12. Bode Plots

For the dead-time system, \[Y(t) = X(t-\tau_d) \qquad \quad G(s) = \frac{Y(s)}{X(s)} = e^{-\tau_ds}\] Amplitude ratio (AR) and phase shift (\(\phi\)) of dead-time system is given by \[\text{AR} = 1 \qquad \quad \phi=-\tau_d\omega\]