= Current-sign uncertainty in dead-time compensation
<Current-sign uncertainty in dead-time compensation> occurs when the direction of measured load <electric current> does not reliably identify its direction during the switching interval being corrected. The recirculation path during <bridge switching dead time> depends on that direction. Manufacturer switching diagrams show how the body <diodes> provide paths when the controlled devices are off.<Using power MOSFETs in DC motor control applications by Nexperia>[IAN50004, §4.1, Figures 5–6: nonoverlap and inductive-current recirculation]{ref}
Use the ideal half-bridge model in <current-polarity dead-time compensation>: bus separation $V_d$, period $T$, effective delay $t_d$, and an actual nonzero current sign $\sigma\in\{-1,1\}$ held constant throughout that interval. Let $a=V_dt_d/T$. A commanded additive correction $au$, where $-1\le u\le1$, leaves average output error
$$
e=a(u-\sigma).
$$
A correct sign gives zero error with $u=\sigma$. An opposite sign gives magnitude $2a$, twice the uncompensated magnitude. For $V_d=48\,\mathrm V$, $t_d=0.5\,\mathrm{\mu s}$ and $T=50\,\mathrm{\mu s}$, $a=0.48\,\mathrm V$ and a wrong full-sign correction gives $0.96\,\mathrm V$ error. These conclusions assume unclipped commands and the stated rail-clamping model.
A <current-sign certificate from sensor delay> combines measurement and motion bounds. Suppose a reading $i_m$ refers to time $t_0-\tau$, has absolute error at most $\epsilon_i$, and the true current satisfies $|di/dt|\le L_i$ from then through the end of $[t_0,t_0+t_d]$. For every time in that switching interval,
$$
|i(t)-i_m|\le b,\qquad b=\epsilon_i+L_i(\tau+t_d).
$$
This follows by adding the measurement error to the integrated derivative bound. A positive sign is certified if $i_m>b$; a negative sign if $i_m<-b$. Within the remaining band, neither sign is certified by those bounds. At equality, a zero can still occur, so strict sign certification requires a strict inequality.
For an original example, take $\epsilon_i=0.020\,\mathrm A$, $L_i=5000\,\mathrm{A/s}$, $\tau=2\,\mathrm{\mu s}$ and $t_d=0.5\,\mathrm{\mu s}$. Then $b=0.0325\,\mathrm A$. A $0.060\,\mathrm A$ reading certifies positive current, whereas $0.025\,\mathrm A$ permits currents from $-0.0075$ to $0.0575\,\mathrm A$. A sign selected solely from the latter reading can therefore be wrong. A bound covering only the sensing instant would miss the delay contribution.
Robust and probabilistic choices answer different questions. If both signs are possible and nothing else is known, the worst-case error is $a(1+|u|)$; its minimum occurs at $u=0$. If instead a validated conditional probability $p=\Pr(\sigma=1)$ is available and mean squared error is the objective, differentiation gives
$$
u_{\rm opt}=2p-1,\qquad \min_u\mathbb E[e^2]=4a^2p(1-p).
$$
For $p=0.75$, the optimal fractional correction is $u=0.5$ and the predicted RMS error is about $0.416\,\mathrm V$ for the bus example. That is a probability-model prediction, not a worst-case sign guarantee.
A proposed validation records sensor timestamps, actual load <electric current>, gate timing and midpoint <electric potential difference> on a common time base. Compare integrated cycle errors in certified and uncertified sign intervals, including crossings within the dead time. A dead band or <Schmitt trigger> can reduce noisy toggling, but holding a previous sign through a genuine crossing can prolong a wrong correction; the relevant test is whether the current-path assumptions and timing bounds hold.
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