How long must a real test run be when its length was sized in a twin with the wrong plant pole?

research/runlength-twin

Real test-run length sized in a wrong-pole twin: exact autocorrelated-cost variance, 3.8× too short (coverage 0.69 vs 0.95) or 2.1× too long depending on the real closed-loop pole, and a pilot-run repair that under-sizes half the time.

11 tests

What it found

A gain designed in a twin whose pole is m× the real one is validated on hardware for a run length chosen in the twin. The variance of the time-averaged cost of a Gaussian AR(1) loop is exact and depends on the closed-loop pole through (1+ρ)/(1−ρ), ρ=a_c², so the twin-sized run is 3.8× too short at m=2, r=0.1 (3,177 vs 12,110 steps; real coverage of a ±5% claim 0.69 vs 0.95 nominal, simulated 0.68) and 2.1× too long at m=1.5, r=5; an oscillating (negative-pole) loop averages as slowly as a sluggish one. Sizing from a real pilot’s lag-one autocorrelation is close to median-unbiased but under-sizes about half the time. Stylised: scalar linear-Gaussian, fixed known gain, normal-approximation interval.

A figure from its own output

Figure produced by research/runlength-twin: run_ratio — runlength-twin/experiments/run_ratio.svg, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.