Robust fatigue-aware adaptive control via cascaded SMO-UKF estimation for nonlinear systems under uncertainties

Jun-Hee Lee; Ganesh Mayilsamy; Baek-Soon Kwon; Jae Hoon Jeong; Jun-Hee Lee; Ganesh Mayilsamy; Baek-Soon Kwon; Jae Hoon Jeong

doi:10.3934/math.2026765

AIMS Mathematics

2026, Volume 11, Issue 6: 18801-18834. doi: 10.3934/math.2026765

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Robust fatigue-aware adaptive control via cascaded SMO-UKF estimation for nonlinear systems under uncertainties

1.
Department of Electronic and Information Engineering, Kunsan National University, 558, Daehak-ro, Gunsan, 54150, Jeonbuk, Republic of Korea
2.
School of Electrical Engineering, Vellore Institute of Technolog-Chennai Campus, Kelambakkam-Vandalur Rd, Chennai, 600 127, Tamilnadu, India
3.
School of Mechanical Engineering & Advanced Machinery Technology Research Institute, Kunsan National University, Republic of Korea
4.
Kunsan National University, 558, Daehak-ro, Gunsan, 54150, Jeonbuk, Republic of Korea

Received: 14 May 2026 Revised: 15 June 2026 Accepted: 18 June 2026 Published: 25 June 2026
MSC : 93C42, 93E10

This paper proposes an adaptive torque control and state estimation method that effectively addresses the trade-off between fatigue load reduction and power generation performance in a nonlinear wind energy conversion system subject to strong turbulence, measurement noise, and model uncertainties. The proposed fatigue load-aware adaptive torque controller dynamically adjusts control weights based on the variability, mismatch, and standard deviation of the aerodynamic torque, thereby reducing drivetrain fatigue loads while minimizing power loss. In addition, to accurately estimate the highly nonlinear and unknown aerodynamic torque, a combined estimator based on SMO and UKF was designed. SMO provides robustness against disturbances and noise, while the UKF enhances estimation accuracy in nonlinear systems, enabling reliable aerodynamic torque estimation. To validate the performance, simulations were conducted under three different turbulence intensities and wind speed profiles. Simulation results demonstrated that the proposed SMO-UKF estimator achieves up to a 2.77% improvement in estimation performance compared to conventional methods. Furthermore, the proposed control strategy reduces fatigue loads by up to 15.52% with negligible reduction in power output.
- SMO,
- UKF,
- torque,
- adaptive control,
- wind turbine system
Citation: Jun-Hee Lee, Ganesh Mayilsamy, Baek-Soon Kwon, Jae Hoon Jeong. Robust fatigue-aware adaptive control via cascaded SMO-UKF estimation for nonlinear systems under uncertainties[J]. AIMS Mathematics, 2026, 11(6): 18801-18834. doi: 10.3934/math.2026765

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Abstract

This paper proposes an adaptive torque control and state estimation method that effectively addresses the trade-off between fatigue load reduction and power generation performance in a nonlinear wind energy conversion system subject to strong turbulence, measurement noise, and model uncertainties. The proposed fatigue load-aware adaptive torque controller dynamically adjusts control weights based on the variability, mismatch, and standard deviation of the aerodynamic torque, thereby reducing drivetrain fatigue loads while minimizing power loss. In addition, to accurately estimate the highly nonlinear and unknown aerodynamic torque, a combined estimator based on SMO and UKF was designed. SMO provides robustness against disturbances and noise, while the UKF enhances estimation accuracy in nonlinear systems, enabling reliable aerodynamic torque estimation. To validate the performance, simulations were conducted under three different turbulence intensities and wind speed profiles. Simulation results demonstrated that the proposed SMO-UKF estimator achieves up to a 2.77% improvement in estimation performance compared to conventional methods. Furthermore, the proposed control strategy reduces fatigue loads by up to 15.52% with negligible reduction in power output.

References

[1]	J. G. Njiri, N. Beganovic, M. H. Do, D. Söffker, Consideration of lifetime and fatigue load in wind turbine control, Renew. Energy., 131 (2019), 818–828. https://doi.org/10.1016/j.renene.2018.07.109 doi: 10.1016/j.renene.2018.07.109
[2]	M. Ucar, M. Hmedi, E. Uzunoglu, E. Oguz, Fatigue load evaluation of multiple floating wind turbine systems, Ocean Eng., 330 (2025), 121101. https://doi.org/10.1016/j.oceaneng.2025.121101 doi: 10.1016/j.oceaneng.2025.121101
[3]	L. Fu, J. Liu, Y. Gao, Y. Zhou, F. Xu, X. Deng, Coordinative optimization for wind farms considering improved fatigue load index, Int. J. Elec. Power, 162 (2024), 110282. https://doi.org/10.1016/j.ijepes.2024.110282 doi: 10.1016/j.ijepes.2024.110282
[4]	L. Qi, M. Zhao, S. Wu, X. Zhang, P. Meng, Y. Zhao, et al., Adaptive torque feed-forward control for wind turbine MPPT considering predicted wind speed characteristics, Int. J. Elec. Power, 167 (2025), 110598. https://doi.org/10.1016/j.ijepes.2025.110598
[5]	Y. Wang, Y. Guo, D. Zhang, H. Liu, R. Song, Analysis and mitigation of the drive train fatigue load for wind turbine with inertial control, Int. J. Elec. Power, 136 (2022), 107698. https://doi.org/10.1016/j.ijepes.2021.107698 doi: 10.1016/j.ijepes.2021.107698
[6]	A. Safaeinejad, M. Rahimi, D. Zhou, F. Blaabjerg, A. sensorless active control approach to mitigate fatigue loads arising from the torsional and blade edgewise vibrations in PMSG-based wind turbine system, Int. J. Elec. Power, 155 (2024), 109525. https://doi.org/10.1016/j.ijepes.2023.109525 doi: 10.1016/j.ijepes.2023.109525
[7]	Z. Li, S. Tian, Y. Zhang, H. Li, M. Lu, Active control of drive chain torsional vibration for DFIG-based wind turbine, Energies, 12 (2019), 1744. https://doi.org/10.3390/en12091744 doi: 10.3390/en12091744
[8]	M. Rahimi, A. Beiki, Efficient modification of the control system in PMSG‐based wind turbine for improvement of the wind turbine dynamic response and suppression of torsional oscillations, Int. T. Electr. Energy, 28 (2018), e2578. https://doi.org/10.1002/etep.2578 doi: 10.1002/etep.2578
[9]	A. Beiki, M. Rahimi, An efficient sensorless approach for energy conversion enhancement and damping response improvement in permanent magnet synchronous generator (PMSG) based wind turbines, Int. T. Electr. Energy, 29 (2019), e2684. https://doi.org/10.1002/etep.2684 doi: 10.1002/etep.2684
[10]	R. Rocha, A sensorless control for a variable speed wind turbine operating at partial load, Renew. Energy, 36 (2011), 132–141. https://doi.org/10.1016/j.renene.2010.06.008 doi: 10.1016/j.renene.2010.06.008
[11]	Y. Wang, Y. Guo, W. Xu, Impact mechanism of frequency response on wind turbine fatigue load, J. Renew. Sustain. Ener., 15 (2023). https://doi.org/10.1063/5.0132363 doi: 10.1063/5.0132363
[12]	A. Cetrini, F. Cianetti, M. L. Corradini, G. Ippoliti, G. Orlando, On-line fatigue alleviation for wind turbines by a robust control approach, Int. J. Elec. Power, 109 (2019), 384–394. https://doi.org/10.1016/j.ijepes.2019.02.011 doi: 10.1016/j.ijepes.2019.02.011
[13]	J. A. Collins, Failure of materials in mechanical design: Analysis, prediction, prevention, John Wiley & Sons, 1993.
[14]	X. Jin, W. Tan, Y. Zou, Z. Wang, Active disturbance rejection control for wind turbine fatigue load, Energies, 15 (2022), 6178. https://doi.org/10.3390/en15176178 doi: 10.3390/en15176178
[15]	A. Safaeinejad, M. Rahimi, D. Zhou, F. Blaabjerg, An efficient power control strategy for active mitigation of blade in‐plane fatigue loading in PMSG‐based wind turbines, IET Renew. Power Gen., 18 (2024), 261–282. https://doi.org/10.1049/rpg2.12923 doi: 10.1049/rpg2.12923
[16]	Q. Yao, Y. Hu, T. Zhao, Y. Guan, Z. Luo, J. Liu, Fatigue load suppression during active power control process in wind farm using dynamic-local-reference DMPC, Renew. Energy, 183 (2022), 423–434. https://doi.org/10.1016/j.renene.2021.10.069 doi: 10.1016/j.renene.2021.10.069
[17]	L. Ren, C. Mao, Z. Song, F. Liu, Study on active disturbance rejection control with actuator saturation to reduce the load of a driving chain in wind turbines, Renew. Energy, 133 (2019), 268–274. https://doi.org/10.1016/j.renene.2018.10.041 doi: 10.1016/j.renene.2018.10.041
[18]	H. Wang, Y. Liu, X. Wang, G. Guo, L. Wang, Dynamic synthetic inertial control method of wind turbines considering fatigue load, Front. Energ. Res., 10 (2023), 1067896. https://doi.org/10.3389/fenrg.2022.1067896 doi: 10.3389/fenrg.2022.1067896
[19]	J. Gallego-Calderon, A. Natarajan, Assessment of wind turbine drive-train fatigue loads under torsional excitation, Eng. Struct., 103 (2015), 189–202. https://doi.org/10.1016/j.engstruct.2015.09.008 doi: 10.1016/j.engstruct.2015.09.008
[20]	M. Ganesh, J. H. Jeong, A lightweight adaptive torque control of PMSG-based offshore wind turbines using a finite-step incremental search strategy for region-Ⅲ operation under variable air density conditions, Ocean Eng., 352 (2026), 124377. https://doi.org/10.1016/j.oceaneng.2026.124377 doi: 10.1016/j.oceaneng.2026.124377
[21]	A. Sambas, A. Mohammadzadeh, S. Vaidyanathan, A. F. M. Ayob, A. Aziz, M. A. Mohamed, et al., Investigation of chaotic behavior and adaptive type-2 fuzzy controller approach for Permanent Magnet Synchronous Generator (PMSG) wind turbine system, AIMS Math., 8 (2023), 5670–5686. https://doi.org/10.3934/math.2023285
[22]	A. K. Alsharidi, S. Rashid, S. K. Elagan, Short-memory discrete fractional difference equation wind turbine model and its inferential control of a chaotic permanent magnet synchronous transformer in time-scale analysis, AIMS Math., 8 (2023), 19097–19120. https://doi.org/10.3934/math.2023975
[23]	H. Polinder, F. F. A. Van der Pijl, G. J. De Vilder, P. J. Tavner, Comparison of direct-drive and geared generator concepts for wind turbines, IEEE T. Energy Conver., 21 (2006), 725–733. https://doi.org/10.1109/TEC.2006.875476 doi: 10.1109/TEC.2006.875476
[24]	E. Gauterin, P. Kammerer, M. Kühn, H. Schulte, Effective wind speed estimation: Comparison between Kalman filter and Takagi–Sugeno observer techniques, ISA T., 62 (2016), 60–72. https://doi.org/10.1016/j.isatra.2015.11.016 doi: 10.1016/j.isatra.2015.11.016
[25]	R. Rocha, A sensorless control for a variable speed wind turbine operating at partial load, Renew. Energy, 36 (2011), 132–141. https://doi.org/10.1016/j.renene.2010.06.008 doi: 10.1016/j.renene.2010.06.008
[26]	O. Barambones, Robust wind speed estimation and control of variable speed wind turbines, Asian J. Control, 21 (2019), 856–867. https://doi.org/10.1002/asjc.1779 doi: 10.1002/asjc.1779
[27]	F. Golnary, K. T. Tse, Novel sensorless fault-tolerant pitch control of a horizontal axis wind turbine with a new hybrid approach for effective wind velocity estimation, Renew. Energy, 179 (2021), 1291–1315. https://doi.org/10.1016/j.renene.2021.07.112 doi: 10.1016/j.renene.2021.07.112
[28]	J. Zhao, L. Mili, A theoretical framework of robust H-infinity unscented Kalman filter and its application to power system dynamic state estimation, IEEE T. Signal Proces., 67 (2019), 2734–2746. https://doi.org/10.1109/TSP.2019.2908910 doi: 10.1109/TSP.2019.2908910
[29]	W. Xu, G. Zong, B. Niu, H. Wang, X. Zhao, Event-based fuzzy adaptive boundary Taylor decoupling control for parabolic PDE cascade systems: a novel nonlinear filters approach, Fuzzy Set. Syst., 542 (2026), 109945. https://doi.org/10.1016/j.fss.2026.109945 doi: 10.1016/j.fss.2026.109945
[30]	W. Zhang, X. Zhao, B. Niu, G. Zong, Integral barrier Lyapunov functions-based adaptive fuzzy event-triggered fault tolerant control for PDE-ODE cascade systems with state constraints: W. Zhang et al., Nonlinear Dynam., 114 (2026), 229. https://doi.org/10.1007/s11071-025-12081-4 doi: 10.1007/s11071-025-12081-4
[31]	M. Lara, F. Vázquez, I. Sandua-Fernandez, J. Garrido, Adaptive active generator torque controller design using multi-objective optimization for tower lateral load reduction in monopile offshore wind turbines, IEEE Access, 11 (2023), 115894–115910. https://doi.org/10.1109/ACCESS.2023.3325840 doi: 10.1109/ACCESS.2023.3325840
[32]	B. Liu, Q. Huang, L. Xu, W. Hu, A nonlinear drivetrain torsional oscillation damper for WTGs: Robust rejection of large disturbances with balanced noise immunity, IEEE T. Sustain. Energ., 17 (2025), 1348–1363. https://doi.org/10.1109/TSTE.2025.3614712 doi: 10.1109/TSTE.2025.3614712
[33]	X. Li, W. Wang, F. Fang, J. Liu, Z. Chen, Improving active power regulation for wind turbine by phase leading cascaded error-based active disturbance rejection control and multi-objective optimization, Renew. Energy, 243 (2025), 122629. https://doi.org/10.1016/j.renene.2025.122629 doi: 10.1016/j.renene.2025.122629
[34]	S. Cheng, Y. Gao, J. Liu, C. Guo, F. Xu, L. Fu, An optimal control strategy considering fatigue load suppression for wind turbines with soft switch multiple model predictive control based on membership functions, Energies, 18 (2025), 4695. https://doi.org/10.3390/en18174695 doi: 10.3390/en18174695
[35]	Y. Wang, S. Zhu, R. Deng, B. Yang, P. Wang, S. Gu, Model predictive control of wind turbine based on deep-dive holistic observer of tower top IMU, Appl. Energ., 392 (2025), 125996. https://doi.org/10.1016/j.apenergy.2025.125996 doi: 10.1016/j.apenergy.2025.125996
[36]	Z. Lin, Z. Chen, J. Liu, Q. Wu, Coordinated mechanical loads and power optimization of wind energy conversion systems with variable-weight model predictive control strategy, Appl. Energ., 236 (2019), 307–317. https://doi.org/10.1016/j.apenergy.2018.11.089 doi: 10.1016/j.apenergy.2018.11.089
[37]	Q. Yao, Y. Hu, H. Deng, Z. Luo, J. Liu, Two-degree-of-freedom active power control of megawatt wind turbine considering fatigue load optimization, Renew. Energy, 162 (2020), 2096–2112. https://doi.org/10.1016/j.renene.2020.09.137 doi: 10.1016/j.renene.2020.09.137
[38]	A. Safaeinejad, M. Rahimi, D. Zhou, F. Blaabjerg, A sensorless active control approach to mitigate fatigue loads arising from the torsional and blade edgewise vibrations in PMSG-based wind turbine system, Int. J. Elec. Power, 155 (2024), 109525. https://doi.org/10.1016/j.ijepes.2023.109525 doi: 10.1016/j.ijepes.2023.109525
[39]	M. Ganesh, S. R. Lee, J. H. Jeong, Y. H. Joo, An improved direct predictive speed control for three-level NPC converter fed PMSG-based offshore wind turbine system with minimum computation, Ocean Eng., 314 (2024), 119705. https://doi.org/10.1016/j.oceaneng.2024.119705 doi: 10.1016/j.oceaneng.2024.119705
[40]	M. Nasiri, J. Milimonfared, S. H. Fathi, A review of low-voltage ride-through enhancement methods for permanent magnet synchronous generator based wind turbines, Renew. Sust. Energ. Rev., 47 (2015), 399–415. https://doi.org/10.1016/j.rser.2015.03.079 doi: 10.1016/j.rser.2015.03.079
[41]	A. A. Basheer, J. W. Park, J. H. Jeong, Robust power extraction in offshore permanent magnet vernier generator wind turbines using noise-resilient wind forecasting and anti-chattering control, Control Eng. Pract., 168 (2026), 106695. https://doi.org/10.1016/j.conengprac.2025.106695 doi: 10.1016/j.conengprac.2025.106695
[42]	S. J. Julier, J. K. Uhlmann, New extension of the Kalman filter to nonlinear systems, Proc. SPIE 3068, Signal processing, sensor fusion, and target recognition Ⅵ, 1997. https://doi.org/10.1117/12.280797
[43]	H. K. Khalil, J. W. Grizzle, Nonlinear systems, Vol. 3. Upper Saddle River, NJ: Prentice Hall, 2002.
[44]	J. A. Moreno, M. Osorio, Strict Lyapunov functions for the super-twisting algorithm, IEEE T. Automat. Contr., 57 (2012), 1035–1040. https://doi.org/10.1109/TAC.2012.2186179 doi: 10.1109/TAC.2012.2186179
[45]	H. J. Sutherland, On the fatigue analysis of wind turbines, Technical Report, Sandia National Labs., US, 1999. Available from: http://www.sars-expertcom.gov.hk/english/reports/reports.html.

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