View Single Post
  #68   Spotlight this post!  
Unread 09-01-2009, 14:54
Adam Y.'s Avatar
Adam Y. Adam Y. is offline
Adam Y.
no team (?????)
 
Join Date: Mar 2002
Location: Long Island
Posts: 1,979
Adam Y. is a splendid one to beholdAdam Y. is a splendid one to beholdAdam Y. is a splendid one to beholdAdam Y. is a splendid one to beholdAdam Y. is a splendid one to beholdAdam Y. is a splendid one to beholdAdam Y. is a splendid one to behold
Send a message via AIM to Adam Y.
Re: Implementing Traction Control for an advantage in the 2009 game

Quote:
Originally Posted by Abwehr View Post
I think you meant first derivative of wheel velocity (or second derivative of wheel position). This is your acceleration.

Here's the rub - encoders are digital sensors, with limited resolution. The "derivative" operator is continuous. You can approximate the derivative with the "difference" (i.e. accel = speed - last_speed), but this is only ever an approximation.

Luckily, the straight difference isn't the only way to approximate the derivative. For example:

accel = -last_last_speed + 2*last_speed - speed;

This is a smoother derivative approximation, but it is now time-delayed (since it is centered around the time of last_speed). This is the tradeoff of filtering - with smoothness comes time delay.
As Adam Savage, Jamie Hyneman, and countless others have said,"Close enough." Mathematically you will never be able to create a differentiators using analog or digital components. It does not actually stop you from implementing systems like PID controllers. You just have to realize that the differentiators only acts like a differentiators at certain frequencies. I wonder how Labview implements analog filters because it does have the capability to use the Laplace transform but its an analog construct.
Quote:
This may break a linear filtering system and limit your max acceleration.
Going much farther would require the expertise of someone with his PHD. At the undergraduate level you really only learn how to implement linear control systems.
__________________
If either a public officer or any one else saw a person attempting to cross a bridge which had been ascertained to be unsafe, and there were no time to warn him of his danger, they might seize him and turn him back without any real infringement of his liberty; for liberty consists in doing what one desires, and he does not desire to fall into the river. -Mill

Last edited by Adam Y. : 09-01-2009 at 15:06.