Erratum: Global versus local Lyapunov approach used in disturbance observer-based wind turbine control

Due to a production error, the equation in section 2.2.1 Global Controller was incorrect.

In section 3.2 Simulation Results: Disturbance Observer Variation, Resulting System Dynamics and Mechanical Loads, at the beginning of subsection Pole locations, Figure 5 instead of Figure 4 was incorrectly referenced.

Due to a production error, the equations in section Discussion, subsection Pole Locations were incorrect.

Due to a production error, the equation in section Error-feedback gains (page 16) was incorrect.

Due a production error, the first paragraph in section Wind speed reconstruction and actuation signals was incorrect. You can find the correct paragraph below:

With the mitigated error-feedback gains , the reconstructed states , especially the reconstructed wind speeds , are mitigated, too (see Eq. 7¹¹): While the reconstructed wind speed of a single and arbitrary time point t = t₁ decreases steadily for the wind speed observer design with a local Lyapunov approach (i.e., ¹⁰, see left column in Figure 6), the reconstructed wind speed for the wind speed observer design with a global Lyapunov approach decreases unsteadily (i.e., , corresponding to the unsteady decrease of the mean Euclidean norm of the wind error state gains of the global wind speed observers (with (w [A, E], see Table 3; i.e., )¹⁰

In the same section, footnotes 12 and 13 were assigned incorrectly, and these have been replaced with footnote 10 in the updated article.

¹⁰The global and local wind speed observers E and J are not taken into account, because of their (closed-loop) pole locations, which are moved beyond the open-loop pole locations, as explained before in the subsection Pole locations.

Footnote 12 was also incorrect, the correct version is:

¹²with two exceptions for the tower side-to-side-bending moments and (see Figure 8B and line 7 in Table A9 as well as line 7 in Table A10.

Due to a production error, section Load Mitigation, paragraph number 3, appears to be interrupted and broken into two parts. This has been corrected into one single paragraph.

In the Appendix, part of section Specification of the LMI constraints was not included in the article. The corrected entire section appears below:

To calculate the mean Euclidian norm of the error-feedback gains [see (26)] and the average, mean Euclidian norm [see (27)] the worksheet Uebersicht_L_Matrizen_Pitchwinkel-YYYY_MM_DD.xlsx is used.

In the Appendix, the section Load Analysis was not included in the article. This has now been added to the article, you can find it below:

Summary

Keywords

global and local Lyapunov approach, Takagi–Sugeno framework, model-based controller and observer design, feedforward-feedback control, linear-matrix-inequality and pole region-based controller design, wind turbine application, elaborated wind turbine simulation model, load analysis

Citation

Frontiers Production Office (2023) Erratum: Global versus local Lyapunov approach used in disturbance observer-based wind turbine control. Front. Control. Eng. 4:1279811. doi: 10.3389/fcteg.2023.1279811

Received

18 August 2023

Accepted

18 August 2023

Published

03 November 2023

Approved by

Frontiers Editorial Office, Frontiers Media SA, Switzerland

Volume

4 - 2023

Updates

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Copyright

© 2023 Frontiers Production Office.

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