Dynamic Systems

Example

Assign a differential system with derivatives in the input.

Plot the magnitude of the response vs frequency, adding circles at selected frequencies. This is done by generating and combining two plots.

Example

A Nichols plot is useful for quickly estimating the closed-loop response of system with unity-feedback, given its open-loop transfer function. For example, let the open-loop transfer function be:

By default a Nichols plot includes constant-phase and constant-magnitude contour plots of a closed-loop system.  From the graph below, the peak closed-loop response is about 5 dB, at 0.8 rad/s, because that is the highest constant-magnitude contour that it touches (estimating).

Here we plot the actual closed-loop response and confirm that the maximum gain is approximately 5 dB, at 0.8 rad/s.