Root Locus for 5th Order Polynomial

Cuthbert Nyack

Applet shows the root locus of a system with a fifth order characteristic equation. The locus has 5 asymptotes at ±36°, ±108° and -180°.

Eg parameters (0.0, 6.0, 12.0, 14.0, 14.0, 4.0, 0.0).
The real open loop poles are at -0.43, -2.02, -3.25 and the cc pole is at -0.15 ± j1.18(calculated from a5 and the 3 real poles).
For K = 1.0 , setting sik = 0 gives the real closed loop poles at -0.56, -1.88, -3.32 and setting sik = 1.19 gives the cc pole at -0.12 ± j1.19. (system stable)

For K = 4.0 , the real closed loop pole is at -3.38 and the cc poles are at -1.3 ± j0.3 and 0.0 ± j1.14. (system oscillatory)

For K = 8.0 , the real closed loop pole is at -3.42 and the cc poles are at -1.44 ± j0.77 and +0.14 ± j1.15.(system unstable)

Gif image below shows how applet should appear.

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