Further Results on Modeling, Analysis, and Control Synthesis for Offshore Wind Turbine Systems

  • Hamid Reza KarimiEmail author
  • Tore Bakka
Part of the Advances in Industrial Control book series (AIC)


Renewable energy is a hot topic all over the world. Nowadays, there are several sustainable renewable power solutions out there; hydro, wind, solar, wave, and biomass to name a few. Most countries have a tendency to want to become greener. In the past, all new wind parks were installed onshore. During the last decade, more and more wind parks were installed offshore, in shallow water. This chapter investigates a comparative study on the modeling, analysis, and control synthesis for the offshore wind turbine systems. More specifically, an \( {\mathcal{H}}_{\infty } \) static output-feedback control design with constrained information is designed. Constrained information indicates that a remarkable performance can be achieved by considering less information in the control loop or in the case of sensor failures in practice. Therefore, a special structure is imposed on the static output-feedback gain matrix in the contest of constrained information. A practical use of such an approach is to design a decentralized controller for a wind turbine. This will also benefit the controller in such a way that it is more tolerant to sensor failure. Furthermore, the model under consideration is obtained by using the wind turbine simulation software FAST. Using Linear Matrix Inequality \( ({\mathcal{L}\mathcal{M}\mathcal{I}}) \) method, some sufficient conditions to design an \( {\mathcal{H}}_{\infty } \) controller are provided. Finally, a comprehensive simulation study will be carried out to illustrate the effectiveness of the proposed methodology for different cases of the control gain structures.


Wind turbine system Control design Modeling Simulation LMI 


\( \beta \)

Blade pitch angle

\( C_{p} \)

Power coefficient

\( F_{t} \)

Thrust force

\( \lambda \)


\( P_{a} \)

Extracted electrical power from the wind

\( \omega_{r} \)

Rotational speed of the rotor


Rotor radius

\( \rho \)

Air density

\( T_{a} \)

Aerodynamic torque

\( \upsilon \)

Wind speed acting on the blades


  1. 1.
    Abdin ES, Xu W (2000) Control design and dynamic performance analysis of a wind turbine induction generator unit. IEEE Trans Energy Convers 15(1):91–96CrossRefGoogle Scholar
  2. 2.
    AlHamaydeh M, Hussain S (2011) Optimized frequency-based foundation design for wind turbine towers utilizing soil-structure interaction. J Franklin Inst 348:1470–1487Google Scholar
  3. 3.
    Bakka T, Karimi HR (2012) Robust \( H_{\infty } \) dynamic output-feedback control synthesis with pole placement constraints for offshore wind turbine systems. Math Probl Eng Article ID 616507Google Scholar
  4. 4.
    Bakka T, Karimi HR (2012) Multi-objective control design with pole placement constraints for wind turbine systems. In: Advances on analysis and control of vibrations—theory and applications. INTECH 2012 ISBN 978-953-51-0699-9, p 179–194Google Scholar
  5. 5.
    Bakka T, Karimi HR (2013) \( H_{\infty } \) Static output-feedback control design with constrained information for offshore wind turbine system. J Franklin Inst 350(8):2244–2260Google Scholar
  6. 6.
    Bakka T, Karimi HR, Duffie NA (2012) Gain scheduling for output \( H_{\infty } \) control of offshore wind turbine. In: Proceedings of the twenty-second international offshore and polar engineering conference, pp 496–501Google Scholar
  7. 7.
    Bakka T, Karimi HR, Christiansen S (2014) Linear parameter-varying modeling and control of an offshore wind turbine with constrained information. IET Control Theory Appl 8(1):22–29CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Bottasso CL, Croce A (2009) Cp-Lambda user manual. Dipartimento di Ingnegneria Aerospaziale, Politecnico di Milano, Italy Google Scholar
  9. 9.
    Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) linear matrix inequalities in systems and control theory. SIAM Studies in Applied Mathematics, vol 15, SIAM, Philadelphia Google Scholar
  10. 10.
    Eggleston DM, Stoddard FS (1987) Wind turbine engineering design. Van Nostrand Reinhold, New YorkGoogle Scholar
  11. 11.
    Jonkman BJ (2009) TurbSim users guide: version 1.50. Technical report NREL/EL-500-46198, National Renewable Energy LaboratoryGoogle Scholar
  12. 12.
    Jonkman J (2010) Definition of the floating system for phase IV of OC3. Technical report NREL/TP-500-47535, National Renewable Energy LaboratoryGoogle Scholar
  13. 13.
    Jonkman J, Buhl ML Jr (2005) FAST users guide. Technical report NREL/EL-500-38230, National Renewable Energy LaboratoryGoogle Scholar
  14. 14.
    Jonkman J, Butterfield S, Musial W, Scott G (2009) Definition of a 5-MW reference wind turbine for offshore system development. Technical report NREL/TP-500-38060, National Renewable Energy LaboratoryGoogle Scholar
  15. 15.
    Kamal E, Aitouche A, Ghorbani R, Bayrat M (2012) Robust fyzzy fault-tolerant control of wind energy conversion systems subjected to sensor faults. IEEE Trans Sustain Energy 3(2):231–241CrossRefGoogle Scholar
  16. 16.
    Larsen TJ (2009) How 2 HAWC2, the user`s manual, Risø-R-1597(ver. 3–9)(EN)Google Scholar
  17. 17.
    Lfberg J (2004) YALMIP a toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD conference, Taipei, TaiwanGoogle Scholar
  18. 18.
    Li D, Song Y, Cai W, Li P, Karimi HR (2014) Wind turbine pitch control and load mitigation using an \( L_{1} \) adaptive approach. Math Probl Eng 2014(Article ID 719803):11Google Scholar
  19. 19.
    Muyeen SM, Ali MH, Takahashi R, Murata T, Tamura J, Tomaki Y, Sakahara A, Sasano E (2007) Comparative study on transient stability analysis of wind turbine generator system using different drive train models. IET Renew Power Gener 1(2):131–141CrossRefGoogle Scholar
  20. 20.
    Rubió-Massegú J, Rossell JM, Karimi HR, Palacios-Quiñonero F (2013) Static output-feedback control under information structure constraints. Automatica 49(1):313–316CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Si Y, Karimi HR, Gao H (2013) Modeling and parameter analysis of the OC3-Hywind floating wind turbine with a tuned mass damper in nacelle. J Appl Math 2013(Article ID 679071):10Google Scholar
  22. 22.
    Si Y, Karimi HR, Gao H (2014) Modelling and optimization of a passive structural control design for a spar-type floating wind turbine. Eng Struct 69:168–182CrossRefGoogle Scholar
  23. 23.
    Sloth C, Esbensen T, Stoustrup J (2011) Robust and fault-tolerant linear parameter-varying control of wind turbines. Mechatronics 21(4):645–659CrossRefGoogle Scholar
  24. 24.
    Yin S, Wang G, Karimi HR Data-driven design of robust fault detection system for wind turbines. Mechatronics. doi:  10.1016/j.mechatronics.2013.11.009
  25. 25.
    Zečević AI, Šiljak DD (2004) Design of robust static output feedback for large-scale systems. IEEE Trans Autom Control 11:2040–2044Google Scholar
  26. 26.
    Zečević AI, Šiljak DD (2008) Control design with arbitrary information structure constraints. Automatica 44(10):2642–2647CrossRefzbMATHMathSciNetGoogle Scholar
  27. 27.
    Zečević AI, Šiljak DD (2010) Control of complex systems: structural constraints and uncertainty. Springer, BerlinGoogle Scholar
  28. 28.
    Zhang F, Leithead WE, Anaya-Lara O (2011) Wind turbine control design to enhance the fault ride-through capability. In: IET conference on renewable power generation, pp 1–6Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Engineering, Faculty of Engineering and ScienceUniversity of AgderGrimstadNorway

Personalised recommendations