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Dynamic Systems


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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