Root Locus for 3 Real Poles, type 0 and 1

Cuthbert Nyack
Applets below show the angle condition for 3 poles when the transfer function is G(s) = K/((T1s + 1)(T2s + 1)(T3s + 1)) or G(s) = K/(s(T1s + 1)(T2s + 1)).
eg parameters (0.0, 1.0, 1.0, 1.0, 1.0) show the angle condition are 3 straight lines starting from the open loop poles and proceeding along the asymptotes at ±60° and -180°.

eg parameters (1.3, 1.0, 0.65, 0.4, 1.0) show the angle condition starting from the closed loop poles ( ~-3.5, ~-0.75 ±j1.4 in this case ), and ending up along the asymptotes at ±60° and -180°.

eg parameters (9.34, 1.0, 0.65, 0.4, 1.0) show the angle condition starting from the closed loop poles on the imaginary axis ( ~ ±j2.8 in this case ), and ending up along the asymptotes at ±60°. In this case, the step response is oscillatory with w = 2.8 and the frequency response has a sharp peak at js = j2.8.



eg parameters (0.0, 1.0, 0.5, 1.0) show the angle condition starting from the open loop poles and proceeding along the asymptotes at ±60° and -180°.

eg parameters (3.0, 1.0, 0.5, 1.0) show the angle condition starting from the closed loop poles on the imaginary axis ( ~ ±j1.4 in this case ), and ending up along the asymptotes at ±60°. In this case, the step response is oscillatory with w = 1.4 and the frequency response has a sharp peak at js = j1.4.



Gif image below shows how the first applet should appear.

Return to main page
Return to page index
COPYRIGHT 2006 Cuthbert Nyack.