Control Systems - Level 3
The P Term
Concept
Proportional control makes the actuator effort proportional to the error:
u(t) = Kp · e(t) where e(t) = setpoint − position
The larger the error, the harder we push. As the plant approaches the setpoint, the error shrinks and the effort tapers smoothly toward zero.
Try it:
- Start with Kp = 1. The mass drifts in lazily and settles short of the target.
- Crank Kp up. The response gets snappier — and eventually starts oscillating.
- There is a sweet spot.
Watch the trade-off: low Kp = slow and sluggish; high Kp = fast but oscillatory. Nothing about this changes even with perfect, noise-free sensors — it’s just how a proportional controller behaves against an inertial plant.
Goal
Tune Kp so the mass reaches the setpoint and stays within ±0.05 for at least 2 seconds, with no more than 0.15 overshoot. Hint: somewhere around Kp = 3-5 tends to work on this plant.