A bang-bang controller with no deadband drifts toward the faster direction

Fact

"Hold the value at target" written as actuate = (value > target) is a relay with no hysteresis. At the switching point it chatters at the sample rate with roughly a 50% duty cycle, so the value does not settle at target — it moves at the average of the two rates.

That average is only zero if the two directions are symmetric. Where they are not — a hook that rises at 1.35× the speed it sinks, a thruster stronger than gravity, a fill rate above the drain rate — the value walks steadily toward the faster direction and leaves the band entirely.

Why it matters

The controller reads as obviously correct, and it is correct in intent, so the drift gets attributed to the plant: to buoyancy, to a clamp, to an integration error. In a test harness it silently invalidates the scenario, because the run that was supposed to hold a depth spends its time somewhere else and reports whatever lives there instead.

How to apply

• Give it a deadband: if (v > hi) up = true; if (v < lo) up = false; with the band wider than one step of the faster rate. That is the whole fix.
• Size the band from the rates, not by eye: lo/hi at least maxRate × dt × 2 apart.
• Suspect this whenever a hold-at-a-value loop ends up pinned at one extreme. Symmetric rates hide it completely, so it appears only once the two directions are tuned differently.