Mathematica provides a full suite of tools needed for the classical analysis and design of control systems, leveraging Mathematica's hybrid symbolic-numeric arithmetic capabilities as well as high-quality visualization methods. Built-in frequency response analysis tools include Bode, Nyquist, and Nichols plots, as well as singular-value visualization.
RootLocusPlot — plot root locations as a parameter varies
BodePlot — magnitude and phase plots of the frequency response
NyquistPlot — polar plot of the frequency response
NicholsPlot — magnitude vs. phase plot of the frequency response
GainPhaseMargins — compute gain and phase margins
SingularValuePlot — plot singular values of the frequency response
PIDTune — automatic PID tuning for any linear system