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Model Predictive Control of Wind Turbines: A Model-Oriented Review of Prediction Models, Control Objectives, and Nonlinear Aerodynamic Formulations

Roya Khalili-Amirabadi, Mohsen Jalaeian-Farimani, Mahdi Ghane

arXiv:2610.31295v1eess.SYcs.SYmath.DSmath.OC

TL;DR

Wind-turbine MPC studies use diverse online predictors, and controller labels alone do not specify the model or pitch dependence propagated by the optimizer. This review classifies the literature by model structure and related design descriptors, identifying a remaining integration challenge that combines flexible prediction, direct nonlinear pitch treatment, explicit load objectives or constraints, and validated model correction.

  • Problem

    Existing reviews and MPC labels do not consistently identify the exact model propagated online, including whether nonlinear applied-pitch dependence is retained.

    Source: §1 · p. 2

  • Method

    The review uses article-level evidence to classify predictor structure, representation, MPC formulation, objective, and validation separately, applying a conservative equation-based criterion to direct nonlinear applied-pitch propagation.

    Source: §1 · p. 2, §2 · p. 2, §5 · p. 6

  • Results

    The verified corpus supports an evidence-bounded integration gap combining flexible drivetrain prediction, direct nonlinear applied-pitch propagation, explicit load constraints or objectives, and validated adaptive or learned model correction.

    Source: §7 · p. 7

  • Takeaways & Limitations

    Separating the online predictor from the validation plant and recording model attributes independently makes article-level comparisons more precise.

    Source: §1 · p. 2, §2 · p. 2

    The identified gap is grounded predominantly in utility-scale megawatt-class studies and is not extended to small-scale turbines, which were not systematically covered.

    Source: §7 · p. 7

Abstract

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Model predictive control (MPC) has been applied to wind-turbine regulation with markedly different internal prediction models, ranging from linearized low-order turbine models to nonlinear, aeroelastic, floating, and data-driven predictors. This review organizes the literature primarily by the model propagated by the controller and treats model order, predictor representation, MPC formulation, control objective, and validation plant as separate descriptors. Primary studies show that low-order linear or piecewise-affine predictors are attractive for constrained power and speed regulation, whereas flexible drivetrain, structural, and floating models are needed when drivetrain twist, tower motion, blade loads, or platform dynamics are explicit control quantities. Nonlinear and economic MPC studies further demonstrate coordinated pitch/torque control across broad operating regions, while preview, repetitive, and data-driven formulations address wind prediction, periodic loads, and model mismatch. Particular attention is given to aerodynamic pitch dependence: variable-pitch turbine dynamics can be non-affine with respect to applied pitch, and the term NMPC alone does not prove that the original nonlinear pitch map is retained inside the optimizer. The review therefore adopts a conservative, equation-based classification for direct nonlinear applied-pitch propagation. Here, direct nonlinear applied-pitch propagation means that the applied pitch at each prediction step is evaluated inside the original nonlinear aerodynamic map, rather than replacing that dependence by a linearized, scheduled, piecewise-affine, or learned surrogate. The literature supports a remaining integration challenge at the intersection of flexible drivetrain prediction, nonlinear aerodynamic pitch treatment, explicit constraints and load objectives, and validated adaptive or learned model correction.

1. INTRODUCTION

Wind-turbine MPC addresses multivariable, constrained control, but studies use varied predictors and control architectures. This review classifies them by the model propagated online, separating that model from the controller label and validation plant.

  • Pitch and generator torque jointly affect power, speed, actuator use, drivetrain motion, and structural loading, motivating MPC’s finite-horizon constrained optimization [Mahmoud and Oyedeji, 2019, Henriksen et al., 2012, Jain et al., 2015].Source: §1 · p. 1
  • Wind-turbine MPC includes linear, nonlinear, economic, preview-enabled, repetitive, floating, and data-driven formulations [Gros et al., 2013, Gros and Schild, 2017, Schlipf et al., 2013, Raach et al., 2014, Liu et al., 2021, Kayedpour et al., 2022].Recent studies also consider real-time, adaptive, and learning-informed implementations [Soleymani et al., 2023, Soleymani et al., 2024, Wen et al., 2026, Jin and Fu, 2026, Yang et al., 2026].Source: §1 · p. 2
  • Unlike reviews organized by strategy or application level, this review classifies studies by controller-internal model structure and records predictor representation, MPC architecture, objective, and validation plant separately.This separation distinguishes, for example, linearized from direct nonlinear applied-pitch dynamics and the online predictor from the validation simulator.Source: §1 · p. 2
  • An MPC or NMPC label alone does not identify the propagated model: studies use continuously linearized, reduced nonlinear, or high-dimensional linear predictors, sometimes validated on more detailed plants [Jain et al., 2015, Schlipf et al., 2013, Evans and Lio, 2022].Variable-pitch turbine dynamics can be non-affine in pitch, so the controller label does not establish that the original nonlinear pitch dependence remains in the optimizer [Bagheri and Sun, 2016, Kong et al., 2020].Source: §1 · p. 2
  • The review synthesizes wind-turbine MPC literature using article-level evidence and makes specific claims about states, constraints, and pitch treatment only when supported by the article or an authoritative publication record.Source: §1 · p. 2

2. REVIEW BASIS AND CLASSIFICATION RULES

The review focuses on turbine-level MPC and distinguishes the online predictor from the physical plant and validation simulator. Its classification records model structure, representation, formulation, objective, and validation independently, with a conservative evidence-based rule for direct nonlinear applied-pitch propagation.

  • The review covers turbine-level prediction containing aerodynamic, mechanical, drivetrain, structural, or floating-turbine dynamics, while excluding converter-switching MPC without turbine mechanical states.Wind-farm supervisory MPC is included only when it informs the turbine predictor used for active-power allocation.Source: §2 · p. 2
  • The physical plant generates the system response, a high-fidelity simulator assesses the controller, and the online predictor is propagated inside the MPC optimization at each update.A higher-fidelity validation simulator does not imply that the same model runs online.Source: §2 · p. 2
  • Five descriptors are tracked independently: physical model structure, predictor representation, MPC formulation, control objective, and validation level.Direct nonlinear applied-pitch propagation is claimed only when equations or explicit descriptions show applied pitch evaluated within the nonlinear aerodynamic map; linearized, scheduled, piecewise-affine, and learned surrogates remain distinct classes.Source: §2 · pp. 2–3

3. PREDICTION MODELS USED IN WIND-TURBINE MPC

The reviewed predictors range from low-order affine models to flexible, aeroelastic, floating, and data-driven representations. The review treats aerodynamic pitch dependence and predictor structure as distinct from the MPC formulation.

3.1 Aerodynamic input structure

  • The aerodynamic power coefficient depends on tip-speed ratio and applied pitch, and turbine dynamics can be non-affine in pitch [Bagheri and Sun, 2016, Kong et al., 2020].Replacing this dependence with local linear or piecewise-affine dynamics does not constitute direct nonlinear aerodynamic propagation [Jain et al., 2015, Odgaard and Hovgaard, 2015, Zhao et al., 2015a, Zhao et al., 2015b].Source: §3.1 · p. 3

3.2 Low-order and flexible drivetrain predictors

  • Low-order or piecewise-affine predictors suit power and speed regulation, while flexible models make drivetrain motion available as an explicit optimization quantity [Zhao et al., 2015a, Zhao et al., 2015b, Jain et al., 2015, Henriksen et al., 2012, Kong et al., 2020].Kong et al. include gearbox, drive-shaft, and tower dynamics and penalize drive-shaft torsion.Source: §3.2 · p. 3

3.3 Structural and aeroelastic predictors

  • Structural prediction ranges from reduced nonlinear control models tested on detailed aeroelastic plants to high-dimensional linearized aeroelastic models with control trajectories parameterized to reduce online optimization variables [Schlipf et al., 2013, Evans and Lio, 2022].Other examples include tower displacement and drivetrain twist objectives, individual-pitch control, and scaled-turbine preview experiments [Jain et al., 2015, Mirzaei et al., 2013, Sinner et al., 2022].Source: §3.3 · p. 4

3.4 Floating offshore wind-turbine predictors

  • Floating-turbine MPC predicts platform-coupled dynamics; Raach et al. combine reduced nonlinear prediction, wind and wave preview, individual pitch, and generator-torque coordination.The floating label does not determine drivetrain model order, and high-fidelity floating reference studies provide validation environments rather than proof of the online predictor used [Thiery et al., 2015, Skaare et al., 2015, Wendt et al., 2019, Bergua et al., 2023].Source: §3.4 · p. 4

3.5 Data-driven and hybrid predictors

  • Data-driven predictors include a cascaded Hammerstein model coordinating pitch and torque without fully nonlinear online optimization, and a subspace repetitive controller imposing blade-pitch angle and rate constraints [Kayedpour et al., 2022, Liu et al., 2021].Adaptive economic control instead learns a correction to reduce mismatch between a reduced-order MPC model and turbine response [Anand and Bottasso, 2026].Source: §3.5 · p. 4

4. MPC FORMULATIONS, OBJECTIVES, AND VALIDATION EVIDENCE

MPC formulation, objective, preview, and fault tolerance are separate from predictor representation. The reviewed studies combine them in different ways, so labels such as “economic,” “preview,” or “fault-tolerant” do not specify the online model.

  • Linear MPC can be computationally attractive, but linearization error may materially degrade performance in nonlinear operating regions [Jain et al., 2015, Odgaard and Hovgaard, 2015].Odgaard and Hovgaard propose parameter adjustment of the linearized model.Source: §4 · p. 4
  • NMPC studies use varied internal nonlinearities, including moving-horizon estimation, LiDAR wind preview, and floating-turbine individual-pitch control [Gros et al., 2013, Schlipf et al., 2013, Raach et al., 2014].The shared NMPC label does not establish which nonlinearities the internal model retains.Source: §4 · p. 4
  • Economic MPC shifts from reference tracking toward operational criteria; examples balance power with drivetrain, tower, and actuator terms or include online rainflow fatigue costs [Gros and Schild, 2017, Kong et al., 2020, Loew and Bottasso, 2022].Kong et al. impose pitch, torque, rate, speed, and electrical-power constraints.Source: §4 · p. 4
  • Preview is a sensing and optimization architecture used across linearized and nonlinear formulations, including scaled experimental validation of preview-enabled blade-pitch MPC [Schlipf et al., 2013, Mirzaei et al., 2013, Sinner et al., 2022].Source: §4 · p. 4
  • Fault tolerance is an MPC function, not a unique predictor class; examples use floating-turbine individual-pitch MPC, drivetrain-and-tower models with constraint reconfiguration, and Takagi–Sugeno models with fault estimation [Thiery et al., 2015, Jain and Yame, 2019, Feng and Patton, 2014].Source: §4 · p. 5

5. DIRECT NONLINEAR APPLIED-PITCH DEPENDENCE

The review distinguishes non-affinity in the pitch channel from nonlinear turbine dynamics generally, and classifies controllers by the model propagated online. It also separates the controller predictor from the plant used for validation.

5. DIRECT NONLINEAR APPLIED-PITCH DEPENDENCE

  • Direct nonlinear applied-pitch propagation is not established by the NMPC label, nonlinear validation dynamics, or a learned nonlinear surrogate alone.The applied pitch must be evaluated inside the original nonlinear aerodynamic map; linearized, PWA, and Hammerstein/neural predictors use different online input representations.Source: §5 · p. 6
  • A nonlinear turbine model and a model non-affine in the pitch control channel are distinct classifications.Bagheri and Sun explicitly describe pitch non-affinity, while Bagheri et al. address a related problem using neural networks and a transformation to control-affine form [Bagheri and Sun, 2016, Bagheri et al., 2022].Source: §5 · p. 6
  • The validation plant and controller predictor must be reported separately because a detailed test plant may not be propagated inside the optimizer.Schlipf et al. use a reduced internal model because the full aeroelastic model is too complex for their NMPC, whereas Evans and Lio retain a high-dimensional linearized aeroelastic model and reduce online decision variables [Schlipf et al., 2013, Evans and Lio, 2022].Source: §5 · p. 7

6. VALIDATION, MODEL REDUCTION, AND COMPUTATIONAL TRACTABILITY

Validation spans nonlinear simulation, detailed aeroelastic and floating-model comparisons, wind-tunnel experiments, and high-fidelity analysis tools. Predictor structure and computational strategy jointly shape the fidelity–tractability trade-off, while metric differences constrain cross-study comparison.

6. VALIDATION, MODEL REDUCTION, AND COMPUTATIONAL TRACTABILITY

  • Validation evidence ranges from nonlinear simulation and detailed aeroelastic plants to a scaled wind-tunnel experiment and floating-wind measurement or wave-tank comparisons.The cited floating references include full-scale measurement/simulation comparison, FAST results against wave-tank data, and platform aerodynamic loading against wind-tunnel measurements [Skaare et al., 2015, Wendt et al., 2019, Bergua et al., 2023].Source: §6 · p. 7
  • High-fidelity structural and aero-hydro-servo-elastic tools support validation or model development but do not by themselves establish high-order online MPC.BeamDyn is a high-fidelity blade solver within FAST, and Yang et al. compare a floating-wind coupling framework with OpenFAST [Wang et al., 2017, Yang et al., 2020].Source: §6 · p. 7
  • Online computational burden depends on predictor form, estimation, decision-variable parameterization, horizon, and solver structure, not state count alone.Examples include real-time NMPC with MHE, trajectory parameterization to reduce optimization degrees of freedom, and a Hammerstein/neural approximation with online linearization and quadratic programming [Gros et al., 2013, Evans and Lio, 2022, Kayedpour et al., 2022].Source: §6 · p. 7
  • Higher-fidelity models can improve prediction of loads and cross-coupled dynamics but increase online cost; linear and PWA models favor structured solvers and update rates at the cost of approximation error.Reduced nonlinear predictors generally require NLP/SQP/RTI iterations and warm starts, while hybrid or data-driven predictors may shift complexity offline but add adaptation or robustness overhead.Source: §6 · p. 7
  • Mean or RMS metrics can hide constraint violations and extreme events, and tower or drivetrain RMS measures are not interchangeable with fatigue measures.Comparisons also depend on wind realization, turbulence, operating region, preview, horizon, baseline tuning, and validation plant.Source: §6 · p. 7

7. RESEARCH GAPS AND OUTLOOK

The review identifies an integrative research opportunity rather than a gap in any single ingredient: combine flexible drivetrain prediction, direct nonlinear applied-pitch aerodynamics, explicit constraints or load objectives, and validated adaptive model correction. It also identifies reporting and corpus-scope boundaries relevant to interpreting that opportunity.

7. RESEARCH GAPS AND OUTLOOK

  • Most individual ingredients of the proposed research direction already appear in the reviewed literature, including flexible/load-aware, real-time/economic, preview, floating, learned, and adaptive MPC.Explicit non-affine wind-turbine control also predates this review outside MPC [Bagheri and Sun, 2016, Bagheri et al., 2022].Source: §7 · p. 7
  • The remaining direction is to integrate flexible drivetrain prediction, direct nonlinear applied-pitch propagation, explicit pitch/torque and drivetrain-load constraints or objectives, and validated adaptive model correction.The review frames this as a sparsely represented combination in the verified corpus, not an absolute first.Source: §7 · p. 7
  • The evidence for this integration gap is predominantly from utility-scale megawatt-class onshore and offshore studies, so the review does not extend the gap claim to small-scale turbines.Small-scale turbines were not systematically covered and may differ in scale-dependent dynamics, actuator bandwidths, sensing, and computational constraints.Source: §7 · p. 7
  • Comparisons can be ambiguous when reports omit online states, pitch representation, validation plant, or whether learning changes the predictor or command-generation layer.The review recommends reporting these details alongside inputs, constraints, estimation, horizon, sampling time, solver, and measured computation time.Source: §7 · pp. 7–8
  • Benchmark suites could improve reproducibility with common turbines, disturbance cases, baselines, validation tiers, reporting, and evaluation scripts; adaptation should be tested against explicit plant-model mismatch.The cited work motivates adaptive correction and assesses fatigue-aware MPC with model mismatch, MHE, and realistic LiDAR processing [Anand and Bottasso, 2026, Loew and Bottasso, 2022].Source: §7 · p. 8

8. CONCLUSIONS

The review concludes that wind-turbine MPC should be classified by its online predictor, optimization, objective, and validation plant rather than by controller label alone. It identifies integrated flexible prediction, nonlinear pitch treatment, explicit load objectives, and validated model correction as a research opportunity.

8. CONCLUSIONS

  • Controller labels alone cannot reliably support comparison; online predictor, optimization formulation, controlled objective, and validation plant should be classified independently.The reviewed models range from low-order linearized and PWA predictors to flexible, floating, reduced nonlinear, and learned models.Source: §8 · p. 8
  • Variable-pitch dynamics can be non-affine in pitch, but “NMPC” alone does not establish that the optimizer retains the original nonlinear aerodynamic map.The review uses an equation-based classification to distinguish nonlinear plants, linearized predictors, PWA approximations, and learned surrogates.Source: §8 · p. 8
  • The review identifies an integrated opportunity combining flexible drivetrain prediction, direct nonlinear applied-pitch aerodynamics, explicit pitch/torque and drivetrain-load objectives or constraints, and validated adaptive model correction.Its potential contribution lies in the verified coexistence of these features and high-fidelity or experimental validation, not any one ingredient in isolation.Source: §8 · p. 8
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