Validation of Linear System

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Syed.Muzaher
Posts: 12
Joined: Mon Aug 28, 2017 4:17 pm
Organization: University of Paderborn
Location: Germany

Validation of Linear System

Postby Syed.Muzaher » Wed Sep 13, 2017 10:33 am

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 state-space model in simulink and was trying to compare the outputs of open-loop linear system with open-loop 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 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."

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

Jason.Jonkman
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Joined: Thu Nov 03, 2005 4:38 pm
Location: Boulder, CO
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Re: Validation of Linear System

Postby Jason.Jonkman » Wed Sep 13, 2017 1:38 pm

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,
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

Syed.Muzaher
Posts: 12
Joined: Mon Aug 28, 2017 4:17 pm
Organization: University of Paderborn
Location: Germany

Re: Validation of Linear System

Postby Syed.Muzaher » Wed Sep 13, 2017 2:22 pm

Dear Jason,
Thank you for your quick help and clearing my doubts.
Best regards
SS


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