Control of tension leg platforms with multiple time-varying delays in offshore floating wind turbines based on LMI method

Abstract

Abstract: In this paper, analysis and control of tension leg platforms (TLP) has been discussed, which is one of the most common offshore floating wind turbine systems. The most important subject about installation of these turbines is how to control and float them on the water. In order to design the controller for the system, first, a non-linear function will be defined as a Lyapunov candidate, then we will prove that TLP systems with multiple time-varying delays, in the presence of foreign force is stable and by linear matrix inequalities (LMI) tool, the controller will be designed. Finally, by simulation in Matlab-Simulink, we show that all of 

Keywords


[1] G. R. Fulton, D.J. Malcolm, H. Elwany, W. Stewart, E. Moroz and H. Dempster, Semi-submersible platform and anchor foundation systems for wind turbine support, National Laboratory of U.S Department of Energy, 2007.
[2] M. Karimirad, Stochastic Dynamic Response Analysis of Spar-Type Wind Turbines with Catenary or Taut Mooring Systems, Ph.D. Thesis, Norwegian University o Science and Technology, 2011.
[3] O. J. Emmerhoff and P. D. Sclavounos, “The slow drift motion of arrays of vertical cylinders,” Journal of Fluid Mechanics, vol. 242, pp.31–50, 1992.
[4] M. Reiszadeh and S. Motaha, “The wind energy potential in the coasts of persian gulf used in design and analysis of a horizontal axis wind turbine,” World Renewable Congress, vol. 15, pp. 4058-4065, 2011.
[5] A. R. Henderson and K. Argyriadis, “Offshore wind turbines on TLPs - Assessment of floating support structures for offhsore wind farms in german waters,” 10th German Wind Energy Conference Bremen, 2010.
[6] T. Perez and T. I. Fossen, “Practical aspects of frequency-domain identification of dynamic models of marine structures from hydrodynamic data,” Ocean Engineering, vol. 38, no. 2, pp. 426–435, 2011.
[7] W. Koo and M.H. Kim, “Freely floating-body simulation by a 2D fully nonlinear numerical wave tank,” Ocean Engineering, vol. 31, no. 16, pp. 2011– 2046, 2004.
[8] J. Jonkman and D. Matha, Quantitative Comparison of the Responses of Three Floating Platforms, National Renewable Energy Laboratory of U.S, Department of Energy, 2010.
[9] T. Shikha, S. Bhatti and D. P. Kothari, “Aspects of technological development of wind turbines,” Journal of Energy Engineering, vol. 129, no. 3, pp. 81–95, 2003.
[10] J. Jonkman, S. Butterfield, W. Musial and G. Scott, Definition of a 5-MW reference wind turbine for offshore system development, National Laboratory of U.S Department of Energy, 2009.
[11] S. Mobayen, “Fast terminal sliding mode controller design for nonlinear second-order systems with time-varying uncertainties,” Complexity, vol. 21, no. 2, pp 239–244, 2015.
[12] M. C. Pai, “Design of adaptive sliding mode controller for robust tracking and model following,” Journal of the Franklin Institute, vol. 347, no. 10, pp. 1837–1849, 2010.
[13] J. W. Lin, C. W. Huang, C. H. Shih and C. Y. Chen, “Fuzzy lyapunov stability analysis and NN modeling for tension leg platform systems,” Journal of Vibration and Control, vol. 17 no. 1, pp. 151-158, 2011.
[14] C. W. Chen, “Modeling, control, and stability analysis for time-delay TLP systems using the fuzzy Lyapunov method,” Neural Computating and Application, vol. 20, pp. 527-534, 2011.
[15] C. Y. Chen, J. W. Lin, W. I. Lee and C. W. Chen, “Fuzzy control for an oceanic structure: A case study in time-delay TLP system,” Journal of Vibration and Control, vol. 16, no. 1, pp. 147-160, 2010.
[16] C. W. Chen, “Delay independent criterion for multiple time-delay systems and its application in building structure control systems,” Journal of Vibration and Control, vol. 19, no. 3, pp. 395-414, 2013.
[17] C. W. Chen, “Applications of the fuzzy Lyapunov linear matrix inequality criterion to a chaotic structural system,” Journal of Vibration and Control, vol. 18, no. 13, pp. 1925-1938, 2012.
[18] فاطمه پیروزمند، نعمت­الله قهرمانی و محمدرضا عاروان، » طراحی کنترل­کننده پیش­بین مقاوم با استفاده از نامساوی‌های ماتریسی خطی برای سیستم کنترل وضعیت ماهواره«، مجله مهندسی برق دانشگاه تبریز، جلد 44، شماره 4، زمستان 93.
[19] H. Li, Y. Gao, L. Wu and H. K. Lam, “Fault detection for T-S fuzzy time-delay systems: Delta operator and input-output methods,” IEEE Transactions on Cybernetic, vol. 45, no. 2, pp. 229-241, 2015.
[20] J. An and G. Wen, “Improved stability criteria for time-varying delayed T–S fuzzy systems via delay partitioning approach,” Fuzzy Sets and Systems, vol. 185, no. 1, pp. 83–94, 2011.
[21] M. L. Lin and C. W. Chen, “Stability analysis of community and ecosystem hierarchies using the Lyapunov method,” Journal of Vibration and Control, vol. 17, no. 13, pp. 1930-193, 2010.
[22] C. W. Chen, “A review of intelligent algorithm approaches and neural-fuzzy stability criteria for time-delay tension leg platform systems,” Journal of Vibration and Control, vol. 20, no. 4, pp. 561-575, 2014.
[23] M. L. Lin and C. W. Chen, “Fuzzy neural modeling for n-degree ecosystems using the linear matrix inequality approach,” Journal of Vibration and Control, vol. 20, no. 1, pp. 82-93, 2014.
[24] C. Casanovas, Advanced Controls for Floating Wind Turbines, M.Sc. Thesis, Massachusetts Institute of Technology, 2014.
[25] C. W. Chen, “Stability conditions of fuzzy systems and its application to structural and mechanical systems,” Advances in Engineering Software, vol. 37. no. 9, pp. 624–629, 2006.
[26] L. A. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338–353, 1965.
[27] فاطمه منفرد، محمدحسین شفیعی و طاهره بینازاد، »طراحی کنترل­کننده ردیاب مقاوم برای یک روبات متحرک غیرهولونومیک دارای لغزش جانبی با روش‌های بازطراحی لیاپانوفی و  غیرخطی «، مجله مهندسی برق دانشگاه تبریز، جلد 54، شماره 5، زمستان 94.
[28] S. Mobayen, “An LMI-based robust tracker for uncertain linear systems with multiple time-varying delays using optimal composite nonlinear feedback technique,” Nonlinear Dynamics, vol. 80, no. 1, pp. 927-917, 2015.
[29] W. Assawinchaichote, E.K. Boukas, S.K. Nguang and P. Shi, “Hfuzzy state-feedback control design for nonlinear systems with D-stability constraints: an LMI approach,” Mathematics and Computers in Simulation, vol. 78, no. 4, pp. 514–531, 2008.
[30] X. Li and C. D. Souza, “Criteria for robust stability and stabilization of uncertain linear systems with state delay,” Automatica, vol. 33, no. 9, pp. 1657–1662, 1997.
[31] F. H. Wang, K. Tanaka and M. F. Griffin, “An approach to fuzzy control of nonlinear systems: stability and design issues,” IEEE Transactions on Fuzzy Systems, vol. 4, no. 1, pp. 14-23, 1996.
[32] F. H. Hsiao, C. W. Chen, Y. W. Liang, S. D. Xu and W. L. Chiang, “T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays,” IEEE Transactions on Circuits and Systems, vol. 52, no. 9, pp. 1883-1893, 2005.
[33] F. H. Hsiao, C. W. Chen, Y. H. Wu and W. L. Chiang, “Fuzzy controllers for nonlinear interconnected TMD systems with external force,” Journal of Chinease Institute of Engineering, vol. 28, no. 1, pp. 175-18, 2005.
[34] F. H. Hsiao, W. L. Chiang, C. W. Chen, S. D. Xu and S.L. Wu, “Application and robustness design of fuzzy controller for resonant and chaotic systems with external disturbance,” International  Journal of Uncertainity, Fuzziness and Knowledge-Based Systems, vol. 13, no. 3, 2005.
[35] F. H. Hsiao, J. D. Hwang, C. W. Chen and Z. R. Tsai, “Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 1, pp. 152 - 163, 2005.
[36] Z. Feng and J. Lam, “Integral partitioning approach to robust stabilization for uncertain distributed time-delay systems,” International Journal of Robust Nonlinear Control, vol. 26, no. 2, pp. 676–689, 2012.
[37] J. Lofberg, “YALMIP: A toolbox for modeling and optimization in MATLAB”, IEEE International symposium on Computer Aided Contol Systems, pp. 284-289, 2004.