Does an inverted-pendulum loop tuned on a fixed-period twin survive missed samples, and does an interval-aware gain fix it?
research/free-pendmiss
On a linearised pendulum (L = 0.5 m) a fixed twin-tuned gain survives any miss probability with slow poles unless the plant is very unstable per sample (limit q = 0.21 at ωh₀ = 1.4), a deadbeat tuning fails by q = 0.03 to 0.10, and a gain recomputed from the actual interval was stable at every q in all 15 cases. Linear, noise-free, simulated.
What it found
Follow-up to free-jittertwin on a second-order plant: the linearised inverted pendulum x′′ = (g/L)x + u, L = 0.5 m, exact zero-order-hold discretisation, interval h0 or 2h0 (missed sample, probability q). Mean-square stability is the exact spectral radius of the second-moment operator; almost-sure stability is a Monte Carlo Lyapunov exponent. A gain fixed at the nominal period with poles at 0.8 tolerates every q up to ωh0 = 0.8 but only q = 0.21 at 1.4; deadbeat tuning allows only q = 0.03–0.10 (almost surely 0.80). A gain recomputed for the elapsed interval was stable at every q in all 15 cases. Linear, noise-free, known plant, one plant length; pole values and sweep points are chosen, not sourced.
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.