No natural damping means P alone can’t save you

A system with zero built-in damping — like a ball rolling on a frictionless beam — can’t be stabilised by proportional control alone, no matter the gain.

Why it works

Proportional-only feedback on a pure double integrator is only marginally stable in theory, and real-world lag (a servo, a sensor) tips it into genuine instability. Derivative action supplies the damping the physical system never had.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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More in Control Systems

• Sample at least twice the fastest signalTo capture a signal faithfully, sample above 2× its highest frequency — in practice 5–10×.
• Aliases fold around half the sample rateA tone above fs/2 reappears mirrored below it — 900 Hz sampled at 1 kHz reads as 100 Hz.
• Find the edge, then back offTuning by hand: raise proportional gain until the loop just oscillates, then halve it.
• Read the oscillationSlow rolling oscillation = too much integral. Fast jitter = too much derivative amplifying noise…

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