Pole Placement 2 Real Poles Companion Matrix

Cuthbert Nyack
This applet shows the transient behaviour of the state vector components x1 for a second order system when A is a companion matrix. The root locus plot is also shown.
The change in the transient behaviour and root locus as the pole placement parameters K and K1 are changed is shown.

The eg parameters (5.0, 0.5, 0.1, 0.0, 1.0) show the transient behaviour with P control without pole placement. Poles are at ~ -0.3 ± j2.2 and the transient behaviour is oscillatory.
Using K1 to place the poles results in the parameters (5.0, 0.5, 0.1, 2.0, 1.0). With this value of K1 = 2.0, the poles have been moved to ~ -1.3 ± j1.8 and the oscillations have been damped out as shown by the pink line. For comparison, the response when only K is used is still shown as the magenta line.

K moves the poles vertically while K1 moves them mostly horizontally, the combination gives flexibility in placing the poles.




Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.