Pole Placement 2 Real Poles Product, Step response and Root locus

Cuthbert Nyack
This applet shows the transient behaviour of the state vector components x1 for a second order system when A is derived from a product of lag factors. 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, 0.4, 1.0). With this value of K1 = 0.4, 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. With this set of state vectors the poles are more sensitive to K1.

Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.