Abstract
This paper deals with delayed sliding mode H∞ control for an offshore steel jacket platform subject to nonlinear self-excited wave force and external disturbance. By using both current and delayed states, a delayed sliding mode H∞ controller is designed to attenuate vibration of the offshore platform. It is observed through simulation results that the delayed sliding mode H∞ controller is capable of reducing the oscillation amplitudes of the offshore platform significantly. Moreover, compared with the delay-free sliding mode H∞ controller, the oscillation amplitudes of the offshore platform under the controllers are almost the same, while the control force required by the delayed sliding mode H∞ controller is less than that by the delay-free sliding mode H∞ controller.
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References
B.–L. Zhang, Q.–L. Han, and X.–M. Zhang, “Recent advances in vibration control of offshore platforms,” Nonlinear Dynamics, no. 89, no. 2, pp. 755–771, Jul. 2017.
M. J. Terro, M. S. Mahmoud, and M. Abdel–Rohman, “Multi–loop feedback control of offshore steel jacket platforms,” Computers & Structures, no. 70, no. 2, pp. 185–202, Jan. 1999.
B.–L. Zhang, Y.–J. Liu, Q.–L. Han, and G.–Y. Tang, “Optimal tracking control with feedforward compensation for offshore steel jacket platforms with active mass damper mechanisms,” Journal of Vibration and Control, vol. 22, no. 3, pp. 695–709, Feb. 2016.
B.–L. Zhang, Y.–J. Liu, H. Ma, and G.–Y. Tang, “Discrete feedforward and feedback optimal tracking control for offshore steel jacket platforms,” Ocean Engineering, vol. 91, pp. 371–378, Nov. 2014.
M. Luo and W. Q. Zhu, “Nonlinear stochastic optimal control of offshore platforms under wave loading,” Journal of Sound and Vibration, vol. 296, nos. 4–5, pp. 734–745, Oct. 2006.
H. J. Li, S.–L. James Hu, and C. Jakubiak, “H2 active vibration control for offshore platform subjected to wave loading,” Journal of Sound and Vibration, vol. 263, no. 4, pp. 709–724, Jun. 2003.
B.–L. Zhang, L. Ma, and Q.–L. Han, “Sliding mode H¥ con–trol for offshore steel jacket platforms subject to nonlinear self–excited wave force and external disturbance,” Nonlin–ear Analysis: Real World Applications, vol. 14, no. 1, pp. 163–178, Feb. 2013.
M. Zribi, N. Almutairi, M. Abdel–Rohman, and M. Terro, “Nonlinear and robust control schemes for offshore steel jacket platform,” Nonlinear Dynamics, vol. 35, no. 1, pp. 61–80, Jan. 2004.
D. H. Kim, “Neuro–control of fixed offshore structures un–der earthquake,” Engineering Structures, vol. 31, no. 2, pp. 517–522, Feb. 2009.
H. Li, J. Wang, L. Wu, H.–K. Lam, and Y. Gao, “Opti–mal guaranteed cost sliding–mode control of interval type–2 fuzzy time–delay systems,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 1, pp. 246–257, Jan. 2018.
H. Li, J. Wang, L. Wu, H. Du, and H. R. Karimi, “Adap–tive sliding mode control for Takagi–Sugeno fuzzy systems and its Applications,” IEEE Transactions on Fuzzy Sys–tems, vol. pp, no. 99, pp. 1–1, Mar. 2017.
Q. H. Ngo and K.–S. Hong, “Sliding–mode antisway con–trol of an offshore container crane,” IEEE/ASME Transac–tions on Mechatronics, vol. 17, no. 2, pp. 201–209, Apr. 2012.
J.Wang, Y. Gao, J. Qiu, and C. K. Ahn, “Sliding mode con–trol for non–linear systems by Takagi–Sugeno fuzzy model and delta operator approaches,” IET Control Theory & Ap–plications, vol. 11, no. 8, pp. 1205–1213, May 2017.
L. A. Tuan, Y. H. Joo, P. X. Duong, and L. Q. Tien, “Pa–rameter estimator integrated–sliding mode control of dual arm robots,” International Journal of Control, Automation and Systems, vol. 15, no. 6, pp. 2754–2763, Dec. 2017.
X. Ma, F. Sun, H. Li, and B. He, “Neural–network–based integral sliding–mode tracking control of second–order multi–agent systems with unmatched disturbances and completely unknown dynamics,” International Jour–nal of Control, Automation and Systems, vol. 15, no. 4, pp. 1925–1935, Aug. 2017.
A. Karami–Mollaee and H. Tirandaz, “Adaptive fuzzy fault tolerant control using dynamic sliding mode,” Interna–tional Journal of Control, Automation and Systems, vol. 16, no. X, pp. 1–8, 2018.
B.–L. Zhang, Q.–L. Han, X.–M. Zhang, and X. Yu, “Integral sliding mode control for offshore steel jacket platforms,” Journal of Sound and Vibration, vol. 331, no. 16, pp. 3271–3285, Aug. 2012.
B.–L. Zhang, Q.–L. Han, X.–M. Zhang, and X. Yu, “Slid–ing mode control with mixed current and delayed states for offshore steel jacket platforms,” IEEE Transactions on Control Systems Technology, vol. 22, no. 5, pp. 1769–1783, Sep. 2014.
S. Huang, M. Cai, and Z. Xiang, “Robust sampled–data H¥ control for offshore platforms subject to irregular wave forces and actuator saturation,” Nonlinear Dynamics, vol. 88, no. 4, pp. 1–17, Feb. 2017.
K. Sivaranjani, R. Rakkiyappan, S. Lakshmanan, and C. P. Lim, “Robust stochastic sampled–data control for offshore steel jacket platforms with non–linear perturbations,” IMA Journal of Mathematical Control and Information, vol. 34, no. 1, pp. 337–357, Mar. 2017.
X.–M. Zhang, Q.–L. Han, “Event–triggered H¥ control for a class of nonlinear networked control systems using novel integral inequalities,” International Journal of Robust and Nonlinear Control, vol. 27, no. 4, pp. 679–700, Mar. 2017.
W. He, G. Chen, Q.–L. Han, and F. Qian, “Network–based Leader–following consensus of nonlinear multi–agent sys–tems via distributed impulsive control,” Information Sci–ences, vol. 380, pp. 145–158, Feb. 2017.
D. Zhang, Z. Xu, H. R. Karimi, and Q.–G. Wang, “Dis–tributed filtering for wwitched linear systems with sensor networks in presence of packet dropouts and quantization,” IEEE Transactions on Circuits and Systems I: Regular Pa–pers, vol. 64, no. 10, pp. 2783–2796, May 2017.
Z.–H. Pang, G.–P. Liu, D. Zhou, and D. Sun, “Design and performance analysis of networked predictive control sys–tems based on input–output difference equation model,” In–ternational Journal of Control, Automation and Systems, no. 15, no. 1, pp. 416–426, Feb. 2017.
C. Peng, M.–R. Fei, E. Tian, and Y.–P. Guan, “On hold or drop out–of–order packets in networked control systems,” Information Sciences, vol. 268, pp. 436–446, Jun. 2014.
X.–M. Zhang, Q.–L. Han, and B.–L. Zhang, “An overview and deep investigation on sampled–data–based event–triggered control and filtering for networked systems,” IEEE Transactions on Industrial Informatics, vol. 13, no. pp.4–16, Feb. 2017.
X.–M. Zhang and Q.–L. Han, “Event–triggered dynamic output feedback control for networked control systems,” IET Control Theory & Applications, vol. 8, no. 4, pp. 226–234, Mar. 2014.
B.–L. Zhang and Q.–L. Han, “Network–based modelling and active control for offshore steel jacket platform with TMD mechanisms,” Journal of Sound and Vibration, vol. 333, no. 25, pp. 6796–6814, Dec. 2014.
B.–L. Zhang, Q.–L. Han, and X.–M. Zhang, “Event–triggered H¥ reliable control for offshore structures in net–work environments,” Journal of Sound and Vibration, vol. 368, pp. 1–21, Apr. 2016.
X.–M. Zhang and Q.–L. Han, “Abel lemma–based finite–sum inequality and its application to stability analysis for linear discrete time–delay systems,” Automatica, vol. 57, pp. 199–202, Jul. 2015.
X.–M. Zhang, Q.–L. Han, and Z. Zeng, “Hierarchical type stability criteria for delayed neural networks via canonical Bessel–Legendre inequalities,” IEEE Transactions on Cy–bernetics, vol. 48, no. 5, pp. 1660–1671, May 2018.
S. Xiao, L. Xu, H.–B. Zeng, and K. Teo, “Improved stabil–ity criteria for discrete–time delay systems via novel sum–mation inequalities,” International Journal of Control, Au–tomation and Systems, vol. 16, no. 4, pp. 1592–1602, Aug. 2018.
J. Wang, X.–M. Zhang, and Q.–L. Han, “Event–triggered generalized dissipativity filtering for neural networks with time–varying delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 27, no. 1, pp. 77–88, Jan. 2016.
Y.–Y. Zhao and J. Xu, “Effects of delayed feedback control on nonlinear vibration absorber system,” Journal of Sound and Vibration, vol. 308, nos. 1–2, pp. 212–230, Nov. 2007.
X.–M. Zhang, Q.–L. Han, and D. Han, “Effects of small time–delays on dynamic output feedback control of offshore steel jacket structures,” Journal of Sound and Vibration, vol. 330, no. 16, pp. 3883–3900, Aug. 2011.
B.–L. Zhang and G.–Y. Tang, “Active vibration H¥ control of offshore steel jacket platforms using delayed feedback,” Journal of Sound and Vibration, vol. 332, no. 22, pp. 5662–5677, Oct. 2013.
J. S. Yang, “Robust mixed H2=H¥ active control for offshore steel jacket platform,” Nonlinear Dynamics, vol.78, no. 2, pp. 1503.1514, Oct. 2014.
H. Nourisola, B. Ahmadi, and S. Tavakoli, “Delayed adaptive output feedback sliding mode control for offshore platforms subject to nonlinear wave–induced force,” Ocean Engineering, vol. 104, pp. 1–9, Aug. 2015.
X.–M. Zhang, M. Wu, J.–H. She, and Y. He, “Delaydependent stabilization of linear systems with time–varying state and input delays,” Automatica, vol. 41, no. 8, pp. 1405–1412, Aug. 2005.
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Recommended by Associate Editor Jong Min Lee under the direction of Editor PooGyeon Park. This work was supported in part by the Key project of Natural Science Foundation of Zhejiang Province of China under Grants LZ19F030001 and LZ13F030001, the National Natural Science Foundation of China under Grants 61773356, 61673357, and 61673148, the Open Foundation of First Level Zhejiang Key in Key Discipline of Control Science and Engineering, and Zhejiang Provincial Natural Science Foundation under Grant LY16F030007.
Bao-Lin Zhang received the Ph.D. in physical oceanography from the Ocean University of China in 2006. He is currently a professor and a dean with the College of Science, China Jiliang University. His current research interests include network-based control systems, time-delay systems, and vibration control systems.
Xiefu Jiang received the Ph.D. in Control Science and Engineering from Southeast University of China in 2001. He is currently a professor with the School of Automation, Hangzhou Dianzi University. His current research interests include networked control systems, time-delay systems and fuzzy systems.
Qiuxuan Wu received the Ph.D. in Control Science and Engineering from Shanghai Jiaotong University in 2007. He is currently an associate professor with the School of Automation, Hangzhou Dianzi University. His current research interests include intelligent control and soft robot.
Gong-You Tang received the Ph.D. in automatic control theory and applications from the South China University of Technology in 1991. He is currently a professor with the College of Information Science and Engineering, Ocean University of China. His main research interests include time-delay systems, nonlinear systems, and networked control systems.
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Zhang, BL., Jiang, X., Wu, Q. et al. Vibration Reduction for Offshore Platforms via Delayed Sliding Mode H∞ Control. Int. J. Control Autom. Syst. 17, 107–116 (2019). https://doi.org/10.1007/s12555-018-0110-1
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DOI: https://doi.org/10.1007/s12555-018-0110-1