ACS133 Physical Systems
Assignment 1
Dr Ross Drummond, Dr Patricio Ortiz
Assignment weighting
15% of overall module grade
Assignment released
Week 7, autumn semester
Assignment due
Week 12, autumn semester (Blackboard/online submission deadline Friday 15
th December,
5pm). 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 any unforeseen issues. For
information on what to submit see ‘Assignment briefing’ below.
Penalties for late submission
Late submission penalties will be applied according to university policy
https://www.sheffield.ac.uk/ssid/assessment/grades-results/submission-marking
Feedback
The aim is to provide feedback to students within two weeks from the submission deadline.
Unfair means
This is an individual assignment. Do not discuss your solutions/work with others. Submitted
work must be wholly your own. Suspected unfair means will be investigated and may lead to
penalties. See https://www.sheffield.ac.uk/ssid/unfair-means/index for guidance.
Extenuating circumstances
You must submit an extenuating circumstances form if you have any medical or special
circumstances that may have affected your performance on the assignment – or to requests
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extension to the deadline. See https://www.sheffield.ac.uk/ssid/forms/circs for more
information.
Assignment briefing
This assignment/report will assess your fundamental understanding of physical systems,
including use of MATLAB/Simulink relevant to the ACS133 module. The assignment is based
on the quarter car suspension model of a sports car; this case study was investigated in the
lectures and laboratory sessions of the autumn semester.
• Your answers must consist of the 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.
• 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.
• 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.
• 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.
• Read the instructions completely, from top to bottom. Do not skip anything.
Help
Assignment briefing, ACS133 course materials and MATLAB inbuilt help is all that is required.
It is stressed that Google is a highly effective tool for troubleshooting MATLAB problems, it
can be very useful for helping coding problems such as these. If you need clarifications on the
assignment, please, get in touch with the relevant academic staff.
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Submitting your work:
You must submit a report document and all your relevant MATLAB/Simulink files.
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, and maximum 10 pages in total. No marks will be
awarded for content that exceeds 10 pages. The report should be saved as a .pdf file format.
Word processing software such as google docs is recommended to produce the report.
MATLAB/Simulink files
In addition to the Turnitin submission, you must also submit – via email – a single zip file (*.zip,
*.7z, *.rar) containing your MATLAB and SIMULINK files for the TASK 1 and TASK 4 described
below. The following 5 files should be in this zip file.
task1.m This file contains your MATLAB code for Task 1.
task1sim.slx This file is your Simulink model for Task 1. Please, pay attention to the extension.
Files “*.slx c” cannot be processed and you will get a mark of zero for the MATLAB
part if you do not submit the “*.slx” file.
task4.m This file contains your MATLAB code for Task 4.
task4sim.slx This file is your Simulink model for Task 4. Please, pay attention to the extension.
Files “*.slx c” cannot be processed and you will get a mark of zero for the MATLAB
part if you do not submit the “*.slx” file.
roadProfile.mat This file is provided. It is required for Task 4.
You must email this to Dr Ortiz at p.ortiz@sheffield.ac.uk. Use your university email account
to do this. Your zip file should be named using the format “ACS133_{my University registration
number}.zip”. For example, in this format, the zip folder name for the student with
Registration number 1111 will be “ACS133_1111.zip”.
Important: Before emailing your files, test your zip to make sure your unzipped code works
when unzipped to a clean empty folder. This is what will happen when it is marked
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Marking criteria
Report, Task 1
Marks will be awarded for correct solutions and methodology, relevant justifications and
supporting discussion.
10
Task 1 MATLAB and Simulink
It will be assessed whether your code runs without errors and repeatedly does so in standalone mode (i.e., not depending on pre-existing values from your workspace); 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 in MATLAB with attention to design, readability and consistency (clear design,
good indenting, sensible variable names, useful comments, good help).
10
Report, Task 2
Marks will be awarded for correct solutions and methodology, relevant justifications and
supporting discussion.
10
Report, Task 3
Marks will be awarded for correct modelling approach and design, solutions and
methodology, relevant justifications and supporting discussion.
20
Report, Task 4
Marks will be awarded for correct modelling approach and design, solutions and
methodology, relevant justifications and supporting discussion.
25
Task 4 MATLAB and Simulink
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 in MATLAB with attention to design, readability and consistency (clear
design, good indenting, sensible variable names, useful comments, good help).
20
Report quality
Use of English, report structure and clarity of writing, quality of figures/plots/diagrams, use
of references and justifications of solutions.
5
Total: 100
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Assignment Tasks
The Scenario:
You are a member of a multidisciplinary team who are tasked to design a sports car
for an international company. Your responsibility includes the car suspension
components, and you are the engineer that will provide recommendations for the
suspension design.
Task 1
Using content from the ACS133 lectures and MATLAB laboratory sessions, create a MATLAB
script file and Simulink model to simulate a quarter car suspension system.
Using your Simulink simulations, consider the step response of the driver’s seat position
(with a step amplitude in the reference displacement r(t) of 0.1 m) for both when the car is in
‘cruise mode’ and in ‘sports mode’. Calculate:
1. the rise time,
2. overshoot,
3. and the settling time (to both 2% and 5% of the final value).
In your report you should make it clear what specific values you have calculated.
Explain the differences between the two step responses and what these differences are
caused by. Comment on how these properties relate to vehicle performance.
In completing Task 1, you should:
• create a single MATLAB script that prompts the user for sports or cruise mode
selection,
• assigns block parameters and any other variables as needed,
• executes the Simulink model,
• produces labelled plots of simulation results,
• and display the findings appropriately.
• You may want to use the ``stepinfo’’ MATLAB function to evaluate the step response.
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Task 2
To avoid any damage to the suspension elements, the designers propose to include
mechanical ‘bump-stops’ to the suspension to keep the relative displacement between the
wheel and chassis within +/- 2cm.
1. Implement this change in your Simulink model, using an appropriate non-linear block,
then plot the wheel’s displacement before and after the design change for both cruise
and sports modes. Refer to Lecture 3 for examples of non-linear blocks and pick one
that would limit this displacement.
2. Explain the new behaviour you observe in the position of the chassis.
You do not need to submit the MATLAB/Simulink model for this task, but please provide the
Simulink model as a figure in the report.
Task 3
Following the design change in Task 2, the chassis movement for the sports mode is now
outside the vehicle’s performance specifications. These specifications are that the wheel’s
absolute displacement (the signal r+x) should have:
• a percentage overshoot less than 72%,
• a settling time (to 2% of the steady-state value) less than 0.25s.
To achieve these specifications, it is proposed to modify the chassis’ spring stiffness and
damping. The following design options are considered:
Table 1: Table of spring stiffness and damping values.
Damping value C2 1000 Ns/m 1500 Ns/m 3000 Ns/m 6000 Ns/m
Spring stiffness K2 5000 N/m 13000 N/m 30000 N/m 50000 N/m
For each combination of C2 and K2 given in Table 1 (above),
1. Calculate (and present in two tables similar to Tables 2 and 3 below) the percentage
overshoot and settling time to 2% of the steady-state value. The ``stepinfo’’ MATLAB
function may prove useful for computing these values.
2. Comment on the impact of changes in C2 and K2 on these performance metrics (the
percentage overshoot and the settling time).
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3. Select an appropriate design from the options given in Table 1 that satisfies the
specifications given at the start of this task. Explain why your chosen design is
appropriate when considering the driver’s comfort- you may want to refer to the step
response to justify your design choice.
[4 marks]
Table 2: Change in chassis settling time to 2% of the final value with the spring coefficient K2 and damping coefficient C2.
Settling time (s)
Suspension damper- C2 (Ns/m)
1000 1500 3000 6000
Suspension
spring- K2 (Ns/m)
5000
13000
30000
50000
Table 3: Change in chassis percentage overshoot (%) with the spring coefficient K2 and damping coefficient C2.
Percentage overshoot (%)
Suspension damper- C2 (Ns/m)
1000 1500 3000 6000
Suspension
spring- K2 (Ns/m)
5000
13000
30000
50000
You do not need to submit the MATLAB/Simulink model for this task, but please provide
appropriate information in your report so that your methodology and results are clear.
Task 4
To validate your proposed design, the project manager wants you to simulate the suspension
behaviour of the whole axle (two wheels) as an independent suspension using a realistic road
profile. The company’s test track will be used for this validation after the prototype car is
ready. The test track’s road profile is provided (in “roadProfile.mat”), estimated separately
for the left and right wheel, sampled at 1sec intervals (90sec for a full lap).
The difference between each wheel’s position and the road profile can be considered as an
indicator of ‘traction’.
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1. Based on the model from Task 2, develop a whole axle model (composed of both
wheels on the axle) and calculate the root mean square error (RMSE) for one lap
between the wheel’s position and the road profile for the cruise mode and the sports
mode (for each wheel).
2. Explain what the RMSE values show about the traction in the two different modes.
3. The difference between the position of the left wheel and the right wheel is an
indicator of horizontal stability; calculate the Mean Absolute Error (MAE) for each
suspension mode and comment on your findings.
To complete Task 4, you should create a single MATLAB script that
• prompts the user for sports or cruise mode selection,
• assigns block parameters, road profiles and any other variables as needed,
• executes the Simulink model,
• produces labelled plots of simulation results,
• performs the RSME and MAE calculations and displays findings appropriately. 
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