[KenWittlief]

Im not saying you cant get a PID control system to work without first characterising the system, and working out the equations

but if you want it to work as well as possible, you need to either do the math, or have an automatic control system that will do the math for you.

There are several variables in a PID system, and you have to pick which ones you want to optimize. Lets say you are controlling the position of a robot arm, an elbow that can bend from 10 to 180 degrees.

what are you trying to accomplish? do you want the arm to move as fast as possible? do you want it to move smoothly? do you want it to stop at the commanded position within 1/10th of a degree?

is overshoot allowable? do you want the same response with the arm fully loaded and with no load (no weight on the arm)? Does it have to work while the robot is moving, or while the elbow (shoulder?) below it is also moving, or the wrist above it? Do you want the arm to resist if another robot trys to move it? To resist or to RESIST! ?

dont get me wrong, a PID controlled drive system is far better than running open loop, even if its not tuned for optimum performance - if you can get it to point where you want the arm to point thats great. But if you start adding other requirements (speed, load variation....) it can take a lot of work (math) to get it tuned.