Disturbance matrix in openFast linearization

Dear all,

I am working on the openFast linearization and trying to get the state equation

\dot{x}=Ax+Bu+Bd*ud.

I noticed that in many papers ud is selected as [Vx, Vy, Vz]^T by Fastv7 or something, but what I got via openFast are horizontal wind speed, vertical power-law shear exponent and propagation direction (the first three elements in the input list). Meanwhile, I cannot find the latter two in OutList. Inversely, Vx, Vy, Vz can be output.

How can I understand the disturbance matrix Bd in openFast correctly? It would be better if Vx Vy Vz can be included in order of inputs.

Thank you very much!
BR,
Yarong

Dear Yarong,

The horizontal wind speed and propagation direction in the linearization of OpenFAST are similar to Vx and Vy , but correspond to the vector magnitude and direction rather than the vector components. Vz is not a standard wind disturbance available in OpenFAST. I would say that the OpenFAST wind disturbance inputs are more commonly used than the vector components. While FAST v7 supported Vz as a wind disturbance input, unlike OpenFAST, it was not commonly used for controls design, and so, was dropped in OpenFAST. Moreover, FAST v7 also supported the horizontal wind speed and direction rather than the vector components.

Best regards,

Dear Jason,

Thank you very much for your clear response in time.

If I understand correctly, I should select horizontal wind speed and propagation direction as the ud vector. Since these two elements cannot be obtained from OutData directly, I also need to transform [Vx, Vy]’ to my ud by \theta=atan(Vy/Vx). Am I right?

Thank you again!

BR,
Yarong

Dear Yarong,

If you want Vx and Vy instead of the vector magnitude and direction, what you propose sounds correct.

Best regards,

Dear Jason,

Are these two the magnitude and direction corresponding to