# Self-scheduled H#INF# Control of a Wind Turbine - A Real Time Implementation

### Florin Sebastian Tudor, Dumitru Popescu, Dan Stefanoiu

#### Abstract

This paper is concerned with the design of robust gain-scheduled controllers with guaranteed H∞ performance for a horizontal axis wind turbine (HAWT) with variable-speed and fixed-pitch. The control problem in terms of Linear Parameter-Varying (LPV) plants is stated and the theoretical background of the design method is given. Due to some interesting properties outlined in this paper, the synthesis problem is reduced to solving off-line a finite-dimensional set of Linear Matrix Inequalities (LMIs), making the controller suited for real-time applications. The computed LPV controller focuses on multiple objectives such as mechanical fatigue reduction, speed regulation and mode stabilization with simultaneously maximizing energy capture. The performances obtained through this control method are discussed and presented by means of a set of simulations. A real-time control algorithm for the large-scale wind turbines is also proposed.

#### References

- Apkarian, P. and Adams, R. (1998). Advanced gainscheduling techniques for uncertain systems. IEEE Transactions on Control Systems Technology 6 (1), 21-32.
- Apkarian, P., Gahinet, P., Becker, G. (1995). Self-scheduled H8 control of linear parameter-varying systems: a design example. Automatica 31(9), 1251-1261.
- Becker, G., Packard, A. (1994). Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback. System & Control Letters, 23 (205-215).
- Bianchi, F. D., De Battista, H., Mantz, R. J. (2007). Wind Turbine Control Systems. Principles, modelling and Gain Scheduling Design. Springer-Verlag, London.
- Burton, T., Sharpe, D., Jenkins, N., Bossanyi, E. (2001). Wind Energy Handbook. John Wiley & Sons, LTD.
- Jain, P. (2011). Wind Energy Engineering, McGraw Hill, U.S.A.
- Lescher, F. (2006). Commande LPV d'une eolienne a vitesse variable pour l'optimisation energetique et la reduction de la fatigue mecanique. Ph.D. thesis, Lille, France.
- Manwell, J. F., McGowan, J. G., Rogers, A. L. (2009). Wind Energy Explained. Theory, design and application. 2nd edition. John Wiley & Sons.
- Packard, A. (1994). Gain scheduled via linear fractional transformations. Systems and Control Letters 22(2), 79-92.
- Pao, L. Y., Johnson, K. E. (2011). Control of Wind Turbines-Approaches, Challenges and Recent Developments, IEEE Control Systems Magazine, 4, 44-62.
- Scherer, C.(1995). Mixed H2 / H8 control, Trends in Control: A European Perspective, Special Contribution to the ECC'95 ed.
- Scorletti, G., El Gahoui, L. (1998). Improved LMI conditions for gain scheduling and related control problems. International Journal of Robust and Nonlinear Control 8(10), 845-877.
- Tóth, R. (2010). Modeling and Identification of Linear Parameter-Varying Systems. Springer - Verlag, Berlin.
- Tudor, F. S. (2011). Modelling and control of a wind turbine. Graduation thesis, Politehnica University of Bucharest.
- Wu, F. (2001). A generalized LPV system analysis and control synthesis framework. International Journal of Control 74(7), 745-759.
- Wu, F., Yang, X., Packard, A., and Becker, G. (1996). Induced L2-norm control for LPV systems with bounded parameter variations rates. International Journal of Nonlinear and Robust Control, 6(9-10), 983-998.
- Zhou, K., Doyle, J., and Glover, K. (1996). Robust and Optimal Control. Prentice-Hall, Englewood Cliffs, USA.

#### Paper Citation

#### in Harvard Style

Sebastian Tudor F., Popescu D. and Stefanoiu D. (2012). **Self-scheduled H#INF# Control of a Wind Turbine - A Real Time Implementation** . In *Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-8565-21-1, pages 402-411. DOI: 10.5220/0004045904020411

#### in Bibtex Style

@conference{icinco12,

author={Florin Sebastian Tudor and Dumitru Popescu and Dan Stefanoiu},

title={Self-scheduled H#INF# Control of a Wind Turbine - A Real Time Implementation},

booktitle={Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2012},

pages={402-411},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004045904020411},

isbn={978-989-8565-21-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - Self-scheduled H#INF# Control of a Wind Turbine - A Real Time Implementation

SN - 978-989-8565-21-1

AU - Sebastian Tudor F.

AU - Popescu D.

AU - Stefanoiu D.

PY - 2012

SP - 402

EP - 411

DO - 10.5220/0004045904020411