Pitch damping ratio in the ideal closed-loop method.

[Daniel.Kim]

Dear Dr. Jason.

I am reading your report “Influence of control on the pitch damping of a floating wind turbine.” In this report, there is one thing I don’t understand. Please help me to understand the following thing.

In page 5, You mentioned that the thrust sensitivity to wind speed is calculated in open-loop and ideal closed-loop. In the ideal closed-loop, the sensitivity is estimated as the slope of the steady-state thrust versus wind speed response presented in Figure 3. In Figure 3, rotor thrust increases according to the wind speed until the rated wind speed. Then, the pitch damping ratio has to increase from 10m/sec to 11.4m/sec in the ideal closed-loop because the sensitivity is positive in Equation (4). However, in Figure 4, the barge pitch damping ratio decreases from 10m/sec to 11.4m/sec even though the sensitivity is positive. Could you let me know what part I am missing regarding this?

Sincerely,
Daniel Kim.

[Jason.Jonkman]

Dear Daniel,

I think Figure 4 may look a little odd because the derivative was computed based on a fairly coarse (1 m/s) wind-speed resolution and a central-difference perturbation scheme was used to compute the derivative numerically. This derivative is likely not accurate right at rated.

Best regards,

[Daniel.Kim]

Dear Dr. Jason.

I got it. Thank you for your time.

Daniel Kim.