A controller tracks a target. Turn the gain up and it tracks faster — but every correction spends effort, and effort costs energy. Scrub the gain and hover the curves: there is no free accuracy. Set the energy price and watch the cheapest gain move — perf-per-watt, made a dial.
A 2nd-order servo under PD control (u = K·(r−x) − v), Node-verified: error falls and effort rises with gain, and total cost = error + price·effort has a single cheapest gain. Built on the reusable probe.js primitive (scrub · hover-to-inspect · semantic color grammar) — the template every figure here is moving to. Runs on your device. · Institute for Physical AI @ BMI