# Car transfer function (from accelerator to wheels)

1. Jan 23, 2008

### Ulysees

Anyone know what a car's transfer function is, ie the dynamic response written as differential equations and diagrams, so a controller can be designed for it (as in the cruise control feature in some luxury cars)?

I mean, many of us are familiar with the torque curve, ie engine torque as a fuction of rpm, but what is the meaning of it in the context of a controller? For example: Say the car is running at constant speed v and the engine is running at constant rate f revs per second. From the torque curve we know the torque that corresponds to the given rpm, and therefore this torque balances the wind resistance and other frictions.

But if you release the accelerator pedal, what would be the transient response of the car speed? We would instantly get less torque at the same rpm, so the graph would not be valid any more. What is the transfer function then?

An example torque curve:

http://myautoworld.com/auto/porsche/porsche-07-gt3/2007_911_GT3_Torque_Curve-US.jpg

Last edited: Jan 23, 2008
2. Feb 29, 2008

### Ulysees

Correction, curves show maximum (full-throttle) torque and power at each value of rpm.

3. Feb 29, 2008

### trambolin

To be able to write a transfer function which I assume from the pedal angle to the speed of the car, you need to have a linear model which is very likely that it is not possible in this case, and you have to model the disturbances and uncertainties probably in a robust control framework.

Of course it depends on what you would like to control, if the dynamics can be approximated by a linear model, then you might compute the impulse response (releasing the pedal suddenly from full throttle). The combustion dynamics can be neglected by some delay for example or a low pass filter. Let say a nicely damped
$$\frac{\alpha\omega^2}{s^2 + 2\omega s + \omega^2}$$

where alpha is the gain of the system as in unit angle in the pedal causes alpha times the resulting speed etc. I am quite positive that you can come up with a simple transfer function but it still would be a rough approximation. If you know what you are modeling you can easily come up with your own chip tuning scheme that let say the controller tries to maximize the torque, where it is usually considered to be rocket science by the car magazines. But then you need to do an identification of the particular car that you are interested. Usually, industrial controllers use a look up table of the given torque-power-speed charts and simple PID control schemes. Here is the very basic usage of it

http://www.engin.umich.edu/group/ctm/examples/cruise/ccPID.html

Last edited: Feb 29, 2008
4. Mar 1, 2008

### Ulysees

I asked someone a while ago about increasing the power of an engine and they said it can be done with what's called an "ECU remap". It's got to do with changing the look-up table of the controller in order to derive a slightly different power curve. Giving a power gain of the order of 5% in my particular car, presumably at the expense of increasing consumption.

But then I discovered there are two identical cars with an identical engine control unit etc and where one has been adjusted to produce more power without any change in consumption! These are two variations of a Mercedes model. Any idea how that can be?

What is the meaning of values in the look-up table? Maximum duration of injection? Something else? How can it make no difference in consumption?

Last edited: Mar 1, 2008
5. Mar 1, 2008

### trambolin

Even the sentence doesn't make sense, does it? More power without consumption! I checked a couple of websites just to give you the real people's opinion. Because I don't believe the use of these stuff anyway, even though I am in the control eng. business. here is one please read the first item on the page.

http://mobilechiptune.co.uk/html/faq.html

And here what they do actually you can also check the Howstuffworks page for nice animations, which I am too lazy to do.

http://mobilechiptune.co.uk/html/chip_tuning.html

6. Mar 1, 2008