Does measurement noise, or dither, hide an actuator deadband the twin lacks?

What it found

At K=0.5, d=0.1 the linear twin’s exact stationary rms is s√(K/(2−K)); the real deadband loop is 27× worse at s=0.01 (0.1591 vs 0.0058) but 0.37× at s=0.05 (0.0107 vs 0.0289), because noise dithers the actuator, so a validation in the high-noise regime would call the deadband harmless. Deliberate dither removes the noise-free stall (rms 0.2000 to 0.0001 at a=d) but only hurts at s=0.05 (0.0103 to 0.0226), and under noise mild under-compensation of the width beats the exact width (0.0053 vs 0.0116 at s=0.02). Follow-up to the deadband twin. Stylised: scalar integrator, single-seed simulations without confidence intervals.

A figure from its own output

Paper, code and results

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

More in Digital twins & sim-to-real

• How large a manoeuvre can a twin without an actuator rate limit be trusted for?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.
• Does a twin with a rigid drivetrain miss the hunting cycle caused by gear backlash?A rigid-drivetrain twin says the PI loop converges but gear backlash makes the real loop hunt at 1.3–2.9× the gap (exactly ∝ h); describing-function prediction 7–10% high, and bistable starts can hide it.
• How wrong is the stopping distance of a twin that models friction as purely viscous?A viscous-only twin never stops (6.5–17.7 s to reach 1e-3…1e-9 vs 1.95 s real) and its fitted gain b + c·E[v]/E[v²] depends on the logged speed range; fitted on [1,3] it overestimates stopping distance ×1.8–17 below and underestimates above v*=7.3, no single viscous gain beats 0.87 worst error over [0.05,3], affine fit recovers exactly.
• Does a twin with correct sliding friction still miss stick-slip hunting from static friction?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.
• How much bandwidth can a controller tuned in a twin with an instantaneous actuator really have?A twin with an instantaneous actuator is stable at any gain; the real loop with lag τ is stable iff τ<kd/kp=2ζ/ωn, hunts at the twin's own ωn, decays no faster than 1/(3τ) for any gains, and the real-optimal bandwidth is ≈0.26–0.46 of the limit.
• How high a bandwidth does a rigid-body twin let you push when the real joint is flexible?A rigid-body twin certifies every PD bandwidth; with load-side sensing the real two-mass loop is unstable above ε_c ≈ δ/ζ of the flexible-mode frequency (exactly independent of mass ratio, unstable at any gain with no modal damping), step-response validation misses it, and the certified bandwidth inherits modal-damping error one-for-one.

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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.