# FAST Linearization with windspeed=0

Hi everyone,

I run FAST Linearization with windspeed=0 and rotspeed=0, but I got a asymmetric K matrix, and I think the K matrix should be symmetric without aerodynamic force.

This K matrix also cause a complex eigenvector, and the eigenvector should be real under symmetric K matrix.

I cannot figure out why this happened, maybe the FAST Linearization not work with windspeed=0?

Does anybody run this case before?

Thank you very much.

Kuangmin Gong

Hi Kuangmin,

FAST creates the linear model using numerical differentiation via the central-difference-perturbation numerical technique. This works well in most cases, but can lead to minor asymmetries in the resulting stiffness (K) matrix due to numerical error. The magnitude of the numerical error depends on the degree of nonlinearity in the model, the size of the perturbations, and the size of the numbers relative to the number formats. Of these, the size of the perturbations are the easiest to control. The default perturbation sizes were determined by testing with many different turbine models, so, are usually quite good. If you wish to change this, however, you can do so near the beginning of SUBROUTINE FAST_Lin.f90/Linearize(). This will require a recompile of the source code.

From the FAST linear output file you sent me in the e-mail corresponding to this post, I looked at the asymmetries and noticed that most of them are quite small relative to their respective diagonal value. The largest asymmetry error is less than a 4% of the corresponding diagonal (and most are much smaller than this). So, I wouldnâ€™t be too concerned about the asymmetry in this case. If you really need a symmetric matrix you can eliminate the minor asymmetry through post-processing by replacing K with 1/2*( K + TRANSPOSE( K ) ).

By the way: the best way to run with a windspeed = 0 is to run with CompAero set False. Using wind files with zero wind speeds simply means that there is no inflow (i.e., still air). However, the vibration of the turbine can still produce (albeit small) aerodynamic forces in the still air. Setting CompAero to False sets all aerodynamic forces to zero (as in a vacuum).

Best regards,