I have read trough “FAST User’s Guide Chapter Linearization” as well as “MBC3 MATLAB codes”. I have some questions about the MBC3 eigenvalues and natural frequency (N.F) calculation.
It is quite straightforward in “FAST User’s Guide Chapter Linearization” to end up with system state matrix - A, control input matrix - B, wind input disturbance matrix - Bd, and output state matrix - C.
Regarding the calculations for eigenvalues in MBC3, the questions are attached.twrfa1.docx
twrfa1.docx (16.6 KB)
Your understanding of how the natural frequencies are derived from the state matrix is correct. For further information on the mathematical background, I recommend reviewing a textbook that covers linear state-space-based models and their solution via the matrix exponential (e.g., a modern controls textbook).
The eignevalues of the state matrix contain information on the natural frequencies and damping ratios of the system.
As described in this forum topic: http://forums.nrel.gov/t/learizing-baseline-5mw-wind-turbine-with-fast/494/1, rigid-body modes show up in MBC3 as a pair of zero-valued (or near-zero-valued) frequencies with +/- inf damping (i.e., eigenvalues with real values only). You should confirm with MSC, but I suspect the ADAMS linearization produces something similar.