Pole Placement 3 Real Poles Product, Step response and Root locus

Cuthbert Nyack
This applet shows the transient behaviour of the state vector components x1 for a third 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, K1 and K2 are changed is shown.

The eg parameters (8.0, 1.0, 1.0, 1.0, 0.0, 0.0) show the transient behaviour with P control without pole placement. Poles are at ~ -3.0 and 0.0 ± j1.73 and the transient behaviour is oscillatory.
Using K1 to place the poles results in the parameters (8.0, 1.0, 1.0, 1.0, 1.0, 0.0). With this value of K1 = 1.0, the poles have been moved to ~ -0.9 ± j1.0 and the oscillations have been damped out.



Using K2 to place the poles results in the parameters (8.0, 1.0, 1.0, 1.0, 1.0, 0.0). With this value of K1 = 1.0, the CC poles have been moved to ~ -1.9 and ~ -0.5 ± j2.8 and the oscillations have been damped but not as satisfactory as with K1.

The combination K, K1 and K2 gives flexibility in placing the poles. (5.6, 1.0, 1.0, 1.0, 0.9, 0.25) places the cc poles at ~ -1.0 ± j1.0.




Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.