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Dead Time and Phase

A pure time delay (dead time) in a system never changes the gain, but produces a phase lag that grows linearly with frequency. At low frequencies this is negligible, but at higher frequencies the dead time alone can eat up a large part of the phase margin and make an otherwise stable loop unstable.

φ=−ωT\varphi=-\omega Tphase lag from dead time T, in radians

Symbols

TTdead times
ω\omegafrequencyrad/s
φ\varphiphase lagrad

Example

T=0.05T=0.05 s at ω=20\omega=20 rad/s:

φ=−20⋅0.05=−1\varphi=-20\cdot0.05=-1 rad ≈−57.3∘\approx-57.3^\circ.

Dead time only changes the phase, never the magnitude – do not fold it into ∣G∣dB|G|_{dB}.
Practise frequency analysis for free →

← Phase Margin · First-order system →

Part of Control Engineering: Frequency analysis.