, *.rar) containing your MATLAB and Simulink files for
the tasks described below. Important: Before submitting your MATLAB files, test your zip to
make ƐƵƌĞLJŽƵƌĐŽĚĞǁŽƌŬƐǁŚĞŶƵŶnjŝƉƉĞĚƚŽĂĐůĞĂŶĞŵƉƚLJĨŽůĚĞƌ͙ƚŚŝƐŝƐǁŚĂƚǁŝůůŚĂƉƉĞŶ
when it is marked.

Marking criteria
The marking scheme is summarised here, but the marker will be focussed on what the student
submission is worth overall and therefore may move some marks from one criteria to another where
appropriate.

Report Task 1
Marks will be awarded for correct solutions and methodology,
relevant justifications and supporting discussion.
8 Marks
Report Task 2
Marks will be awarded for correct solutions and methodology,
relevant justifications and supporting discussion.
12 Marks
MATLAB and Simulink
Covering tasks 1 and 2 combined, it will be assessed whether
your code runs without errors and repeatedly does so; not
dependent on pre-existing values in workspace; gives the right
answers and/or accompanying text and/or correct plots with
attention to detail regarding units, labels, etc., and you have
shown proficiency with MATLAB, Simulink and your GUI in your
attention to design, readability and consistency (clear design,
good indenting, sensible variable names, useful comments,
good quality help).
25 Marks
Report quality
Use of English, report structure and clarity of writing, quality of
figures/plots/diagrams, use of references and justifications of
solutions.
5 Marks



TOTAL

50 Marks


Assignment Tasks
Consider a system with two thermal capacitances ( 1C and 2C ). Heat is supplied to the first
capacitance at the rate 1( )q t by a heater, and heat is lost at the left end to the environment. The
first capacitance is connected to the second one through the thermal resistance 2R . The second
capacitance is connected on the right side to the environment that has the temperature aT . Except
for the thermal resistances 1R , 2R and 3R , the enclosure is assumed to be perfectly insulated.


The system model is given by
1 1 1 2
1 12 1 1 1 1 2
2 2 1
2 23 2 3 2 2
1 1 1 1
1 1 1 ,
a
a
q
C R C C R C R
C R C R C R
T T T T
T T T T



where
1 2
12
1 2
,R RR
R R

and
2 3
23
2 3
.R RR
R R


Hence, using the substitutions 1 1Ö aT T T and 2 2Ö aT T T , the following incremental model is
obtained
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ͳ
ܥଵܴଵଶ
ߠ෠ଵ ൌ
ͳ
ܥଵ
ݍଵ ൅
ͳ
ܥଵܴଶ
ߠ෠ଶ

ߠ෠ሶଶ ൅
ͳ
ܥଶܴଶଷ
ߠ෠ଶ ൌ
ͳ
ܥଶܴଶ
ߠ෠ଵǡ

which corresponds to the following equations in the Laplace domain
ȣ෡ଵሺݏሻ ൬ݏ ൅
ͳ
ܥଵܴଵଶ
൰ ൌ
ͳ
ܥଵ
ܳଵሺݏሻ ൅
ͳ
ܥଵܴଶ
ȣ෡ଶሺݏሻ

ȣ෡ଶሺݏሻ ൬ݏ ൅
ͳ
ܥଶܴଶଷ
൰ ൌ
ͳ
ܥଶܴଶ
ȣ෡ଵሺݏሻ

Using these equations, the following transfer functions are derived

2 1 2 2
2
2 2 12 231
2
1 12 2 23 1 2 12 23 2
1
Ö ( )
1 1( ) ( )
s C C R
R R RQ s s s
C R C R C C R R R
4

and

2
2 2
1 1 12 1 2 23 1 2 12 231
2 2
3 2 2 12 23 2 12 231
2 2 2 2 2 2
1 12 2 23 1 12 1 2 12 23 1 2 12 23 2 1 2 12 23 2
1 1 1 1
Ö ( )
2 1 1 1( )
( )
( ) ( )
s s
C C R C C R C C R Rs
R R R R R RQ s s s s
C R C R C R C C R R C C R R R C C R R R
4








Task 1
Consider the model described above with the following default values:
1
2
1
2
3
50 /
60 /
10 /
10 /
10 /
293.15 kelvin (20 Celsius)oa
C J K
C J K
R Ks J
R Ks J
R Ks J
T







Implement the model in MATLAB and Simulink, using Simulink for the model and MATLAB to set
parameters, call the model and plot the simulation results. Simulate the system with 1 0q for ten
minutes then apply a step input of amplitude 3 . Allow the system to reach steady state and plot in
a single figure: the temperatures 1( )tT , 2 ( )tT and the input heat flow 1( )q t . Plot the time in minutes
on the X-axis.
For each temperature ( 1T and 2T ), report the steady state value and the time required to reach
2%r of the steady state value.

Task 2
Create a MATLAB GUI that allows a user to explore different values for the model parameters and
the corresponding response from the system. It is also your task to explore the system enough to
be able to understand the impact of each parameter in the response of the system and to be able
to describe the significance of that parameter in the actual thermal system modelled.

For example: to begin exploring the system, increase the value of the second thermal resistance to
2 50 /R Ks J and plot the system's response. What are the main differences compared to the
response in Task 1? Relate the differences in the system's response with the actual thermal system
described in the assignment. Reset the parameters to the default case, then repeat this process for
three more cases with different values of 1) 1R or 3R , 2) 1C or 2C , and 3) aT .