PID Control

A PID controller looks at the error between where the robot is and where it should be, and decides how hard to push. Each of its three terms fixes a different problem.

Kp, proportional Ki, integral Kd, derivative Friction (steady push)

The controller

$$u(t) = K_p\,e(t) + K_i \int_0^t e(\tau)\,d\tau + K_d\,\frac{de(t)}{dt}$$

Here $e(t)$ is the error, the target position minus the robot position, and $u(t)$ is the push the controller asks the motor for.

What to notice

P only. The robot moves toward the target, but with high Kp it overshoots and swings back and forth. With friction on, it also stops short of the flag, because a small error makes too small a push to beat friction. That gap is steady-state error.

Add D. The derivative term pushes against fast motion, like a brake. The swinging dies out and the overshoot shrinks.

Add I. The integral term adds up error over time, so a small error that lasts eventually builds enough push to close the gap. Too much Ki brings the overshoot back.