State Vector 3 Real Poles 1 Real Zero Companion Matrix, Step response and Bode Plot

Cuthbert Nyack
This applet shows the transient behaviour of the state vector components x1, x2 and x3 for a third order system when A is a companion matrix. The Bode plot for the output x1 is also shown.
In this case, the x1 response is the standard response for a third order system. The x2 response is a differentiated version of the x1 response with an advance in phase and the x3 response is a differentiated version of the x2 response with an advance in phase.

The eg parameters (11.3, 1.0, 1.0, 1.0, 10.0, 2.0, 0.4) show that the system response is oscillatory and unstable for larger K.

The eg parameters (8.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9) show that the oscillations in the system response is damped by the zero.




Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.