# 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
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 (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.