ORTSF Delay-Margin Certificate

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1. #1

   For the constructed linear plant model with (poles , dominant pole ), and the integrating controller model , the phase margin is

   $$\varphi_{\mathrm{PM}} = \frac{\pi}{2} - \arctan\!\left(\frac{\omega_c}{p}\right),$$
2. #2

   and that modeled loop has the delay margin

   $$\Delta t_{\max} = \frac{\varphi_{\mathrm{PM}}}{\omega_c}.$$
3. #3

   Separately, consider the scalar additive delayed-feedback reduction on one dominant inconsistent mode,

   $$e_{t+1} = \rho e_t - K_c e_{t-d}.$$
4. #4

   For this recurrence, with , the condition

   $$\rho + |K_c| < 1$$