State Vector 2 Real Poles Partial Fraction Expansion, 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 + x₂ response is the standard response for a second order system.
The eg parameters (2.0, 1.1, 1.2, 1.0, 0.1) show that as the poles get close together x1 and x2 are almost out of phase but with sufficient difference so that their sum gives the output.

The eg parameters (2.0, 0.1, 7.0, 1.0, 1.0) show that as the poles get far apart, then the output is dominated by one component of the state vector.

Gif image below shows how applet should appear.

Return to main page
Return to page index