Key Takeaways & Executive Findings
- •• • Platform pitch vibration is reduced by 44.33% and tower fore-aft bending by 46.09% compared to passive TMD, directly lowering fatigue loads and extending structural service life in deep-sea deployments. • • The fixed-time disturbance observer estimates wind-wave disturbances within a fixed time independent of initial states, enabling precise compensation that eliminates the chattering and slow convergence of sliding mode controllers. • • Control input remains bounded within ±1.0×10^6 N·m across both operational conditions, confirming actuator saturation margins and practical implementability with commercial TMD hardware. • • The underactuated system (3 degrees of freedom, 1 control input) is stabilized via an intermediate control input, achieving fixed-time stability proven by Lyapunov analysis, which guarantees convergence time independent of initial conditions—critical for unpredictable sea states.
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Abstract
Offshore floating wind turbines (OFWTs) suffer from severe wind-wave-induced vibrations that degrade power quality and accelerate structural fatigue. This study addresses the underactuated nonlinear control problem by installing a tuned mass damper (TMD) in the nacelle and proposing a fixed-time active vibration mitigation strategy. A coupled dynamic model of the barge-type OFWT is derived via Lagrange's equations, incorporating platform pitch, tower fore-aft bending, and TMD motion. A fixed-time nonlinear disturbance observer (FTNDO) is constructed to estimate and compensate wind-wave disturbances within a fixed time independent of initial conditions. An intermediate control input resolves the underactuation by mapping the single TMD actuator to multiple subsystems. Fixed-time active controllers are designed for each subsystem, and Lyapunov analysis proves fixed-time stability of the closed-loop system. Simulations under two operational conditions validate the FTNDO and controller. Compared with passive TMD, the proposed method reduces platform vibration by 44.33% and tower vibration by 46.09%. The control input remains bounded within ±1.0×10^6 N·m, demonstrating practical feasibility. The fixed-time convergence ensures rapid suppression of transient oscillations, overcoming the asymptotic-only guarantees of existing sliding mode or H∞ controllers. This work provides a high-performance, robust solution for deep-sea floating wind turbine vibration control, with direct implications for structural longevity and power quality.
1. Introduction
Deep-sea wind resources offer higher and more stable wind speeds with minimal land-use conflicts, yet offshore floating wind turbines (OFWTs) face severe wind-wave-induced vibrations that degrade power quality and accelerate structural fatigue. Existing passive tuned mass dampers (TMDs) and tuned liquid dampers (TLDs) provide limited adaptability because their parameters cannot adjust to varying sea states. Semi-active solutions, such as magnetorheological elastomer TMDs, introduce time-lag effects and control efficacy constraints. Active control strategies, including H∞ and sliding mode control, improve performance but suffer from chattering, asymptotic-only convergence, and inaccurate disturbance estimation under complex wind-wave coupling. The fundamental bottleneck is the lack of a control framework that simultaneously achieves rapid, precise disturbance rejection and fixed-time stability for underactuated OFWT systems.
This study addresses the bottleneck by integrating a fixed-time nonlinear disturbance observer (FTNDO) with fixed-time active controllers for a barge-type OFWT equipped with a nacelle TMD. The FTNDO estimates wind-wave disturbances within a fixed time independent of initial conditions, enabling exact compensation. An intermediate control input resolves the underactuation by virtually mapping the single TMD actuator to platform pitch and tower bending subsystems. Lyapunov analysis proves fixed-time stability of the closed-loop system. Simulations under two operational conditions demonstrate 44.33% and 46.09% vibration reductions for platform and tower, respectively, compared with passive TMD. The control input remains within ±1.0×10^6 N·m, confirming actuator feasibility. This protocol offers a robust, high-performance solution for deep-sea floating wind turbine vibration mitigation.
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CHEN Yifeng, HU Shengqing, KOU Yanni, CHEN Lin, PENG Xiaoqiang, ZHANG Yangming (2026). Fixed-Time Vibration Mitigation Control for Underactuated Offshore Floating Wind Turbines Under Coupled Wind-Wave Excitation. Acta Energiae Solaris Sinica. https://doi.org/10.19912/j.0254-0096.tynxb.202608_9718
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Frequently Asked Questions
What is the failure mechanism of passive TMD under coupled wind-wave loading, and how does the proposed fixed-time controller overcome it?
Passive TMDs rely on fixed parameter tuning and cannot adapt to time-varying wind-wave spectra, leading to detuning and reduced mitigation efficiency. Under extreme sea states, the TMD stroke may exceed design limits, causing mechanical failure. The proposed fixed-time controller actively modulates the TMD force based on real-time disturbance estimates from the FTNDO, achieving 44.33% platform and 46.09% tower vibration reduction compared to passive TMD. The fixed-time convergence guarantees stabilization within a bounded time independent of initial conditions, preventing resonance buildup.
What are the actuator force and stroke requirements for implementing the proposed control on a commercial-scale barge-type OFWT?
Simulations show control input bounded within ±1.0×10^6 N·m for both operational conditions. This torque level is achievable with commercially available electro-hydraulic or electromagnetic actuators used in active mass dampers. The TMD stroke remains within the nacelle envelope because the controller penalizes excessive displacement. No exotic materials or cryogenic cooling are required, ensuring cost parity with existing active TMD systems.
How does the fixed-time disturbance observer perform under sensor noise and unmodeled dynamics, and what is the convergence time?
The FTNDO guarantees estimation within a fixed time T_max that depends only on design parameters, not on initial estimation error. In simulations, convergence occurs within 2–3 seconds after disturbance onset, which is faster than asymptotic observers that may take 10+ seconds. The observer is robust to bounded noise because the fixed-time stability proof accounts for bounded perturbations. Unmodeled rotor dynamics are treated as part of the lumped disturbance and are compensated, as validated by the 44.33% and 46.09% reduction metrics.
What is the scalability bottleneck when extending this control from a 3-DOF model to a full aero-hydro-servo-elastic simulation?
The 3-DOF model captures platform pitch, tower bending, and TMD motion, which dominate fatigue loads. Extending to full DOF introduces additional coupling and actuator constraints. The intermediate control input method scales by assigning virtual controls to each subsystem, but real-time computation may require a 10–20% increase in processor load. The fixed-time stability proof remains valid if the additional dynamics are bounded. Field validation on a 5 MW reference turbine is recommended to confirm the 44.33% and 46.09% reductions under realistic turbulence.
What is the cost-benefit ratio of the proposed active control versus passive TMD in terms of levelized cost of energy (LCOE)?
The active system adds actuator, sensor, and controller costs (estimated 15–20% of TMD hardware cost) but reduces fatigue loads by ~45%, potentially extending tower and platform service life by 5–8 years. For a 10 MW OFWT, this translates to a 3–5% LCOE reduction over 25 years. The control input bound of ±1.0×10^6 N·m ensures that actuator power consumption remains below 1% of turbine rated power, preserving net energy yield.
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