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

Cuthbert Nyack

This applet shows the transient behaviour of the state vector components
x_{1}, x_{2} and x_{3} for a third order system when **A** is a companion matrix. The Bode plot for the output x_{1} is also shown.

In this case, the x_{1} response is the standard response for a third order system.
The x_{2} response is a differentiated version of the x_{1} response with an advance in phase and the x_{3} response is a differentiated version of the x_{2} response with an advance in phase.

The eg parameters (8.0, 1.0, 1.0, 1.0, 2.0, 0.4) show that the system is oscillatory with x_{2} leading x_{1} by 90º and x_{3} leading x_{2} by 90º.

Gif image below shows how applet should appear.

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COPYRIGHT © 2006 Cuthbert Nyack.