Magnitude of Characteristic Equation for 2 Real Poles

Cuthbert Nyack
Applets below show magnitude and phase in the s plane of the characteristic equation with poles at -a, -b.
For (0.4, 3.0, 1.0, -50.0, 40.0, 25) closed loop poles are real and are at -2.774 and -1.225.
For (3.0, 3.0, 1.0, -20.0, 40.0, 15) closed loop poles are complex conjugate and are at -2.0 ± j1.414.
For (4.0, 0.0, 0.0, -30.0, 40.0, 15) closed loop poles are on the imaginary axis are at -0.0 ± j2.0.




Applet show that for real CL poles (0.4, 3.5, 0.5, 1.0, -60.0, 40.0, 0.8) there is a bifuraction in phase along the real axes between the 2 poles.
For CC CL poles (5.0, 3.0, 1.0, 1.0, -30.0, 40.0, 0.8) there is a bifuraction in phase along a line parallel to the imaginary axis and extending from the poles to infinity.




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COPYRIGHT 2006 Cuthbert Nyack.