Dead time is what creates a gain ceiling. Remove it and every standard tuning formula divides by zero, because there is no longer a phase limit to respect — the difficulty was never the lag, it was the delay.
A lag reduces gain gradually and only ever approaches 90° of phase; a delay adds phase without limit, so at some frequency the correction arrives exactly out of step and the loop drives itself. That is the real ceiling, and every tuning rule is a rule about staying under it. It is why every method backs the gain off as dead time rises, and why θ/τ predicts how hard a loop will be far better than any other single number.
Real loops always have some delay — sampling, transport, actuator response — so the zero-dead-time case is a limit rather than a design point. And past θ/τ ≈ 1 the conclusion inverts: no PID tuning helps, and the answer is a predictor, a slower loop, or removing the delay.
Estimate with the rule, then check it against the calculator that models it properly.
Open PID Control →Dead time is what creates a gain ceiling. Remove it and every standard tuning formula divides by zero, because there is no longer a phase limit to respect — the difficulty was never the lag, it was the delay. A lag reduces gain gradually and only ever approaches 90° of phase; a delay adds phase without limit, so at some frequency the correction arrives exactly out of step and the loop drives itself.