PID Control

Try this

1. Press P only and raise Kp slowly. The arm reaches the target faster, but swings past it and back more and more.
2. At 2 seconds a weight is hung on the arm. With P control alone the arm stops a little below the target. The red arc is the remaining error.
3. Press PI. The integral term pushes the remaining error out bit by bit and lifts the arm back to the target, at the cost of more oscillation.
4. Raise Kd. It brakes the arm's speed and the oscillation shrinks.
5. Lower Kp and raise only Ki, and the arm swings wider and wider until it diverges. Gains have limits.

What is modelled

The plant is a servo that positions an arm with a motor. As a transfer function:

G(s) = K / ( s (τs + 1) ),   K = 8,  τ = 0.15 s

The target is 1, a constant load is applied at 2 s, and the control period is 1 ms. The derivative acts on the measurement, not the error, so the output does not spike when the target changes suddenly.

What each gain does

In real motor control the output hits a voltage limit, so anti-windup is also needed to stop the integral growing without bound.