# FAST linearization model in Simulink

Hi everyone,

I am now doing some work on model based offshore wind turbine control. To get an accurate mathematic model, I linearized the the NREL 5 MW wind turbine with Tension leg platform with 10 m/s constant wind velocity in still water. To check the linearized result, I built a model in simulink and compared the simulation results with FAST output. I only switched the platform 6 DOF, tower 2 DOF, generator and Drivetrain rotational-flexibility DOF true.

The result is that: some outputs match quite well (platform sway, platform roll, YawBrTDyp) while others do not (see the attachment).

Another interesting thing I observed is that: the steady state FAST linearization found is reasonable. However, the simulink output decay to other steady state values.

I am wondering it is normal or abnormal for this difference. Is there anything I did wrong or ignored in my work? Hopefully, some one can help me to solve this problem. I am just a beginner with the FAST linearization module. Thank you very much in advance.

It seems that I failed to attach my result due to “Sorry, the board attachment quota has been reached”. Can anyone help me upload the attachment?

Sincerely,
Zhongyou.Wu

I have increased the size of the attachment quota, so please try to upload it again.

Hi Bonnie,

Thank you very much for your quick reply. I can now attach my simulation result.

By the way, I also have tried the state space model in Simulink using the linearized result by FAST. The output is consistent with the second order output result. Both of them failed to match the FAST output.
The comparison between Linearization and FAST.pdf (294 KB)

Dear Zhongyou Wu,

The linearized model output by FAST is only valid for small perturbations about the operating point. It looks like you want your operating point to be based on steady 10-m/s wind. Thus, the wind-input disturbance represents a deviation from 10 m/s; you are setting this disturbance to 10 m/s, which actually implies a wind speed of 10 + 10 = 20 m/s, so, it is natural for the linearized model output to differ from the steady-state FAST solution. Likewise for the other input, state, and output perturbations.

I hope that helps.

Best regards,

Hello Dr. Jonkman,

Your reply helped me realize my mistake. Thank you so much.

You are totally right. The input to my linearized model should be small deviations (delta u and delta w) around the operating point. It is also true for the output. When I add the output (delta y) to the steady point, the results match quite well.

For the platform sway and roll motion, the result did not match so well (see the attachment). It seems that the platform sway and roll motion are strongly coupled with the rotor speed velocity.

Sincerely,
Zhongyou. Wu
The comparison between Linearization modle and FAST-2.docx (90.2 KB)

Dear Zhongyou Wu,

I’m not sure I know why some outputs are better captured by the linear model than others, but to understand why, it may help to simplify the model to study this more e.g. by eliminating degrees of freedom.

Best regards,

Hello Dr. Jonkman,

Thank you for your quick reply and helpful suggestion. I will do more simulations to look into the reason for this phenomenon later.

Sincerely,
Zhongyou.Wu

Dear Jason

I have a question about the linear model. I linearized FAST at 10 m/s. My Linear time invariant model is perturbed with a wind speed of 0.1m/s added to the output (yop). The result is in the attachment. You said that the linearized model output is only valid for small perturbations about the operating point. I would know if it is possible to control this model with a state space controller by changing wind speed? In this way i want to use the LTI-Model instead of nonlinear FAST model.

Best regards,
Damba

Dear Damba,

I’m sorry, but I’m not really sure that I understand your question.

Best regards,

Dear Jason,

Thanks for the replay,
I realised that i need some clarifications about the feature of linearised model. Could you explain me please what i can do with the linearized model of FAST? I think i can use the matrices als feedback controller or estimator for pitch control in FAST nonlinear model.
Now i try to replace the nonlinear Model of FAST (S-Function) with the state space model in my attachement. So i could use this model as my whole Wind Turbine model whithout the S-Function. I hope you can understand now my question.

Best regards,
Damba

Dear Damba,

I suppose you could use the linearized model in Simulink as a replacement for the nonlinear FAST S-Function, as you are proposing, as long as you understand the simplifications of the linear model (e.g. only valid for small deviations about the operating point, uniform (not turbulent wind), etc.).

Best regards,

Dear Jason,

Thanks for your replay. that is what i want to do. however the S-Function is working at different wind speed. i don’t know how i can control this model for different wind speed if i have one matrix for every operating point.

Best regards,
Damba

You can control it by using such techniques as linear quadratic or poles placement, which matches with the state space representation of the model

Dear Ali,

Thanks for your replay. I will try with this method.

Best regard
Damba

You are welcome for further discussions