Several improvements have been made to the DynamicSystems package, including:
Extended FrequencyResponse to handle differential equations with input derivatives.
Extended all models to accept linear, non-differential systems.
Added frequencies option to all frequency-based plots, which permits specifying the precise frequencies at which expressions are evaluated.
Extended Grammians to work with discrete systems.
Added NicholsPlot to the context menu.
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.
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.
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