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nonlinear state-space model

Posted: Fri Apr 26, 2019 12:54 am
by zarei.atefe
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 state-space model of the 1.5 MW wind turbine available in the FAST test.
It is essential for me to have those non-linear equations to design a nonlinear controller without linearization. How can I access them?

Thanks.

Re: nonlinear state-space model

Posted: Fri Apr 26, 2019 6:48 am
by Jason.Jonkman
Dear Zarei.Atefe,

FAST / OpenFAST itself employs nonlinear equations and each module is written in state-space 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,

Re: nonlinear state-space model

Posted: Tue Jun 11, 2019 1:59 am
by zarei.atefe
Hello
thanks for your answer
To design a non-linear 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.

Re: nonlinear state-space model

Posted: Tue Jun 11, 2019 3:20 am
by Jason.Jonkman
Dear Zarei,

Just a few comments:
  • FAST v8.16 does not include pitch-actuator 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?
Best regards,

Re: nonlinear state-space model

Posted: Tue Jun 11, 2019 3:53 am
by zarei.atefe
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.

Re: nonlinear state-space model

Posted: Tue Jun 11, 2019 4:28 am
by Jason.Jonkman
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,

Re: nonlinear state-space model

Posted: Tue Jun 11, 2019 5:00 am
by zarei.atefe
thanks
and So, my question is, a nonlinear relation between the pitch angle and the rotor speed is available?

Re: nonlinear state-space model

Posted: Tue Jun 11, 2019 6:33 am
by Jason.Jonkman
Dear Zarei,

I guess your asking about the aerodynamic torque as function of tip-speed ratio and blade-pitch 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 forum--but the output would be a tabulated relationship. You could fit a function to this tabulated surface to have nonlinear relationship.

Best regards,

Re: nonlinear state-space model

Posted: Tue Jun 11, 2019 8:12 am
by zarei.atefe
Thank you very much for your help
Now, my question is, as you say, since non-linear equations of region 3 wind turbines are not specifically available, so can not design nonlinear controllers which require nonlinear dynamics?

Re: nonlinear state-space model

Posted: Tue Jun 11, 2019 8:16 am
by Jason.Jonkman
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,

Re: nonlinear state-space model

Posted: Tue Jun 11, 2019 11:12 am
by zarei.atefe
i need the nonlinear differential equations of the wind turbine for region 3 goals.
But I can not find them.

thanks.

Re: nonlinear state-space model

Posted: Tue Jun 11, 2019 2:26 pm
by Jason.Jonkman
Dear Zarei,

I believe I've already answered your question.

Best regards,

Re: nonlinear state-space model

Posted: Wed Jun 12, 2019 12:53 am
by zarei.atefe
thanks.