# State Vector 2 Real Poles Companion Matrix, Step response and Bode Plot

Cuthbert Nyack

This applet shows the transient behaviour of the state vector components
x_{1} and x_{2} for a second 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 second order system
while the x_{2} response is a differentiated version of the x_{1} response with an advance in phase.

The eg parameters (30.0, 0.2, 1.0, 1.0, 0.2) show that as the gain
is increased, the oscillation frequency increases and the amplitude
of x_{2} also increases because of the derivative.

Gif image below shows how applet should appear.

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COPYRIGHT © 2006 Cuthbert Nyack.