FAST Linearization

Dear Hernan,

Equation 3.5 is a first-order linear state space model with one state (rotor speed), one control input (collective blade-pitch angle) and one wind disturbance (mean hub-height wind speed). You can get this model directly through a linearization analysis in FAST v8 with a model where only the generator DOF is enabled in ElastoDyn and LinInputs = 1 in the FAST primary input file. In the resulting “A” and “B” matrices, you’ll have to eliminate the azimuth angle as a state, as described in my post dated May 13, 2016 in the following forum topic: Learizing Baseline 5MW Wind Turbine with FAST - #76 by Jason.Jonkman. In the resulting “B” matrix, you can ignore all inputs except HWindSpeed and BlPitchComC.

Figure 3.10 on page 34 is a graph of the steady-state rotor torque as a function of mean wind speed and blade-pitch angle for a fixed rotor speed. To get this graph, you could run FAST with the torque and pitch controllers disabled (with the generator DOF disabled), and run a series of simulations at different fixed wind speeds and pitch angles at a fixed rotor speed (rated), recording the steady-state solution for rotor torque for each simulation.

I hope that helps.