Step Response and Nyquist plot for Distance/Velocity Lag

Cuthbert Nyack

The Applet below show the nyquist 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-^bs/(s + a),
C(s)/R(s) = Ke-^bs/(s + a + Ke-^bs)

With the resolution of the plot he eg Parameters (2.3, 1.0, 1.0, 1.0, 1.0, 2.03) show the step response of the system with D/V lag being delayed by "b" and oscillatory(pink plot) . Using w = 2.03, the angular frequency = ~ 2.03rad/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 green.
Comparing the yellow with the red curve shows the effect of the D/V lag on the Nyquist plot and it is the increased phase lag which causes the system to become unstable. The Nyquist plot of the system with D/V lag shows the characteristic spiral shape as the phase lag increases without limit as the frequency increases. The eg parameters (1.9, 1.46, 2.0, 2.0, 2.0, 1.22) shows the spiral "opened out". These parameters mean that the system is oscillatory with K = 1.9 and angular frequency 1.22.

Gif image below shows how applet should appear.

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