How large a manoeuvre can a twin without an actuator rate limit be trusted for?

research/slew-twin

A twin without an actuator rate limit is exact only for x₀ ≤ r/k; beyond it the real loop overshoots (0.90 of x₀ at x₀/r=10⁴) and settles in O(amplitude) steps, with an empirical overshoot threshold 2n(2n−1) for k=1/n.

7 tests

What it found

The real loop x⁺ = x + a⁺, with the command rate-limited to r per step, is scale-invariant: it depends only on ρ = x₀/r, while the first-order twin does not. The twin is exact iff x₀ ≤ r/k (difference 0 at 0.999×, 0.1–0.6% of x₀ at 1.01×). Beyond that the real loop overshoots the target (0.23 of x₀ at ρ=100, 0.90 at 10⁴, k=0.3) and settles in O(ρ) steps (29418 at ρ=10⁵ vs the twin’s 13). For k=1/n the overshoot threshold is empirically ρ*=2n(2n−1) (not proved); avoiding overshoot needs a rate limit 12–38× lower than keeping the twin exact. Stylised: scalar plant, no noise or delay.

A figure from its own output

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

Paper, code and results

More in Digital twins & sim-to-real

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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.