Dead time Bode plot

Example 8.5. What are the Bode and Nyquist plots of a dead time function G(s) = e-6s ... 

Bode plots for transfer functions with dead time... 

The whole idea of handling dead time applies to other types of frequency-domain plots, but the Bode plot is the easiest to learn from. 

For a first order function with deadtime, the proportional gain, integral and derivative time constants of an ideal PID controller. Can handle dead-time easily and rigorously. The Nyquist criterion allows the use of open-loop functions in Nyquist or Bode plots to analyze the closed-loop problem. The stability criteria have no use for simple first and second order systems with no positive open-loop zeros. 

Construct the Bode diagram and Nyquist plot of a first-order system with dead time, having a transfer function... 

Figure 17.6 Bode plots for pure dead-time system.

As was derived in chapter 9, the amplitude ratio for a dead-time process is 1.0 and the phase shift -0)6. The amplitude ratio for the process becomes then AR (second-order process) x AR(dead-time process). The phase shift of the process becomes then (second-order process) + dead-time process). Figure 32.3 shows the Bode diagram in which the logarithm of the amplitude ratio and the phase shift are plotted against the frequency O). For the amplitude ratio two asymptotes emerge, one for low frequencies a>- ) (static behaviour) en one for high frequencies 0)- °° (high-frequency behaviour). The values can easily be calculated from ... 

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