Hello everyone,

I have a question regarding openfast linearization so any help would be appreciated.

I am looking to implement individual control of the blades. I rely on the linearized model. For this, I use the openFAST linearization module.

- DoF enabled: GenDof, all ptfm motions.
- Wind: 18 m/s
- Number of times to linearize: 36

4.rotor speed: 12.1 rpm

To avoid excessive calculation time, I restrict the number of linearizations to 36, i.e. one linearization every 10 degrees. Then with matlab I extrapolate the state model to go from 36 to 360. I then calculate the control gains. When I plot the gains as a function of the azimuth angle, with FAST V7 we obtain gains which vary periodically depending on the angle but for Openfast, we do not find the same trend as you can see on the two images.

Thanks in advance

Dear @salic.tom,

The way you are linearizing sounds OK to me.

What do you mean when you say?:

with matlab I extrapolate the state model to go from 36 to 360

Do you mean that you interpolate, say, to 1,2,3,4,5,6,7,8,9 from 0 and 10 degrees azimuth?

How are calculating the control gains?

Are you plotting the results versus the azimuth angle of one blade or for each blade?

Best regards,

Dear Jason Jonkman,

Do you mean that you interpolate, say, to 1,2,3,4,5,6,7,8,9 from 0 and 10 degrees azimuth?

Sorry, I don’t understand what you mean… I interpolate the Fourier transform of the function values in X to produce n equally spaced points. Here X is the gains control and n is 360. The objective being to be able to use this gain over a range of values from 1 to 360 to modify the gains according to the position of the blade. So I ask myself the question is it relevant to use an interpolation to go from a matrix [m,n,36] to a matrix [m,n,360]?On the figure I trace the evolution of a value of the matrix B according to the angle. I have a periodic evolution but then we lose this periodic signal when calculating the gains. However, this method works with FAST V7.

The control gains are calculated by the LQR method. I solve the riccati equation to get the solution P and then we get K_gain=R^{-1}B^{T}P.

The plotted results represent the evolution of the gains as a function of the azimuth position of the three blades.

Best Regards

Dear @Jason.Jonkman

Do not reply to this message I finally succeeded. There was an error in my matrix calculation… Sorry for the loss of time.

Have a nice day