# Nyquist Plot for 1 Real Pole, 2 Complex Conjugate Poles and 1RP2CCP

Cuthbert Nyack
Applet shows the Nyquist plot and step response for 1 real(yellow,blue), 2 complex conjugate(orange,cyan) and 3(1 real, 2 complex conjugate)(red,green) pole system. Since all systems are type 0, then plots start on the +ve real axis.
First order plot occurs in the first quadrant(phase from 0 to -90°), second order starts in the first and ends in the second quadrant(phase from 0 to -180°). Both systems are always stable.
Third order plot starts in the first and ends in the third quadrant(phase from 0 to -270°).
eg parameters (3.24, 1.0, 0.5, 1.0, 0.6, 1.0, 1.5) show 3rd order system being oscillatory at ~1.5rad/s.
(1.69, 1.0, 0.5, 1.0, 1.0, 1.0, 1.45) show 2nd order system having a phase margin of 60° at ~1.45rad/s.
(1.45, 1.0, 0.5, 1.0, 1.0, 1.0, 0.99) show 3rd order system having a phase margin of 60° at ~1.45rad/s and gain margin of ~7dB.
(4.15, 1.0, 0.5, 1.0, 1.0, 2.5, 1.62) show 3rd order system having a phase margin of -10° at ~1.62rad/s and gain margin of ~-2dB.
(10.14, 0.4, 0.2, 5.0, 2.0, 1.0, 5.02) show combination(red) of 1 real and 2 cc poles.
(1.0, 2.1, 0.12, 2.1, 1.0, 3.0, 2.1) show that 1st order has a phase delay of 45° at w = a and 2nd has phase delay of 90° at w = (a2 + b2)½.

Gif image below shows how applet should appear.