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Simulation and Animation of a Quarter-Car Automotive Suspension Model

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4.5 | 8 ratings Rate this file 40 Downloads (last 30 days) File Size: 94.9 KB File ID: #35478 Version: 1.0
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Simulation and Animation of a Quarter-Car Automotive Suspension Model


James Allison (view profile)


A standard linear quarter-car model is simulated and then animated.

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This model was developed for use in teaching modeling, simulation, and optimization in graduate engineering courses. The simulation is particularly useful for demonstrating different simulation designs that are optimized for different applications (e.g., maximum handling capability, maximum comfort, etc.). The model is based on the electric vehicle case study found in this dissertation:

This code was used in the creation of this corresponding video, used for teaching:

Note: this submission does not include code for the multi-objective optimization highlighted in the youtube video.

Required Products MATLAB
MATLAB release MATLAB 7.13 (R2011b)
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Comments and Ratings (22)
21 Aug 2016 Sankar Narayanan

Hi.. Is there any way to change the road profile data..

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27 Apr 2016 Henry Piz  
21 Apr 2016 James Allison

James Allison (view profile)


I would first point you to the following journal paper:

and then my dissertation:
(chapter on EV design)

Both discuss these metrics. If I remember correctly my dissertation cites at least one reference that compares the simple metrics I use in these models to much more sophisticated metrics (e.g., frequency-based constraints for comfort). The reference then concludes that the simple integral of acceleration metric is very accurate even though it is not very complex. There should be other references that address both rattle space and handling.

Regarding multi-objective optimization, I would suggest the following review article:

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21 Apr 2016 AMRITAM DAS

Hi, Prof.James Allison. You have mentioned that you can't upload the optimization code. But can you at least provide a document or slides which explain the theory behind defining maximum handling capability, maximum comfort and design a multi-objective optimization problem. I am doing my thesis on similar topic. I believe it will be of great help.

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01 Apr 2016 James Allison

James Allison (view profile)

Thank you Patrick for pointing out a fix for newer versions of MATLAB.

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01 Apr 2016 Patrick Bright

Works on R2015b if you change 'refresh' to 'drawnow'

26 Jan 2016 James Allison

James Allison (view profile)

I've not tested this code on more recent versions of MATLAB. The animation worked well with R2011b, but perhaps the animation no longer works with more recent releases of MATLAB.

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27 Dec 2015 Xaris

Xaris (view profile)

I can only see the plots and the picture of the suspension. I can't see the kinematic vision

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15 Nov 2015 Changhong Wang  
13 Mar 2015 James Allison

James Allison (view profile)

Naveen: IRI_737b is a .mat file included with this submission. You need to make sure it is on your path to run this code.

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07 Mar 2015 NAVEEN KUMAR

Hello Mr, James Allison sir,
it seems some thing missing in this part of the program,
Error using load
Unable to read file IRI_737b: No such file or directory.

Error in Untitled5 (line 43)
load IRI_737b % road profile data

plz can u halp me sir..

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24 Sep 2013 ben

ben (view profile)

Hello Mr, James Allison

it seems some thing missing in this part of the program, [~, ....

[~,istart] = min(abs(xstart-road_x));
xend = curr_x + fw;
[~,iend] = min(abs(xend-road_x));
xpstart = xstart-curr_x;

can you help please? because i cant run it .. it gives me this error

??? Error: File: plotsusp.m Line: 42 Column: 3
Expression or statement is incorrect--possibly unbalanced (, {, or [.

06 Sep 2013 James Allison

James Allison (view profile)

Saman: Thank you for your interest in the optimization code. I decided not to distribute it because I use it in optimization classes that I teach. You might be interested in this submission:

It includes the optimization code, but is a more complex example.

To answer your other question, f1 is an interface function between qcar (the simulation) and fmincon.

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06 Sep 2013 James Allison

James Allison (view profile)

Saman: Thank you for your *interest* in the optimization code. ...

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23 Aug 2013 saman abdanan

Hi James
Could you please add (opt_qcar) or send it to me ( I saw your simulation on youtube for optimization. Could you please explain what was f1 in your m.file line 17?

21 Mar 2013 James Allison

James Allison (view profile)

Alexandru: Perhaps there is another function 'ss' on your path that is superseding the built-in ss function:

You can use the 'which' command to find out if this is the issue.

Another possibility is the ss is part of the control system toolbox. If you don't have that toolbox, then ss will not work.

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21 Mar 2013 Alexandru


I am interested in your app. But I have problems when running it. I get this error:
Undefined function 'ss' for input arguments of type 'double'.

Error in sim_qcar (line 48)
qcar = ss(Aqcar,Bqcar,Cqcar,Dqcar);

What am I missing?
Thank you!

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27 Nov 2012 James Allison

James Allison (view profile)

umf is a multiplication factor that allows quick exploration of road profiles with different levels of roughness. It should be set to 1 for the output to correspond to the road profile in the .mat file.

Nice catch Louis. Yes, dt should be changed to dt2 on line 62.

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18 Oct 2012 Louis

Louis (view profile)

Very helpful model, I have two comments though:
1. I think umf should be set to 1 (or removed)
2. on line 62 the division by dt should be changed to a division by dt2

These two details made the script output inaccurate results; the script otherwise gives consistent results.

05 Sep 2012 Chegireddy Venkateswara Reddy

nice demo

07 Aug 2012 Mayur

Mayur (view profile)


Thanks for this model. I am trying to understand what umf = 3 is, and why you have used it. Could you please explain.


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05 Apr 2012 Olexander Zhytenko

very nice !!!

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