Dear Nikita,
Your analysis approach sounds similar to the one discussed in the following forum topic: FAST: Tower Model, where my comments likely apply (particularly, my Aug 06, 2014 post).
Regarding aerodynamic damping, a FAST linearization analysis (currently available only in FAST v7) can produce a linear state-space model that includes aerodynamic damping. Alternatively, I’ve seen publications (not NREL’s) that discuss how to estimate aerodynamic damping for a given rotor.
Best regards,