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 x1 and x2 for a second 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 second order system while the x2 response is a differentiated version of the x1 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 x2 also increases because of the derivative.

Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.