Why are the stability margin (gain and phase) plots inaccurate when using the linear analysis tool in Simulink Control Design 6.6 (R2007a)?

When using the Control Design Tools to perform linear analysis, I encounter a problem when I select the bode plot option and set the characteristics to be 'All Stability Margins'. In the generated bode plot, there is an offset (i.e. the markers are off) in the displayed points vs. the calculated margins on the graph.

Answer 1

[MathWorks Support Team]

This offset is due to a limitation in the built-in scaling algorithm for state-space models used in the Simulink Control Design Tool and this enhancement has been introduced to remove the offset in R2008a version.

The markers are off because they are computed from the ZPK form of the linearized model. The state-space and ZPK responses disagree by a large factor (in other words, the Bode plot is inaccurate).

Systems with infinite energy are challenging, because the scaling algorithm emphasizes accuracy over the frequency band with the most energy. The current heuristics to detect and eliminate integral action are not robust enough, and result in rare failures, as in the present case.

There is no simple workaround for this offset, but you can edit the function "xscale.m" and replace the line

w = 10.^[-8;-6;-5;-4;-3;-2;-1;0;1;2;3;4.3;6;8];

with the intersection of this vector with the frequency range of interest, which depends on the use case.