Does a twin that models each axis alone certify gains that actuator coupling destabilises?

What it found

For a two-axis loop x’ = x − kGx with cross-gain c, the stable-gain limit is 2/(1+√p) (p=c₁₂c₂₁≥0) or 2/(1+|p|) (p<0) instead of the twin’s 2, so a twin-certified 10% margin (k=1.8) fails at c=1/9, and no positive gain is stable once √p≥1. The twin-deadbeat gain has real rate √|p|, not 0 (6–270 steps to 10⁻⁶ for c=0.1–0.95 vs 1). A diagonal gain fitted from logs is 1+cρ for input correlation ρ (Monte Carlo matches to four digits), giving real rate c(1+ρ)/(1+cρ) (0.300 at ρ=0, 0.461 at ρ=1); the unbiased full fit has variance ∝ 1/(1−ρ²) (verified within 5%), so near-collinear logs make coupling unidentifiable while the per-axis fit returns a confident wrong gain. Follow-up to the control twin. Stylised: linear constant coupling, two axes, noiseless plant.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

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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.