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Individual Pitch Angle Control of a Variable Speed Wind Turbine Using Adaptive Fractional Order Non-Singular Fast Terminal Sliding Mode Control

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Abstract

Pitch angle control strategy has been applied to mitigate the influence of mechanical load and also output power control at above-rated wind speeds. In this paper, a wind turbine is modeled based on simplified two-mass model and an adaptive fractional-order non-singular fast terminal sliding mode controller (AFO-NFTSMC) is proposed based on individual pitch control strategy to control pitch angle of wind turbine against uncertainties and external disturbances. To do this, the single-blade approach is used and the wind turbine is divided into aerodynamics and mechanical subsystems and governing equations of each subsystem are derived. By designing and applying the AFO-NFTSMC to the two-mass model, system behavior is observed and simulated in terms of step and turbulent wind speed inputs. In addition, to verify the validity of the AFO-NFTSMC, the proposed controller is implemented in the FAST environment in which the wind speed profiles are generated using TurbSim. In order to analyze the environmental effects on the dynamic behavior of the system, the controller performance is explored in presence of parametric uncertainties. Simulation results reveal the priority and high-precision performance of the controller compared to conventional adaptive and adaptive sliding mode controller. Moreover, rotor speed tracking error is evaluated and demonstrated through different criteria.

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References

  1. The World Wind Energy Association (2016). WWEA Half-year Report 2016. The 15th WWEC2016: Tokyo; October–November.

  2. Carlin, P. W., Laxson, A. S., & Muljadi, E. B. (2003). The history and state of the art of variable-speed wind turbine technology. Wind Energy: An International Journal for Progress and Applications in Wind Power Conversion Technology, 6(2), 129–159.

    Article  Google Scholar 

  3. Fazlollahi, V., & Taghizadeh, M. (2016). Modeling and design of dynamic state feedback controller with wind speed estimator, in variable speed wind turbines. Modares Mechanical Engineering, 16(4), 361–371.

    Google Scholar 

  4. Gang, X. (2011). Research on application of fuzzy PID in collective pitch control system. In IEEE 2011 International Conference on Control, Automation and Systems Engineering (CASE) (pp. 1–4).

  5. Bossanyi, E. A. (2003). Individual blade pitch control for load reduction. Wind Energy: An International Journal for Progress and Applications in Wind Power Conversion Technology, 6(2), 119–128.

    Article  Google Scholar 

  6. Zhang, Y., Chen, Z., Cheng, M., & Zhang, J. (2011). Mitigation of fatigue loads using individual pitch control of wind turbines based on FAST. In 2011 46th International Universities' Power Engineering Conference (UPEC) (pp. 1–6) VDE.

  7. Yang, Z., Li, Y., & Seem, J. E. (2011). Individual pitch control for wind turbine load reduction including wake modeling. Wind Engineering, 35(6), 715–738.

    Article  Google Scholar 

  8. Larsen, A. J., & Mogensen, T. S. (2006). Individuel pitch regulering af vindmølle (Master's thesis, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark).

  9. Friis, J., Nielsen, E., Bonding, J., Adegas, F. D., Stoustrup, J., & Odgaard, P. F. (2011, December). Repetitive model predictive approach to individual pitch control of wind turbines. In IEEE 2011 50th IEEE Conference on Decision and Control and European Control Conference (pp. 3664–3670).

  10. Jespersen, S., & Oldenbürger, R. (2016). Individual Pitch Control for Load Mitigation. Group, 2017.

  11. Leithead, W. E., Neilson, V., Dominguez, S., & Dutka, A. (2009). A novel approach to structural load control using intelligent actuators. In IEEE 2009 17th mediterranean conference on control and automation (pp. 1257–1262).

  12. Leithead, W. E., Neilson, V., & Dominguez, S. (2009). Alleviation of unbalanced rotor loads by single blade controllers.

  13. Han, Y., & Leithead, W. E. (2014). Combined wind turbine fatigue and ultimate load reduction by individual blade control. Journal of Physics: Conference Series, 524(1), 012062.

    Google Scholar 

  14. Yi, H., & Leithead, W. E. (2012). Alleviation of extreme blade loads by individual blade control during normal wind turbine operation. In Proceedings of EWEA.

  15. Sørensen, K. L., Galeazzi, R., Odgaard, P. F., Niemann, H., & Poulsen, N. K. (2014). Adaptive passivity based individual pitch control for wind turbines in the full load region. In IEEE 2014 American Control Conference (pp. 554–559).

  16. Mazare, M., & Taghizadeh, M. (2019). Adaptive backstepping robust control of a 3-[P2(US)] parallel robot on optimal trajectory. International Robotics and Automation Journal, 5(3), 101–110.

    Article  Google Scholar 

  17. Mazare, M., Taghizadeh, M., & Aghaeinezhad, S. M. (2019). Individual pitch angle robust control of a variable speed wind turbine to mitigate mechanical loads. Modares Mechanical Engineering, 19(4), 937–945.

    Google Scholar 

  18. Mokhtari, M., Taghizadeh, M., & Mazare, M. (2019). Optimal adaptive high-order super twisting sliding mode control of a lower limb exoskeleton robot. Modares Mechanical Engineering, 18, 117–125.

    Google Scholar 

  19. Mazare, M., Taghizadeh, M., & Pourgholi, M. (2018). Nonlinear model predictive multivariable control for trajectory tracking of a type of delta—parallel robot. Latin American Journal of Solids and Structures, 14(6), 1040–1063.

    Google Scholar 

  20. Mokhtari, M., Taghizadeh, M., & Mazare, M. (2020). Hybrid adaptive robust control based on CPG and ZMP for a lower limb exoskeleton. Robotica. https://doi.org/10.1017/S0263574720000260

  21. Mazare, M., & Najafi, M. R. (2016). Adaptive control of a 3-PUU parallel robot on optimized trajectories generated by harmony search algorithm. Modares Mechanical Engineering, 16(11), 187–198.

    Google Scholar 

  22. Mazare, M., Taghizadeh, M., & Kazemi, M. G. (2018). Optimal hybrid scheme of dynamic neural network and PID controller based on harmony search algorithm to control a PWM-driven pneumatic actuator position. Journal of Vibration and Control, 24(16), 3538–3554.

    Article  MathSciNet  Google Scholar 

  23. Yang, T., et al. (2019). Neural network-based adaptive antiswing control of an underactuated ship-mounted crane with roll motions and input dead zones. IEEE Transactions on Neural Networks and Learning Systems, 31(3), 901–914.

    Article  MathSciNet  Google Scholar 

  24. Sun, N., et al. (2019). Adaptive control for pneumatic artificial muscle systems with parametric uncertainties and unidirectional input constraints. IEEE Transactions on Industrial Informatics, 16(2), 969–979.

    Article  Google Scholar 

  25. Jonkman, J., Butterfield, S., Musial, W., & Scott, G. (2009). Definition of a 5-MW reference wind turbine for offshore system development (No. NREL/TP-500-38060). National Renewable Energy Lab.(NREL), Golden, CO (United States).

  26. Podlubny, I. (1998). Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Amsterdam: Elsevier.

    MATH  Google Scholar 

  27. Li, C., & Deng, W. (2007). Remarks on fractional derivatives. Applied Mathematics and Computation, 187(2), 777–784.

    Article  MathSciNet  Google Scholar 

  28. Li, Y., Chen, Y., & Podlubny, I. (2010). Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability. Computers and Mathematics with Applications, 59(5), 1810–1821.

    Article  MathSciNet  Google Scholar 

  29. Aguila-Camacho, N., Duarte-Mermoud, M. A., & Gallegos, J. A. (2014). Lyapunov functions for fractional order systems. Communications in Nonlinear Science and Numerical Simulation, 19(9), 2951–2957.

    Article  MathSciNet  Google Scholar 

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Correspondence to Mostafa Taghizadeh.

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Aghaeinezhad, S.M., Taghizadeh, M., Mazare, M. et al. Individual Pitch Angle Control of a Variable Speed Wind Turbine Using Adaptive Fractional Order Non-Singular Fast Terminal Sliding Mode Control. Int. J. Precis. Eng. Manuf. 22, 511–522 (2021). https://doi.org/10.1007/s12541-020-00439-0

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  • DOI: https://doi.org/10.1007/s12541-020-00439-0

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