Dear All,

Can anyone help me please with the following things.

When i was working with the linear model of the the wind turbine, I got stuck by the following options.

Firstly, my objective was to design a LQR controller for the pitch control of the wind turbine. For it, I required the state matrices and the disturbance matrices. These matrices can be formed with the linearization of the wind turbine. Now, the problem associated with it is, I do not know which DOFs do i have to disable to get the correct LQR model. I have doubts regarding operating points and equilibrium points too. For ex, linearization is dependent upon linearized point or equilibrium point, i.e., the linearization point obtained after simulation? or do we have to define the linearization point using initial condition for our study? Moreover, which should we prefer for deisgn of LQR controller for region 3.

I hope that any one can shed some light into this matter.

Moreover, after obtaining the linerization file, and doing mbc transform, I got the avg state and disturbance matrices, but how do I implement these in the simulink model.?

Do I just specify the gain found by LQR toolbox in the simulink model or do we add something else?

additionally, for implementing LQR we require state feedback measurements. So, do we get these measurements by the corresponding force associated with the respective DOFs or by some other method? Please Elaborate more on this.

P.S : For offshore floating structure, platform DOF’s have to be enabled. How should i utilized this DOF in deriving collective blade pitch controller, Kindly tell me , what is the use of this…

Please find typical linearization attachment file(lin file )

This linearized model file was generated by FAST (v7.02.00d-bjj, 20-Feb-2013) on 26-Nov-2015 at 18:11:47.

The aerodynamic calculations were made by AeroDyn (v13.00.02a-bjj, 20-Feb-2013).

NREL 5.0 MW Baseline Wind Turbine for Use in Offshore Analysis.

Some Useful Information:

Type of steady state solution found Trimmed collective blade pitch (TrimCase = 3)

Azimuth-average rotor speed, RotSpeed (rad/s) 1.26711E+00

Period of steady state solution (sec) 4.95868E+00

Iterations needed to find steady state solution 295

Displacement 2-norm of steady state solution (rad) 7.73484E-04

Velocity 2-norm of steady state solution (rad/s) 8.22548E-05

Number of equally-speced azimuth steps, NAzimStep 24

Order of linearized model, MdlOrder 1

Number of active (enabled) DOFs 2 ( 4 states)

Number of control inputs, NInputs 2

Number of input wind disturbances, NDisturbs 1

Number of output measurements 2

Order of States in Linearized State Matrices:

Row/column 1 = Platform pitch tilt rotation DOF (internal DOF index = DOF_P)

Row/column 2 = Variable speed generator DOF (internal DOF index = DOF_GeAz)

Row/column 3 to 4 = First derivatives of row/column 1 to 2.

Order of Control Inputs in Linearized State Matrices:

Column 1 = electrical generator torque (N·m) 4.30404E+04 op

Column 2 = rotor collective blade pitch (rad) 1.83874E-01 op

Order of Input Wind Disturbances in Linearized State Matrices:

Column 1 = horizontal hub-height wind speed (m/s) : See selected wind file for op

Order of Output Measurements in Linearized State Matrices:

Row 1 = GenSpeed (rpm)

Row 2 = PtfmPitch (deg)

Linearized State Matrices:

--------- Azimuth = 0.00 deg (with respect to AzimB1Up = 0.00 deg) ---------

op State | op | A - State | B - Input | Bd - Dstrb

Derivativs | States | Matrix | Matrix | Matrix

6.427E-06 | 2.489E-02 | 0.000E+00 0.000E+00 1.000E+00 0.000E+00 | 0.000E+00 0.000E+00 | 0.000E+00

1.267E+00 | 4.712E+00 | 0.000E+00 0.000E+00 0.000E+00 1.000E+00 | 0.000E+00 0.000E+00 | 0.000E+00

-7.709E-06 | 6.427E-06 | -1.401E-02 -2.685E-08 -4.008E-02 -2.220E-04 | 5.897E-15 -3.184E-03 | 6.603E-05

1.353E-05 | 1.267E+00 | -9.254E-03 -7.443E-06 -1.959E+00 -5.529E-01 | -2.215E-06 -8.352E-01 | 2.433E-02

op Output | This colmn | C - Output | D - Trnsmt | Dd - DTsmt

Measurmnts | is blank | Matrix | Matrix | Matrix

1.174E+03 | | 0.000E+00 0.000E+00 0.000E+00 9.263E+02 | 0.000E+00 0.000E+00 | 0.000E+00

1.426E+00 | | 5.730E+01 0.000E+00 0.000E+00 0.000E+00 | 0.000E+00 0.000E+00 | 0.000E+00