Subsection SINGULAR VALUES
Singular
Values
The first window of this subsection displays the singular value (SV) plot of the frequency response of the LTI current model (the frequency range is chosen automatically).
The button S.Vectors opens the following window in which it's possible to analyze all the Singular Vectors of the current model:
for every Singular Vector, the two graphics represent the absolute value of its components along the system outputs and inputs at the frequency wo indicated in the relative edit-field; the text-fields S.Vector and S.Value indicate, respectively, the index and the absolute value of the considered vector, while in the frame below them is reported the rank of the transfer matrix of the model
Gs(jwo) = C inv( jwo I - A) B + D
and its 2-norm condition number that represents the ratio in dB of the largest singular value to the smallest one (large condition numbers indicate a nearly singular matrix Gs).
The buttons << and >> select another singular vector, while the button SAME allows to re-examine the same one at a new frequency value.
The button Norm(G(jw)) allows to visualize, in a new window, the graphic of the maximum singular value of Gs(jwo) along the plane inputs-outputs (the default wo is 0.001). This graphic is a contour plot of the matrix Gs(jwo) that treats the value in Gs as heights above a plane and plot its level curves with different colors chosen in accordance with the current color map (the default color map is JET which ranges from blue to red, and passes through the colors cyan, yellow, and orange).
Inside the relative window, the user can modify the reference frequency wo and view the new graphic pressing the PLOT button.
Note: all
the graphics are associated with a popup menu that can be activated pressing the right mouse button
over them.