Dear Jason,
I’m sorry I still need your help.
I checked the links you provided and other relevant links，
FAST linearization V7.
I’m sorry that I still don’t know what to do to eliminate the generator rotor azimuth and convert my four state model to a three state model.
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I obtained AvgAMat matrix and AvgCMat matrix by using azimuth averaging, but the column related to generator azimuth state is actually not zero. Does this mean that I cannot eliminate generator azimuth as a state?
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If possible, in the AvgAMat matrix I obtained, two to four columns correspond to three states respectively, DrTr, GeAz, QD_ DrTr。 These three states are just the three state variables I need to design the controller.What can I do to eliminate the generator azimuth and change it to 3 × 3？
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Correspondingly, in the AvgBMat matrix, one to four rows represent GeAz, QD_ DrTr,QD2_ GeAz and QD2_ DrTr, if i want to eliminate generator azimuth and change it to 3 ×1, which row should I delete?
Thank you in advance.
Kind regards,
Dear Jason，
I have another question.
I reviewed the linearized output file.
Whether the first two lines of matrix B correspond to the generator azimuth and the torsional angle of the transmission system, rather than the generator speed and the torsional rate of the transmission system.
The 3-4 rows of matrix B should correspond to the motor speed and drive train torsion rate, not the motor acceleration and power train torsion acceleration.
If so, to convert a four state model to a three state model, do you simply delete the first row and column of matrix A and the first row of matrix B?
Thank you in advance.
Kind regards,
Dear @Xiang.Li,
If so, to convert a four state model to a three state model, do you simply delete the first row and column of matrix A and the first row of matrix B?
Yes, that is correct. You should also delete the first column of C. I can’t fully see what is in AvgAMat(4,1), but my guess is the values in the first column of A are generally much smaller than values in the other columns. Numerical truncation and round off mean some of the values may not be exactly zero. But you can remove them anyway.
For 4 state model with:
dx = { Q_GeAz, Q_DrTr, QD_GeAz, QD_DrTr }^T
then:
dxdt = { QD_GeAz, QD_DrTr, QDD_GeAz, QDD_DrTr }^T
and the state-space matrix is:
dxdt = A * dx + B * du
dy = C * dx + D * du
So, the rows of A and B correspond to dxdt.
Best regards,
Dear Jason，
This is the complete value of matrix A，
I deleted the first row and column of matrix A and the first row of matrix B
The following spatial equation of state is constructed,
But I’m not sure it’s right
Thank you in advance.
Kind regards,
Dear @Xiang.Li,
Indeed, it looks like the values in the first column of A are very small relative to other nonzero values in A. I agree with how you reduce A to 3x3 and B to 3x1.
Best regards,
Dear Jason，
Thanks for your time, I appreciate it.
Kind regards,
How do I know which inputs are in the rotating frame? Can you explain a bit and give me some examples? Thanks
Dear @Kashyap.Subham,
In OpenFAST, whether or not the inputs, outputs, and states are in a rotating frame of reference are written to the linearization (.lin) output file.
In FAST v7, the only input in the rotating frame of reference is the independent blade-pitch input.
Best regards,
Sorry sir, I fail to understand.
let’s say I have blade root moments as an output set. Is it in the rotating frame of reference or not? What about tower base moments?
In general, what is the basic idea behind the concept?
thanks
subham
Dear @Kashyap.Subham,
Yes, blade load and motion-related states, inputs, and outputs expressed uniquely for each blade are typically expressed in a rotating frame of reference; that is, in a coordinate system that rotates with the rotor rotation (tower loads would not). Whether a state, input, or output are in a fixed or rotating frame of reference will impact how the linearization model should be post-processed, e.g., using the multi-blade coordinate transformation (MBC3).
I would suggest reviewing the MBC3 documentation for more information: matlab-toolbox/MBC/docs/MBC3.pdf at main · OpenFAST/matlab-toolbox · GitHub.
Best regards,
