Assignment weighting

15% of overall module grade

Assignment released

Week 7,autumn semester

Assignment due

Week 12, autumn semester (Blackboard/online submission deadline Friday 15th 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. Seehttps://www.sheffield.ac.uk/ssid/unfair-means/indexfor 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 extension   to   the   deadline.    Seehttps://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.

Assignment Tasks

The Scenario:

You area member of a multidisciplinary team who are tasked to design a sportscar 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’sseat 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.

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 yourSimulink 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%,

•   asettling 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.

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).

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.

Table 3: Change in chassis percentage overshoot (%) with the spring coefficient K2 and damping coefficient C2.

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’ .