Dear all,

I’ve a question regarding some linearization results I’ve got, which I couldn’t understand. So I guess your help is needed

I’m trying to linearized the 5MW standard wind turbine with the following features:

Enabled DOF: GenDOF

Enabled Control Inputs: individual pitch of blade 1,2,3

Also As recommended by FAST User’s guide I’ve set the following

```
TrimCase = 3 (Collective Pitch)
YCMode = 0
PCMode = 0
VSContrl = 1
VS_RtGnSp = 9999.9E-9
VS_RtTq = 43093.55 [N.m] (rated torque)
VS_Rgn2K = 9999.9E-9
VS_SlPc = 9999.9E-9
BlPitch(i) = 12.0534 [deg] (i=1,2,3)
RotSpeed = 12.1 [rpm]
```

Also didnot include any platform effects.

```
PtfmModel = 0
```

The wind input is a 16 m/s constant wind without any turbulence or shear components.

Sample of wind input file

```
Time HorSpd WndDir VerSpd HorShr VerShr LnVShr GstSpd
! (sec) (m/s) (deg) (m/s) (-) (-) (-) (m/s)
0.000 16.000 0.000 0.000 0.000 0.000 0.000 0.000
0.025 16.000 0.000 0.000 0.000 0.000 0.000 0.000
0.050 16.000 0.000 0.000 0.000 0.000 0.000 0.000
0.075 16.000 0.000 0.000 0.000 0.000 0.000 0.000
```

The linearized equation of motion is of the form

M*q’’+C*q’ + K*q = a1*beta1 + a2*beta2 + a3*beta3

q is the GenDOF

beta1,beta2,beta3 are the individual blade pitch angles

Taking a look at the linearized equations of motions before doing azimuth averaging, and plotting the gains a1, a2, a3 as functions of the azimuth angle will give the following

as far as I know is that the gains a1, a2, a3 are the aerodynamic gains which I expected, in such simplified model, to be equal to each other and constant (not changing with azimuth angle).

Any ideas how to explain the dependency on azimuth angle.

Thanks in advance.

Edited to correct a mistake:

Actually the plotted gains F1, F2, F3 are the same gains a1, a2, and a3 mentioned in the equation.