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Simulation and Animation of a Quarter-Car Automotive Suspension Model

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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:

http://deepblue.lib.umich.edu/handle/2027.42/58449

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

http://www.youtube.com/watch?v=_jKceIHn6tc

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

Comments and Ratings (28)

Tibor Kicsid

I have the same problem as ben and BS CE. The error code is:
??? Error: File: plotsusp.m Line: 42 Column: 3
Expression or statement is incorrect--possibly unbalanced (, {, or [.

Error in ==> sim_qcar at 79
        plotsusp([z0(i), z1(i)*zmf, z2(i)*zmf, t(i)],road_x,road_z,x(i),umf);

Any idea how to solve the problem?

Thank you

Lucas Almeida

What the unit of the z1 amd z2 vector(suspension travel)? The unit, according to the code appears to be in centimeters.

James Allison

James Allison (view profile)

Sankar: You could change the road profile data by replacing the .mat file with one you generate, as long as the units, spatial resolution, and variable names are identical.

James Allison

James Allison (view profile)

Lucas: If I remember correctly, the unit is meters. The profile was generated using filtered noise, as described in Section 8.3.3 of: http://systemdesign.illinois.edu/publications/All08b.pdf

What is the unit of the pavement profile? And by what method did you get the profile? Thank you

BS CE

BS CE (view profile)

Mr. Allison, I have found following while running the function as in video....

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

Error in ==> sim_qcar at 79
        plotsusp([z0(i), z1(i)*zmf, z2(i)*zmf, t(i)],road_x,road_z,x(i),umf);

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

Henry Piz

James Allison

James Allison (view profile)

Amritam:

I would first point you to the following journal paper:
http://systemdesign.illinois.edu/publications/All14b.pdf

and then my dissertation:
http://systemdesign.illinois.edu/publications/All08b.pdf
(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:

http://link.springer.com/article/10.1007%2Fs00158-003-0368-6

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.

James Allison

James Allison (view profile)

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

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

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.

Xaris

Xaris (view profile)

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

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.

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..
 

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 [.

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:

http://www.mathworks.com/matlabcentral/fileexchange/40504

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.

James Allison

James Allison (view profile)

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

saman abdanan

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

James Allison

James Allison (view profile)

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

http://www.mathworks.com/help/control/ref/ss.html

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.

Alexandru

Hello,

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!
Alex

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.

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.

Mayur

Mayur (view profile)

James,

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

Thanks,
Mayur

very nice !!!

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