Does a twin with correct sliding friction still miss stick-slip hunting from static friction?

research/stiction-twin

A twin with the right sliding friction says the PID loop converges, and with no stiction it does; a breakaway excess Fs−Fc makes the real loop stick-slip hunt at ≈0.5–0.9 ΔF/kp (independent of Fc), and short runs can mistake a long stick for convergence.

8 tests

What it found

Unit mass under PID, frictionless twin stable (error below 1e-58). With F_s=F_c (sliding friction identified correctly) the real loop converges in all 15 cases tried, so that twin validates. With a stiction excess ΔF=F_s−F_c it hunts in stick-slip at 0.54–0.93 ΔF/k_p in four of five gain settings, independent of F_c (0 to 20) and of the start, falling with damping; one setting (k_d=4, k_i=5) converges. Scaling is bit-exact for power-of-two scales but the cycle is unique only to about three digits. Negative result: a 1000 s run can show a motionless “converged” error for large F_c/k_i while a 20 000 s run still hunts; the amplitude constant has no closed form here. Follow-up to the backlash twin. Stylised: unit mass, Coulomb plus static friction, noiseless.

A figure from its own output

Figure produced by research/stiction-twin: timestep — stiction-twin/experiments/timestep.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.