Validation of Linear System
Moderator: Bonnie.Jonkman

 Posts: 24
 Joined: Mon Aug 28, 2017 4:17 pm
 Organization: University of Paderborn
 Location: Germany
Validation of Linear System
Dear Jason,
I have few confusions regarding validation of linear system.
Background:
I have created MBC_A,MBC_B,MBC_C,MBC_D matrices through running getmats__f8 and mbc3 commands.
I took the avg of above mentioned matrices through "MBC_Avg(B,C,D) = mean(MBC_(B,C,D), 3)" commands respectively (is it correct to use this command in this particular case?).
Problem:
Now I created the statespace model in simulink and was trying to compare the outputs of openloop linear system with openloop nonlinear system but my outputs are not matching they are not even close.
Relevent Information:
I have gone through these two threads (viewtopic.php?f=30&t=1873&p=9536&hilit=linear+model+simulink+test#p9536) and (viewtopic.php?f=30&t=1593) thoroughly. The information i get from your posts there is as follows:
1: "linear model is defined in terms of perturbations about the operating point e.g. y = y_op + dy for system outputs, so, you should either add the operating point value (y_op) to the output of the linear model or subtract the operating point value from the output of the nonlinear for comparison."
2: "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 10m/s wind. Thus, the windinput 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 steadystate FAST solution. Likewise for the other input, state, and output perturbations."
Questions:
1: As I have lineraized my system around 18 m/s, so If I apply 0.1 m/s wind speed as input to linear system then will it be considered 18.1 m/s for the system? (so on and so forth for every input)
2: In order to get my linear system validated, should I add my respective nonlinear output into my linear output? e.g. y = y_op + dy (as in my case: nonlinear Gen Speed (rpm)+linear Gen Speed (rpm) should be compared to nonlinear Gen Speed (rpm)).
Note: To compare rotating outputs I have to apply inverse MBC transform.
Best Regards
Syed Shah
I have few confusions regarding validation of linear system.
Background:
I have created MBC_A,MBC_B,MBC_C,MBC_D matrices through running getmats__f8 and mbc3 commands.
I took the avg of above mentioned matrices through "MBC_Avg(B,C,D) = mean(MBC_(B,C,D), 3)" commands respectively (is it correct to use this command in this particular case?).
Problem:
Now I created the statespace model in simulink and was trying to compare the outputs of openloop linear system with openloop nonlinear system but my outputs are not matching they are not even close.
Relevent Information:
I have gone through these two threads (viewtopic.php?f=30&t=1873&p=9536&hilit=linear+model+simulink+test#p9536) and (viewtopic.php?f=30&t=1593) thoroughly. The information i get from your posts there is as follows:
1: "linear model is defined in terms of perturbations about the operating point e.g. y = y_op + dy for system outputs, so, you should either add the operating point value (y_op) to the output of the linear model or subtract the operating point value from the output of the nonlinear for comparison."
2: "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 10m/s wind. Thus, the windinput 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 steadystate FAST solution. Likewise for the other input, state, and output perturbations."
Questions:
1: As I have lineraized my system around 18 m/s, so If I apply 0.1 m/s wind speed as input to linear system then will it be considered 18.1 m/s for the system? (so on and so forth for every input)
2: In order to get my linear system validated, should I add my respective nonlinear output into my linear output? e.g. y = y_op + dy (as in my case: nonlinear Gen Speed (rpm)+linear Gen Speed (rpm) should be compared to nonlinear Gen Speed (rpm)).
Note: To compare rotating outputs I have to apply inverse MBC transform.
Best Regards
Syed Shah

 Posts: 2951
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
 Contact:
Re: Validation of Linear System
Dear Syed,
Yes, I agree that MBC_AvgB can be calculated as mean(MBC_B,3) etc.
Regarding (1), "yes," if the wind speed operating point is 18 m/s, then a perturbation of 0.1 m/s results an effective wind speed of 18.1 m/s.
Regarding (2), you should add the linearized output (dy) to the operating point output (y_op) for comparison to the nonlinear solution (y) i.e. y = y_op + dy.
I hope that helps.
Best regards,
Yes, I agree that MBC_AvgB can be calculated as mean(MBC_B,3) etc.
Regarding (1), "yes," if the wind speed operating point is 18 m/s, then a perturbation of 0.1 m/s results an effective wind speed of 18.1 m/s.
Regarding (2), you should add the linearized output (dy) to the operating point output (y_op) for comparison to the nonlinear solution (y) i.e. y = y_op + dy.
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
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: 24
 Joined: Mon Aug 28, 2017 4:17 pm
 Organization: University of Paderborn
 Location: Germany
Re: Validation of Linear System
Dear Jason,
Thank you for your quick help and clearing my doubts.
Best regards
SS
Thank you for your quick help and clearing my doubts.
Best regards
SS

 Posts: 24
 Joined: Mon Aug 28, 2017 4:17 pm
 Organization: University of Paderborn
 Location: Germany
Re: Validation of Linear System
Dear Jason,
I have few confusions regarding validation of linear system.
Background:
I have created a statespace model in simulink in order to compare the outputs of nonlinear system with linear system.
Problem:
I have done the comparison with the above mentioned procedure. but having issues in comparing the results of the rotating blade loads.
I have done the inverse MBC transformation on rotating blade loads of linear system by taking the azimuth output from the statespace model. (I guess this is the issue because I am taking the linearized azimuth)
Questions
1: My question is how to perform the correct inverse MBC transformation to compare the results of rotating blade loads of both the linear and nonlinear systems??
2: which azimuth is to use for this purpose?
Best Regards
Syed Shah
I have few confusions regarding validation of linear system.
Background:
I have created a statespace model in simulink in order to compare the outputs of nonlinear system with linear system.
Problem:
I have done the comparison with the above mentioned procedure. but having issues in comparing the results of the rotating blade loads.
I have done the inverse MBC transformation on rotating blade loads of linear system by taking the azimuth output from the statespace model. (I guess this is the issue because I am taking the linearized azimuth)
Questions
1: My question is how to perform the correct inverse MBC transformation to compare the results of rotating blade loads of both the linear and nonlinear systems??
2: which azimuth is to use for this purpose?
Best Regards
Syed Shah

 Posts: 2951
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
 Contact:
Re: Validation of Linear System
Dear Syed,
As discussed in the following forum topic: viewtopic.php?f=4&t=1903, once you linearize the FAST model, apply MBC3, and azimuthaverage the resulting matrices, you'll end up with a linear statespace model without the azimuth state. Thus, when comparing the linear and nonlinear models, I would suggest applying MBC3 to the result of the nonlinear model in order to compare to the result of the linear model.
Best regards,
As discussed in the following forum topic: viewtopic.php?f=4&t=1903, once you linearize the FAST model, apply MBC3, and azimuthaverage the resulting matrices, you'll end up with a linear statespace model without the azimuth state. Thus, when comparing the linear and nonlinear models, I would suggest applying MBC3 to the result of the nonlinear model in order to compare to the result of the linear model.
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: 24
 Joined: Mon Aug 28, 2017 4:17 pm
 Organization: University of Paderborn
 Location: Germany
Re: Validation of Linear System
Dear Jason,
Thank you for your quick help.
1: If i want to apply MBC3 on the bladeloads of the non linear system how do i apply it? what is the correct way?
2: do i need to perform the MBC3 transformation to the individual blade pitch angle inputs before applying to the to the linear system ? because the system and the outputs are MBC3 transformed. if yes how to do this?
Thank you for your quick help.
1: If i want to apply MBC3 on the bladeloads of the non linear system how do i apply it? what is the correct way?
2: do i need to perform the MBC3 transformation to the individual blade pitch angle inputs before applying to the to the linear system ? because the system and the outputs are MBC3 transformed. if yes how to do this?

 Posts: 2951
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
 Contact:
Re: Validation of Linear System
Dear Syed,
Regarding (1), look at the MBC3 manual (https://nwtc.nrel.gov/system/files/MBC3.pdf) and you'll find matrices relating how to transform outputs in the rotating frame to outputs in the fixed frame through application of MBC3.
Regarding (2), yes, the linear system has been transformed through MBC3, so, the input bladepitch angle perturbations are not perturbations of blades 1, 2, and 3; instead, they are perturbations of the MBCtransformed 0, C, and S terms. Again. see the MBC3 manual for more information.
Best regards,
Regarding (1), look at the MBC3 manual (https://nwtc.nrel.gov/system/files/MBC3.pdf) and you'll find matrices relating how to transform outputs in the rotating frame to outputs in the fixed frame through application of MBC3.
Regarding (2), yes, the linear system has been transformed through MBC3, so, the input bladepitch angle perturbations are not perturbations of blades 1, 2, and 3; instead, they are perturbations of the MBCtransformed 0, C, and S terms. Again. see the MBC3 manual for more information.
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: 24
 Joined: Mon Aug 28, 2017 4:17 pm
 Organization: University of Paderborn
 Location: Germany
Re: Validation of Linear System
Dear Jason,
Thank you for your time.
so what I have concluded from your statement is, if following are the inputs to the state space system.
u1; horizontal wind speed (steady/uniform wind), m/s
u2; vertical powerlaw shear exponent, 
u3; IfW Extended input: propagation direction, rad
u4; Blade Pitch1, (rad)
u5; Blade Pitch2, (rad)
u6; Blade Pitch3, (rad)
u7; Yaw moment, Nm
u8; Generator torque, Nm
u9; Collective Pitch, (rad)
the u4, u5 and u6 are considered by the system as 0, C, and S terms, instead of individual bladepitch angle perturbations?
Best Regards
Syed Shah
Thank you for your time.
so what I have concluded from your statement is, if following are the inputs to the state space system.
u1; horizontal wind speed (steady/uniform wind), m/s
u2; vertical powerlaw shear exponent, 
u3; IfW Extended input: propagation direction, rad
u4; Blade Pitch1, (rad)
u5; Blade Pitch2, (rad)
u6; Blade Pitch3, (rad)
u7; Yaw moment, Nm
u8; Generator torque, Nm
u9; Collective Pitch, (rad)
the u4, u5 and u6 are considered by the system as 0, C, and S terms, instead of individual bladepitch angle perturbations?
Best Regards
Syed Shah

 Posts: 2951
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
 Contact:
Re: Validation of Linear System
Dear Syed,
After you apply MBC3 to the linear system matrices, I agree that inputs u4u6 i.e. pitch angles for blades 13 are converted to pitch angle 0, C, and S terms.
Best regards,
After you apply MBC3 to the linear system matrices, I agree that inputs u4u6 i.e. pitch angles for blades 13 are converted to pitch angle 0, C, and S terms.
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: 24
 Joined: Mon Aug 28, 2017 4:17 pm
 Organization: University of Paderborn
 Location: Germany
Re: Validation of Linear System
Dear Jason,
Thank you for your help and clearing my doubts.
Best regards
Syed Shah
Thank you for your help and clearing my doubts.
Best regards
Syed Shah

 Posts: 24
 Joined: Mon Aug 28, 2017 4:17 pm
 Organization: University of Paderborn
 Location: Germany
Re: Validation of Linear System
Dear Jason,
I have a problem in validating the above mentioned (in previous posts of this topic) MBC averaged system with the nonlinear system.
I have linearized system at 18m/s wind speed and if below are the input to the MBC averaged state space system;
u1; horizontal wind speed (steady/uniform wind), m/s
u2; vertical powerlaw shear exponent, 
u3; IfW Extended input: propagation direction, rad
u4; Blade Pitch angle 0 term, (rad)
u5; Blade Pitch angle C term, (rad)
u6; Blade Pitch angle S term, (rad)
u7; Yaw moment, Nm
u8; Generator torque, Nm
u9; Collective Pitch, (rad)
then after I apply the unit step input only at u4 = (1*pi/180), the SrvD GenTq, (kN·m), ED RotSpeed, (rpm), ED GenSpeed, (rpm) decreases. Rest of the inputs are zeros.
In my opinion due to the decrease in torque the rotspeed and genspeed is also decreasing. Torque should not decrease ideally. why torque is decreasing? kindly can you shed some light on the issue?
Best Regards
Syed Shah
I have a problem in validating the above mentioned (in previous posts of this topic) MBC averaged system with the nonlinear system.
I have linearized system at 18m/s wind speed and if below are the input to the MBC averaged state space system;
u1; horizontal wind speed (steady/uniform wind), m/s
u2; vertical powerlaw shear exponent, 
u3; IfW Extended input: propagation direction, rad
u4; Blade Pitch angle 0 term, (rad)
u5; Blade Pitch angle C term, (rad)
u6; Blade Pitch angle S term, (rad)
u7; Yaw moment, Nm
u8; Generator torque, Nm
u9; Collective Pitch, (rad)
then after I apply the unit step input only at u4 = (1*pi/180), the SrvD GenTq, (kN·m), ED RotSpeed, (rpm), ED GenSpeed, (rpm) decreases. Rest of the inputs are zeros.
In my opinion due to the decrease in torque the rotspeed and genspeed is also decreasing. Torque should not decrease ideally. why torque is decreasing? kindly can you shed some light on the issue?
Best Regards
Syed Shah

 Posts: 2951
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
 Contact:
Re: Validation of Linear System
Dear Syed,
What generator or torquecontrol model did you enable when you linearized the model? The choice of modeling and linearization operating point will explain why the drop in rotor speed is leading to a drop in generator torque.
Best regards,
What generator or torquecontrol model did you enable when you linearized the model? The choice of modeling and linearization operating point will explain why the drop in rotor speed is leading to a drop in generator torque.
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: 24
 Joined: Mon Aug 28, 2017 4:17 pm
 Organization: University of Paderborn
 Location: Germany
Re: Validation of Linear System
Dear Jason,
I Have enabled "SIMPLE VARIABLESPEED TORQUE CONTROL" model.
Best regards
Syed Shah
I Have enabled "SIMPLE VARIABLESPEED TORQUE CONTROL" model.
Best regards
Syed Shah

 Posts: 2951
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
 Contact:
Re: Validation of Linear System
Dear Syed,
The simple variabletorque controller has no region where a negative change in rotor speed leads to a positive change in generator torque.
Best regards,
The simple variabletorque controller has no region where a negative change in rotor speed leads to a positive change in generator torque.
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: 24
 Joined: Mon Aug 28, 2017 4:17 pm
 Organization: University of Paderborn
 Location: Germany
Re: Validation of Linear System
Dear Jason,
Then why do the rotspeed decreases with the the step increase in input of pitch angle?
Best regards,
Syed Shah
Then why do the rotspeed decreases with the the step increase in input of pitch angle?
Best regards,
Syed Shah
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