## Compare Linear Model with Nonlinear Model in Control Design.

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Mohamed.Fekry
Posts: 29
Joined: Mon Dec 25, 2017 5:47 am
Organization: Zagazig University
Location: Egypt

### Compare Linear Model with Nonlinear Model in Control Design.

Dear All
I am trying to design a controller for the Nrel 5MW Wind Turbine (WT) based on the linearization of the OpenFast V2.5.0 for rotor speed regulation.
Although I stabilized the non-linear WT based on that linearization using simple state feedback controller at the linearized operating point, I am not able to stablize the linear model for the same gains. The linear model of WT required another values of state feedback gains which is greatly different from the ones of nonlinear model. Also, both models gives different response for the same input.
Are there any suggestions in order to get similar response with no big difference between the linear and nonlinear model of WT?
Note that: I simplified the WT model to only one DOF of the genrator (GenDOF). So, I have only two states:
Displacement of variable speed generator DOF (Q_GeAz in rad)
Velocity of variable speed generator DOF (QD_GeAz in rad/s)

The linearization has been made at a pitch angle of 11.5 (deg) with a wind speed of 16 m/s.
The state feedback gains are (K = 10.0981 2.5407 = place(A,B,[-.01 -0.6]))
Attachments
NLWT.jpg (227.49 KiB) Viewed 116 times
LWT.jpg (192.61 KiB) Viewed 116 times

Jason.Jonkman
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Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
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### Re: Compare Linear Model with Nonlinear Model in Control Design.

Dear Mohamed,

• I would not expect that you'd use the generator-azimuth state when controlling rotor speed through collective pitch. It looks like you've zeroed out the effect in the nonlinear model, but not in the linear model.
• MBC and azimuth-averaging should eliminate the influence of the generator-azimuth state, which should then be removed from the linear model before use. This is discussed e.g. in the following forum topic: viewtopic.php?f=4&t=1903.
• The linear model represents perturbations about the operating point. So, I would not expect that you'd derive the pitch angle by adding 12*pi/30*K(2) to it.
• Minor comment, but the rated speed for the NREL 5-MW baseline wind turbine is 12.1 rpm, not 12 rpm.
I hope that helps.

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

Mohamed.Fekry
Posts: 29
Joined: Mon Dec 25, 2017 5:47 am
Organization: Zagazig University
Location: Egypt

### Re: Compare Linear Model with Nonlinear Model in Control Design.

Thank you so much