Routh Hurwitz Criterion for 5th Order Polynomial

Cuthbert Nyack

This Applet shows the Routh Hurwitz criterion applied to a system with a 5th order polynomial as its characteristic equation . They allow the effect of gain and pole locations on the stability of the system to be studied. The step response of the system is also shown.

The first Applet shows the variation of the elements in the first column of the RH array as a function of gain from 0 to K
The second shows the more conventional array with the step response added. When the system is oscillatory the frequency can be calculated from the auxiliary equation or measured from the step response.

some eg parameters and their stability are shown below:-

(20.0, 3.0, 9.0, 9.0, 12.0) unstable for K > 6.7.
(20.0, 7.0, 7.0, 17.0, 7.0) unstable for K > 10.3.
(20.0, 2.0, 10.0, 10.0, 10.0) unstable for K > 8.7.
(20.0, 3.5, 6.0, 16.0, 7.0) unstable for K < 2.5 and K > 16.5.
(20.0, 3.5, 6.0, 16.0, 7.0) unstable for K < 3.4 and K > 7.8.

Gif images below shows how applet should appear.

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