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arxiv: 2310.15463 · v1 · submitted 2023-10-24 · 📡 eess.SY · cs.SY

Nested Control Co-design of a Spar Buoy Horizontal-axis Floating Offshore Wind Turbine

Saeid Bayat , Yong Hoon Lee , James T. Allison This is my paper

Pith reviewed 2026-05-24 07:02 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords floating offshore wind turbinecontrol co-designspar buoyannual energy productionreduced-order modelopen-loop optimal controlmultidisciplinary optimization
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The pith

A nested control co-design approach increases annual energy production of a spar-buoy floating offshore wind turbine by more than 11 percent.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that conventional sequential design of the physical structure and its controller leaves substantial performance untapped in floating offshore wind turbines. It instead uses a nested control co-design method that optimizes both plant parameters and control inputs together via open-loop optimal control. The method runs on a reduced-order model chosen for speed while retaining key couplings among aeroelasticity, hydrodynamics, and structural dynamics. This simultaneous treatment produces more than an 11 percent rise in annual energy production relative to a baseline design. The result supplies design engineers with concrete directions for exploiting plant-control interactions that sequential methods overlook.

Core claim

By applying a nested CCD approach with open-loop optimal control to a simplified reduced-order model of a horizontal-axis FOWT with spar buoy platform, the annual energy production objective improves by more than eleven percent over the baseline design while fully accounting for plant-control coupling.

What carries the argument

Nested control co-design using open-loop optimal control applied to a reduced-order model that captures multidisciplinary physics couplings and plant-control interactions.

If this is right

  • Optimization studies at this fidelity supply system design engineers with insights into directions that leverage plant-control coupling.
  • The method provides a template for future higher-fidelity CCD studies that use more detailed turbine models.
  • CCD avoids suboptimal results that arise when control design follows plant design in systems with strong coupling.
  • The approach is advantageous for FOWT systems because of their complex interactions across physics disciplines.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The reported gain suggests that similar co-design methods could reduce levelized cost of energy for offshore wind projects.
  • The nested CCD framework may transfer directly to other coupled renewable systems such as wave-energy devices.
  • Experimental validation on a physical spar-buoy prototype would test whether the predicted AEP improvement holds under real wind and wave variability.

Load-bearing premise

The reduced-order model is sufficiently rich to capture the important multidisciplinary physics couplings and plant-control design coupling associated with the horizontal-axis FOWT system.

What would settle it

A higher-fidelity simulation of the co-designed parameters that yields an AEP gain below 11 percent would falsify the performance improvement at this model fidelity.

Figures

Figures reproduced from arXiv: 2310.15463 by James T. Allison, Saeid Bayat, Yong Hoon Lee.

Figure 1
Figure 1. Figure 1: Schematic of the complete spar buoy-based FOWT [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schematics illustrating plant design variables: (a) [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: XDSM of the nested CCD problem depicting the solution process for the overall FOWT CCD problem. The inner-loop [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Free wind velocity values and the corresponding [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Wind profiles in 100 seconds of time horizon for [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Optimized tower and blade designs for the CCD [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Optimized blade power and thrust coefficients as functions of tip speed ratio (λ) and blade pitch angle (θb). (a) Power coefficient surface; (b) thrust coefficient surface. blade design variables optimized. The converged design solution indicates that the tower height has increased to a particular height (here, 83.12 m) that is larger than the baseline tower height (77.60 m) design. In addition, the tower … view at source ↗
Figure 10
Figure 10. Figure 10: Resulting tower shape for the two design points [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Optimal tower shapes for two distinct allowable [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Generated power curves under various scenarios. Sub-figures refer to power curves of steady and varied wind cases for [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Trajectories of control inputs and model outputs [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Trajectories of model dynamic outputs, including [PITH_FULL_IMAGE:figures/full_fig_p017_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Optimal control performed on the “tower only” plant design given in Tab. 3 without and with additional wave loading. [PITH_FULL_IMAGE:figures/full_fig_p019_15.png] view at source ↗
read the original abstract

Floating offshore wind turbine (FOWT) systems involve several coupled physical analysis disciplines, including aeroelasticity, multi-body structural dynamics, hydrodynamics, and controls. Conventionally, physical structure (plant) and control design decisions are treated as two separate problems, and generally, control design is performed after the plant design is complete. However, this sequential design approach cannot fully capitalize upon the synergy between plant and control design decisions. These conventional design practices produce suboptimal designs, especially in cases with strong coupling between plant and control design decisions. Control co-design (CCD) is a holistic design approach that accounts fully for plant-control design coupling by optimizing these decisions simultaneously. CCD is especially advantageous for system design problems with complex interactions between physics disciplines, which is the case for FOWT systems. This paper presents and demonstrates a nested CCD approach using open-loop optimal control (OLOC) for a simplified reduced-order model that simulates FOWT dynamic behavior. This simplified model is helpful for optimization studies due to its computational efficiency, but is still sufficiently rich enough to capture important multidisciplinary physics couplings and plant-control design coupling associated with a horizontal-axis FOWT system with a spar buoy floating platform. The CCD result shows an improvement in the objective function, annual energy production (AEP), compared to the baseline design by more than eleven percent. Optimization studies at this fidelity level can provide system design engineers with insights into design directions that leverage design coupling to improve performance. These studies also provide a template for future more detailed turbine CCD optimization studies that utilize higher fidelity models and design representations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript presents a nested control co-design (CCD) approach that employs open-loop optimal control (OLOC) on a simplified reduced-order model of a spar-buoy horizontal-axis floating offshore wind turbine. It reports that simultaneous optimization of plant and control design variables yields an improvement of more than 11% in annual energy production (AEP) relative to a baseline design, while asserting that the reduced-order model remains sufficiently rich to capture key multidisciplinary couplings.

Significance. If the reduced-order model fidelity were demonstrated, the work would provide a computationally tractable template for exploiting plant-control synergies in FOWT design and could guide subsequent higher-fidelity CCD studies. The nested CCD formulation itself is a clear methodological contribution.

major comments (1)
  1. [Abstract] Abstract: the assertion that the simplified model 'is still sufficiently rich enough to capture important multidisciplinary physics couplings and plant-control design coupling' is not accompanied by any quantitative validation (e.g., side-by-side comparison of platform motions, rotor speed, or power against OpenFAST or experimental data). Because the reported >11% AEP gain is obtained entirely by optimizing inside this same model, any systematic discrepancy in the omitted dynamics (hydro-elastic coupling, nonlinear mooring, turbulent inflow) directly scales the claimed improvement and must be addressed before the numerical result can be considered load-bearing.
minor comments (1)
  1. The baseline design parameters and the precise definition of the AEP objective (including wind-speed distribution and control constraints) should be stated explicitly in the main text or a table to allow reproduction of the 11% figure.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The single major comment raises an important point regarding model validation that we address directly below. We believe the nested CCD methodology remains a valuable contribution even within the reduced-order setting, but we agree that additional justification is warranted.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that the simplified model 'is still sufficiently rich enough to capture important multidisciplinary physics couplings and plant-control design coupling' is not accompanied by any quantitative validation (e.g., side-by-side comparison of platform motions, rotor speed, or power against OpenFAST or experimental data). Because the reported >11% AEP gain is obtained entirely by optimizing inside this same model, any systematic discrepancy in the omitted dynamics (hydro-elastic coupling, nonlinear mooring, turbulent inflow) directly scales the claimed improvement and must be addressed before the numerical result can be considered load-bearing.

    Authors: We agree that the manuscript would be strengthened by quantitative evidence supporting the fidelity of the reduced-order model. The model is constructed from standard, literature-established reduced-order representations of spar-buoy FOWT dynamics (linearized hydrodynamics, quasi-static mooring, and blade-element momentum aerodynamics with dynamic inflow), which have been shown in prior work to capture the dominant plant-control couplings relevant to AEP optimization. Nevertheless, the referee is correct that no direct side-by-side comparison with OpenFAST or experimental data is presented. We will revise the manuscript to add a new subsection that reports such comparisons for representative operating conditions, including platform pitch, rotor speed, and power time series. In the revised text we will also qualify the >11% AEP figure as a relative improvement demonstrated within a validated reduced-order modeling framework, and we will discuss the expected impact of omitted nonlinear effects on the absolute gain. This addresses the concern that discrepancies could scale the reported benefit. revision: yes

Circularity Check

0 steps flagged

No circularity; AEP gain is direct output of optimization on stated model

full rationale

The paper reports an >11% AEP improvement obtained by executing nested CCD (open-loop optimal control) on its reduced-order model. No step reduces by the paper's own equations to a fitted parameter, self-defined quantity, or self-citation chain. The model-fidelity statement is an explicit modeling assumption, not a derivation that collapses to its inputs. The result is therefore an independent optimization outcome rather than a renaming or tautology.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the adequacy of the reduced-order model for capturing couplings and on standard assumptions of open-loop optimal control; no new entities are postulated.

free parameters (1)
  • Plant and control design variables
    The CCD optimization tunes these variables to maximize AEP; their specific values are not listed in the abstract.
axioms (1)
  • domain assumption The reduced-order model is sufficiently rich to capture important multidisciplinary physics couplings and plant-control design coupling
    Explicitly stated in the abstract as the justification for using the model in optimization studies.

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