[Rick TYler]

Even before I read Al's impressive post, I was thinking that this is nearly a chaotic system, and the only good way to guarantee a desired result (such as "I want to go 20% faster") is to test YOUR controllers, batteries, mechanisms, drive train, and wheels and map the desired PWM values to the desired behavior of the motor/device you are controlling. In this case, empiricism is better than theory, although it certainly doesn't hurt to learn the theory, too.