Bode & Stability Margins

Margins are what you quote in a design review, and delay margin is the one that predicts field failures — dead time costs phase without costing any gain, so it eats margin invisibly. Every added sample period, filter and network hop spends some of it. Aim for 45–60° phase margin and at least 6 dB of gain margin.

Valid for the minimum-phase, open-loop-stable form shown — an open-loop-unstable plant needs a full Nyquist test, not the Bode criterion. Dead time is modelled exactly (not as a Padé approximation), so the phase lag it contributes is right at every frequency. The delay margin is the single most useful output: it tells you how much extra latency the loop can absorb before it goes unstable, which is what a firmware change or a busier network actually adds. For a first-order-plus-dead-time plant with ultimate gain and period, see Loop Stability; to tune from these numbers, PID Tuning.