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### Closed loop eigenvalues

Posted: **Tue May 15, 2012 1:57 am**

by **Tore.Bakka**

I am trying to make a contorller for the OC3 5MW floating turbine. I have some questions about the closed loop eigenvalues that I hope someone can help me with.

I linearize the model about its initial conditions with a constant windspeed of 15 m/s. I fill out the CampellDiagram.xls and look at the open loop natural frequencies and damping ratios. I am now wondering if there are any guidelines to where the closed loop eigenvalues should be? Or where they definitely should not be? For example for the open loop surge motion I get a natural frequency of 0.00169 Hz, is there any upper and lower limits to this frequency? Or is it enough that I make sure that the pitching frequency is lower than the surge motion frequency, for the closed loop system? Also, is it correct of me to assume that as long as the pitching frequency is lower than the lowest structural frequency, we will avoid negativ aerodynamic damping at high windspeeds?

Regards,

Tore

### Re: Closed loop eigenvalues

Posted: **Tue May 15, 2012 6:28 am**

by **Jason.Jonkman**

Dear Tore,

I would say that setting the blade-pitch controller natural frequency below the lowest structural frequency would be sufficient to avoid the blade-pitch-controller-induced negative damping of floating platform motion, but that this condition may not be necessary. For instance, just because a structural natural frequency is below the blade-pitch controller natural frequency doesn't mean that there will be negative damping -- the controller may not influnece a particular low-frequency mode or their may be sufficient hydrodynamic damping in that mode to overcome any aerodynamic-induced negative damping. For the OC3-Hywind system, for example, we found it necessary to place the blade-pitch controller natural frequency below the platform-pitch natural frequency, but not lower than the platform-surge natural frequency, which is quite a bit lower. It is noted that the problem is not trivial because -- due to nonlinearities in the system -- the structural natural frequencies vary with operational state.

Also, please be aware that dropping the blade-pitch controller natural frequency comes at the expense of greater rotor-speed excursions, which may not be desirable.

Please also note, however, that the surge natural frequency that I've predicted for the OC3-Hywind spar system is around 0.008 Hz, which is quite a bit higher than the frequency you are reporting. I'm not sure this is causing the difference, but it may be caused you have linearized your model about initial conditions, as opposed to linearization about a steady-state condition. In general, I recommend that you always linearize a model about a steady-state condition.

I hope that helps.

Best regards,

### Re: Closed loop eigenvalues

Posted: **Wed May 16, 2012 12:47 am**

by **Tore.Bakka**

Hi Jason,

Thank you for the helpful replay. This gives me a good startingpoint in choosing the controller frequency.

I linearized the model as you suggested, about a steady-state condition with a wind speed of 15 m/s. But I think I am reading the campell diagram wrong. I think I have pasted inn all the values that should be pasted in. But for some reason I get 23 Mode Numbers with my 22 states. Is it correct that Mode Number 1 (blue field) gives the frequency and damping ratio to state nr 1? This gives me some funny values.

Tore

### Re: Closed loop eigenvalues

Posted: **Wed May 16, 2012 6:33 am**

by **Jason.Jonkman**

Dear Tore,

As described in this forum topic:

viewtopic.php?f=13&t=621, generator-DOF-induced rigid-body modes show up in MBC3 as a pair of zero-valued (or near-zero-valued) frequencies with +/- inf damping. Thus, this mode can add one more mode than you have DOFs enabled. I suspect this is why you are getting 23 modes for a 22-DOF system.

I'm not sure I understand your last question. It may help to paste your results into the forum.

Best regards,

### Re: Closed loop eigenvalues

Posted: **Wed May 16, 2012 7:37 am**

by **Tore.Bakka**

Hi Jason,

I read the other forum topics and I also suspect this is the reason for the extra mode. My last question conserns the interpretation of the campell diagram. Perhaps you could help me understand the diagram better. I attached the excel sheet. Is it correct that the natural frequency for for example surge motion is 0.0082Hz because it has both red text and green background, platform pitch is 0.031Hz because of the green background and will influence the surge motion most because of the red text? Is this how the sheet works?

Regards,

Tore

### Re: Closed loop eigenvalues

Posted: **Fri May 18, 2012 5:13 pm**

by **Jason.Jonkman**

Dear Tore,

The spreadsheet shows the contributions of each DOF to each full-system mode. In the spreadsheet, the mode shapes can be interpreted by comparing the relative magnitude of the DOFs within a given mode and comparing across modes. The green background corresponds to the maximum value of the mode shape magnitude within a row (across modes) and the red bod text corresponds to the maximum value of the mode shape magnitude within a column (within a given mode). So, the highlighted cells usually are indicative of the mode. Your interpretation of the platform-surge and platform-pitch modes is correct.

Usually, the rigid-body generator-DOF mode corresponds to modes 1 and 2; in your example, however, it is showing up as modes 1 and 7 (you can tell by the very high damping).

I hope that helps.

Best regards,

### Re: Closed loop eigenvalues

Posted: **Mon May 21, 2012 12:13 am**

by **Tore.Bakka**

Thanks so much for quick and helpful reply.

Tore

### Re: Closed loop eigenvalues

Posted: **Tue Oct 02, 2018 10:05 am**

by **Joannes.Olondriz**

Dear everyone,

I am trying to identify the closed-loop poles and zeros of the platform-pitch mode to analyze the negative platform damping effect in three floating platforms (barge, spar, and TLP) with the 5MW wind turbine. I did it with the barge and TLP platform after linearizing with FAST 7 without problems. However, the spar model (OC3-Hywind) that I took from [

http://wind.nrel.gov/public/jjonkman/NRELOffshrBsline5MW/FAST_v7.00-v7.01/NRELOffshrBsline5MW_OC3Hywind.zip] does not present the zero in the right-half-plane. Meaning the system does not the negative platform damping effect, when the

https://www.nrel.gov/docs/fy10osti/47535.pdf technical report suggest the contrary in the '6 Control System Properties' section.

There is any extra Morison element added to this model? Increasing platform-pitch mode damping to avoid the negative platform damping?

Any other suggestion why can not see that effect?

Thank you in advance,

Joannes

### Re: Closed loop eigenvalues

Posted: **Tue Oct 02, 2018 10:32 am**

by **Jason.Jonkman**

Dear Joannes,

The OC3-Hywind spar model does have Morison-type viscous drag. Regardless, I would expect the platfom-pitch mode to be stable in open loop. It is in closed loop (with active pitch control) where platform-pitch stability problems could occur.

Best regards,