Root Locus and Magnitude Condition of 3 Real Poles and 1 Real Zero

Cuthbert Nyack
In the applet below, the red-blue boundary shows the magnitude condition, and the closed loop poles can be found by locating the point on the magnitude condition where the angle condition is also satisfied.

For parameters (1.5, 1.0, 0.5, 4.0, sr, si), the closed loop poles for K = 4 can be found by agjusting sr, si until the angle condition is satisfied. f = -180.2° for sr = -0.59, si = 1.51. f = -540° for sr = ~-1.824, si = 0.0. The closed loop poles are at ~-1.824, ~-0.59 ± ~j1.51 for K = 4.

Gif image showing how applet should appear is shown below.

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COPYRIGHT 2006 Cuthbert Nyack.