01 · Question
What does closing the loop change?
How should a one-joint pendulum behave when its controller knows only position error versus both position error and velocity?
02 · Prediction
Position correction should need damping.
P-only control should push on position error and tend to overshoot or oscillate. Adding derivative feedback should damp motion and settle more cleanly.
Controller structure · conceptual
Derivative feedback changes what the controller can notice.
The two rows summarize the control laws used in the comparison. This is a controller schematic, not a replay of recorded simulator data.
03 · Experiment
Keep the mechanism small.
A MuJoCo pendulum used one rigid link, one hinge, gravity, and one motor. The same script exposed constant, P, and PD control through direct state and control values: qpos, qvel, and ctrl.
04 · What happened
The prediction matched the run.
P-only behavior overshot or oscillated more. PD behavior was visibly more damped and settled more cleanly.
05 · Model update
Position error and velocity answer different questions.
P answers “how far from target?” D adds “how fast am I moving?” That was enough evidence to move on rather than polish this controller.
Source