nonlinear statespace model
Moderator: Bonnie.Jonkman

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nonlinear statespace model
hello
I want to design a nonlinear individual pitch controller for wind turbine load reduction in my master's thesis, but I don't have the nonlinear statespace model of the 1.5 MW wind turbine available in the FAST test.
It is essential for me to have those nonlinear equations to design a nonlinear controller without linearization. How can I access them?
Thanks.
I want to design a nonlinear individual pitch controller for wind turbine load reduction in my master's thesis, but I don't have the nonlinear statespace model of the 1.5 MW wind turbine available in the FAST test.
It is essential for me to have those nonlinear equations to design a nonlinear controller without linearization. How can I access them?
Thanks.

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 Location: Boulder, CO
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Re: nonlinear statespace model
Dear Zarei.Atefe,
FAST / OpenFAST itself employs nonlinear equations and each module is written in statespace form (in terms of inputs, outputs, states, and parameters. See the FAST modularization framework for more information: https://www.nrel.gov/docs/fy13osti/57228.pdf.
Best regards,
FAST / OpenFAST itself employs nonlinear equations and each module is written in statespace form (in terms of inputs, outputs, states, and parameters. See the FAST modularization framework for more information: https://www.nrel.gov/docs/fy13osti/57228.pdf.
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

 Posts: 10
 Joined: Mon Apr 22, 2019 7:13 am
 Organization: self
 Location: iran
Re: nonlinear statespace model
Hello
thanks for your answer
To design a nonlinear controller, I must have a nonlinear equation of pitch actuator and blade root bending moment related to the 13th test of FAST8.16. Can you give me them?
In fact, I want the nonlinear relation of the attached equation related to the 13th test of FAST8.16.
thanks.
thanks for your answer
To design a nonlinear controller, I must have a nonlinear equation of pitch actuator and blade root bending moment related to the 13th test of FAST8.16. Can you give me them?
In fact, I want the nonlinear relation of the attached equation related to the 13th test of FAST8.16.
thanks.
 Attachments

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 Posts: 4347
 Joined: Thu Nov 03, 2005 4:38 pm
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Re: nonlinear statespace model
Dear Zarei,
Just a few comments:
Just a few comments:
 FAST v8.16 does not include pitchactuator dynamics, unless these are implemented by the user within the controller.
 The nonlinear equations of motion used by FAST are very large and cannot be written down in a forum post.
 What is theta in your equation?
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

 Posts: 10
 Joined: Mon Apr 22, 2019 7:13 am
 Organization: self
 Location: iran
Re: nonlinear statespace model
theta is the output pitch angle given into the model.
Is it possible to email The nonlinear equations of motion used by FAST to me ?
My work depends heavily on having nonlinear equations of motion and pitch actuator.
thanks for your help.
Is it possible to email The nonlinear equations of motion used by FAST to me ?
My work depends heavily on having nonlinear equations of motion and pitch actuator.
thanks for your help.

 Posts: 4347
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
 Contact:
Re: nonlinear statespace model
Dear Zarei,
As I said, pitch actuator dynamics are not intrinsically included in FAST.
Please see the following post on our forum for information on the FAST theory basis: viewtopic.php?f=4&t=424. WBut while the structural nonlinearities can be clearly seen e.g. in the "unofficial FAST theory manual", the aerodynamic nonlinearities are more difficult to write down because e.g. the blade element / momentum (BEM) theory depends on the solution to nonlinear algebraic equations.
Best regards,
As I said, pitch actuator dynamics are not intrinsically included in FAST.
Please see the following post on our forum for information on the FAST theory basis: viewtopic.php?f=4&t=424. WBut while the structural nonlinearities can be clearly seen e.g. in the "unofficial FAST theory manual", the aerodynamic nonlinearities are more difficult to write down because e.g. the blade element / momentum (BEM) theory depends on the solution to nonlinear algebraic equations.
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

 Posts: 10
 Joined: Mon Apr 22, 2019 7:13 am
 Organization: self
 Location: iran
Re: nonlinear statespace model
thanks
and So, my question is, a nonlinear relation between the pitch angle and the rotor speed is available?
and So, my question is, a nonlinear relation between the pitch angle and the rotor speed is available?

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 Location: Boulder, CO
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Re: nonlinear statespace model
Dear Zarei,
I guess your asking about the aerodynamic torque as function of tipspeed ratio and bladepitch angle? Such a surface can be calculated by FAST (including structural deformations), or by standalone AeroDyn (without structural deformations)as discussed in other topics on this forumbut the output would be a tabulated relationship. You could fit a function to this tabulated surface to have nonlinear relationship.
Best regards,
I guess your asking about the aerodynamic torque as function of tipspeed ratio and bladepitch angle? Such a surface can be calculated by FAST (including structural deformations), or by standalone AeroDyn (without structural deformations)as discussed in other topics on this forumbut the output would be a tabulated relationship. You could fit a function to this tabulated surface to have nonlinear relationship.
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

 Posts: 10
 Joined: Mon Apr 22, 2019 7:13 am
 Organization: self
 Location: iran
Re: nonlinear statespace model
Thank you very much for your help
Now, my question is, as you say, since nonlinear equations of region 3 wind turbines are not specifically available, so can not design nonlinear controllers which require nonlinear dynamics?
Now, my question is, as you say, since nonlinear equations of region 3 wind turbines are not specifically available, so can not design nonlinear controllers which require nonlinear dynamics?
Last edited by zarei.atefe on Tue Jun 11, 2019 10:27 am, edited 1 time in total.

 Posts: 4347
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
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Re: nonlinear statespace model
Dear Zarei,
I'm not familiar with nonlinear optimal control theory. What form do the equations need to be in? Do you need an analytical expression or are tabulated relationships and/or calls directly to FAST usable?
Best regards,
I'm not familiar with nonlinear optimal control theory. What form do the equations need to be in? Do you need an analytical expression or are tabulated relationships and/or calls directly to FAST usable?
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

 Posts: 10
 Joined: Mon Apr 22, 2019 7:13 am
 Organization: self
 Location: iran
Re: nonlinear statespace model
i need the nonlinear differential equations of the wind turbine for region 3 goals.
But I can not find them.
thanks.
But I can not find them.
thanks.

 Posts: 4347
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
 Contact:
Re: nonlinear statespace model
Dear Zarei,
I believe I've already answered your question.
Best regards,
I believe I've already answered your question.
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

 Posts: 10
 Joined: Mon Apr 22, 2019 7:13 am
 Organization: self
 Location: iran
Re: nonlinear statespace model
thanks.
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