The Applet below show the Bode plot of a first order type 0 system with and without distance-velocity or transport lag. The open and closed loop transfer function of the system is:-

G(s) = Ke-

C(s)/R(s) = Ke-

The eg Parameters (2.27, 1.0, 1.0, x) show the system with D/V lag being oscillatory(pink plot). Using hpos, the period is ~3.07s and w = ~ 2.05rad/s.

The plots show that the system is oscillatory when both the gain and phase margins are zero. The step response without the D/V lag is shown in cyan.

The yellow and red curves show that the magnitude plot is unaffected by the D/V lag. Comparing the green with the orange curve shows the effect of the D/V lag on the phase and it is this effect which causes the system to become unstable.

The value of K for instability is very dependent on b(eg, b = 1.5, K = 1.73), (b = 0.5, K = 3.87).

Gif image below shows how applet should appear.

COPYRIGHT © 2006 Cuthbert Nyack.