[JonA]

Tim Wescott wrote a excellent piece for Embedded Systems Programming back in October 2000 entitled PID without a PhD giving a really detailed but easily approachable explanation of how PID control works as well as tuning a PID controller.

Tuning a system while it is not under load will result in a very poorly tuned system. While it will account for the plant (motor and gears and whatnot) it will not account for the robot's inertia or the friction in the drive.

Have you ever commanded your robot to go straight forward only to have it veer off to one side or another over time? PID can help. Having closed loop control on your robot's wheels will try to make sure all of your wheels are spinning at the rate you commanded (and by extension make sure your robot is doing what you told it to do) and will compensate to provide some disturbance rejection. The feedback can also be used to then calculate the current position and orientation of a robot when dead-reckoning.