The graph below shows the response of a 2nd order system to a non-zero initial conditions. The system's poles are denoted by an x. You can change pole locations by dragging them on the complex plane. As you change the pole location the corresponding system descriptor are updated. In addition to grid lines on the graph show lines of constant damping (radial lines) and lines of constant natural frequency (arcs). Experiment with how pole locations and notice how a change in the pole location affect the time domain response and response descriptors.
After experiment with this system, go back to this experiment and notice how the addition of poles and zeros affect the response. Our descriptors are valid for only a first or second order systems but can be used to approximate higher order systems that have dominate polesTotal Response of a DEQ
|Settling Time, ts (sec)||1||Damping Ratio, ζ||1|
|Damped Frequency, ωd (rad/s)||1||Natural Frequency, ωn (rad/s)||1|