Abstract
Due to the small-waterplane-area of a semi-submersible platform, not only are the surge and sway responses affected by the roll and pitch damping, but also roll and pitch motions may be induced by the propeller activity of the dynamic positioning (DP) system. The coupling characteristics of the dynamic responses between the degrees-of-freedom (DOFs) of the horizontal plane and the vertical plane can no longer be neglected. Therefore, traditional DP control strategies based on the horizontal DOFs are not suitable for the DP of a semi-submersible platform. The Cummins equation is widely used to simulate the response in the time domain. This equation, in which the convolution integral terms are replaced by the state-space model, is directly used to design the DP control strategy used in this study. The advantage of this model is that the coupling effects of the horizontal plane motions and vertical plane motions are considered. Because the sensors can only measure the dynamic motions of the platform, a static output feedback controller using L ∞ performance is designed to reject persistent environmental disturbances for the fully coupled dynamic model. Lyapunov function-based stability analysis is used to guarantee the stability. Finally, simulation results in the time domain are provided to specify the proposed controller design.
Similar content being viewed by others
References
Sørensen JA (2011) A survey of dynamic positioning control systems. Annu Rev Control 35:123–136
Perez T, Fossen TI (2011) Practical aspects of frequency-domain identification of dynamic models of marine structures from hydrodynamic data. Ocean Eng 38:426–435
Tannuri EA, Kubota LK, Pesce CP (2006) Adaptive control strategy for the dynamic positioning of a shuttle tanker during offloading operations. J Offshore Mech Arct 128:203–210
Tannuri EA, Agostinho AC, Morishita HM, Moratelli LJ (2010) Dynamic positioning systems: an experimental analysis of sliding model control. Control Eng Pract 18(10):1121–1132
Fossen TI, Grøvlen A (1998) Nonlinear output feedback control of dynamically positioned ships using vectorial observer backstepping. IEEE Trans Contr Syst Technol 6(1):121–128
Skjetne R, Fossen TI, Kokotovic PV (2005) Adaptive maneuvering, with experiments, for a model ship in a marine control laboratory. Automatica 41:289–298
Girard AR, Empey DM, Webster WC, Hedrick JK (2003) An experimental testbed for mobile offshore base control concepts. J Mar Sci Technol 7(3):109–118
Zhou L, Moan T, Riska K, Su B (2013) Heading control for turret-moored vessel in level ice based on Kalman filter with thrust allocation. J Mar Sci Technol 18(4):460–470
Balchen JG, Jenssen NA, Mathisen E, Sælid S (1980) A Dynamic positioning system based on Kalman filtering and optimal control. Model Identif Control 1(3):135–163
Sørensen AJ, Strand JP (2000) Positioning of small-waterplane-area marine constructions with roll and pitch damping. Control Eng Pract 8:205–213
Cummins W (1962) The impulse response function and ship motions. Schiffstechnik 47:101–109
Kristiansen E, Egeland O (2003) Frequency dependent added mass in models for controller design for wave motion ship damping. In: Proceedings of sixth IFAC conference on manoeuvring and control of marine craft MCMC’03, Girona, Spain
Kristiansen E, Hjuslstad A, Egeland O (2005) State-space representation of radiation forces in time-domain vessel models. Ocean Eng 32:2195–2216
McCabe A, Bradshaw A, Widden M (2005) A time-domain model of a floating body using transforms. In: Proceedings of the sixth European wave and tidal energy conference. University of Strathclyde, Glasgow
Fossen TI, Smogeli ØN (2004) Nonlinear time-domain strip formulation for low-speed manoeuvring and station keeping. Model Identif Control 25(4):201–221
Scherer C, Gahinet P, Ghilali M (1997) Multiobjective output-feedback control via LMI optimization. IEEE Trans Autom Control 42(7):896–911
Chen H, Guo KH (2005) Constrained H ∞ control of active suspensions: an LMI approach. IEEE Trans Control Syst Technol 13(3):412–421
Abedor J, Nagpal K, Poolla K (1996) A linear matrix inequality approach to peak-to-peak gain minimization. IEEE Trans Robust Nonlinear 6:899–927
Jhi HL, Tseng CS (2012) Robust static output feedback fuzzy control design for nonlinear discrete-time systems with persistent bounded disturbances. Int J Fuzzy Syst 14(1):131–140
Wu HN, Li HX (2009) Adaptive neural control design for nonlinear distributed parameter systems with persistent bounded disturbances. IEEE Trans Neural Netw 20(10):1630–1644
Khosravi A, Jalali A (2008) A new LMI solution in the L1 optimal problem for wind turbine-induction generator unit. Appl Math Comput 206:643–650
Sadeghi MS, Momeni HR, Amirifar R (2008) H ∞ and L 1 control of a teleoperation system via LMIs. Appl Math Comput 206:669–677
Ogilvie TF (1964) Recent progress toward the understanding and prediction of ship motions. In: The fifth symposium on naval hydrodynamics, pp 3–128
Li YC, Teng B (2002) Wave action on maritime structures. Ocean press, Peking, pp 90–95 (in Chinese)
Fossen TI (2005) A nonlinear unified state-space model for ship maneuvering and control in a seaway. J Bifurc Chaos 15(9):2717–2746
Xiao-Fu JI, Hong-Ye SU, Jian CHU (2007) Peak-to-peak gain minimization for uncertain discrete systems: a matrix inequality approach. ACTA Autom Sin 33(7):753–756
Boyd S, Ghaoui LE, Feronb E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM studies in applied mathematics, vol 15. SIAM, Philadelphia
Löfberg J (2004) YALMIP: a toolbox for modeling and optimization in Matlab. In: Proceedings of IEEE symposium on computer-aided control system design, Taipei, Taiwan
Kocvara M, Sting M (2006) PENBMI user’s guide. http://www.penopt.com
Herion D, Löfberg J, Kocvara M, Sting M (2005) Solving polynomial static output feedback problems with PENBMI. In: Proceedings of conference on decision and control, and European control conference, Sevilla, Spain, pp 7581–7586
Zhu H (2011) Studies on the motion performance of a semi-submersible platform and the heave motion damping system using moveable heave-plate. Harbin Institute of Technology, Harbin, pp 57–62
DNV-OS-E301 (2010) Position mooring. Det Norske Veritas, Høvik, pp 32–34
Sørensen AJ (2012) Marine control systems: propulsion and motion control of ships and ocean structures. Lecture notes. Department of Marine Technology, NTNU
Acknowledgments
This work was financially supported by the National Fundamental Research Program of China (Program 973, Grant No. 2011CB013705) and the National Natural Science Foundation of China (Grant No. 51221961). The support is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Liang, H., Li, L. & Ou, J. Coupled control of the horizontal and vertical plane motions of a semi-submersible platform by a dynamic positioning system. J Mar Sci Technol 20, 776–786 (2015). https://doi.org/10.1007/s00773-015-0322-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00773-015-0322-5