# About unit when calculating control gain(Kp and KI)

Dear Jason.

I have two questions about the unit.

First, I am calculating the gain value in blade pitch control using below equation.

Kp=(2*(Drivetrain Inertia)(rated low-speed shaft rotational speed)(damping ration)(natural frequency))/(Gearbox ratio-Sensitivity Power to Pitch)

Could you let me know the exact unit of rated low-speed shaft rotational speed in the above equation? (either rpm or rad/sec)

Second, I got the power sensitivity to blade pitch as below from FAST linearization.
I got the sensitivity -7.485E+03 from D-Trnsmt Matrix. Then what is the exact unit for the sensitivity? (either kw/deg or kw/rad)

Order of Control Inputs in Linearized State Matrices:

Order of Input Wind Disturbances in Linearized State Matrices:

None selected

Order of Output Measurements in Linearized State Matrices:

Row 1 = WindVxi (m/sec)
Row 2 = RotPwr (kW)
Row 3 = GenPwr (kW)
Row 4 = BldPitch1 (deg)
Row 5 = RotSpeed (rpm)
Row 6 = GenSpeed (rpm)
Row 7 = GenTq (kN-m)

Linearized State Matrices:

--------- Azimuth = 0.00 deg (with respect to AzimB1Up = 0.00 deg) ---------
op State | op | A - State | B - Input
Derivativs | States | Matrix | Matrix
0.000E+00 | 0.000E+00 | 0.000E+00 1.000E+00 | 0.000E+00
0.000E+00 | 0.000E+00 | -1.093E+03 -3.832E+00 | -9.485E-02

## op Output | This colmn | C - Output | D - Trnsmt Measurmnts | is blank | Matrix | Matrix 1.200E+01 | | 0.000E+00 0.000E+00 | 0.000E+00 3.335E+03 | | -1.892E+06 -6.723E+03 | -7.485E+03 0.000E+00 | | 0.000E+00 0.000E+00 | 0.000E+00 2.652E+00 | | 0.000E+00 0.000E+00 | 5.730E+01 1.700E+01 | | 0.000E+00 0.000E+00 | 0.000E+00 1.530E+03 | | 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 | | 0.000E+00 0.000E+00 | 0.000E+00

Thank you.
HyoungChul Kim.

Dear HyoungChul Kim,

The units in your equation for Kp should be consistent e.g. kg, m, s, N, rad. The rotational speed should be in rad/s.

The units are given in the linearization output file:

That is, the blade-pitch input is in rad and the output RotPwr is in kW, so, -7.485E+03 has the units of kW/rad.

Best regards,

Dear Jason.