Research Papers

Optimum Design of a Passive Suspension System of a Semisubmersible for Pitching Reduction

[+] Author and Article Information
Hongzhong Zhu

Research and Education Center for
Advanced Energy Materials,
Devices, and Systems,
Kyushu University,
Kasuga 816-8580, Japan
e-mail: zhuhongzhong@riam.kyushu-u.ac.jp

Changhong Hu

Research Institute for Applied Mechanics,
Kyushu University,
Kasuga 816-8580, Japan
e-mail: hu@riam.kyushu-u.ac.jp

Yingyi Liu

Research Institute for Applied Mechanics,
Kyushu University,
Kasuga 816-8580, Japan
e-mail: liuyingyi@riam.kyushu-u.ac.jp

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 22, 2016; final manuscript received June 13, 2016; published online August 11, 2016. Assoc. Editor: Evangelos Papadopoulos.

J. Dyn. Sys., Meas., Control 138(12), 121003 (Aug 11, 2016) (8 pages) Paper No: DS-16-1048; doi: 10.1115/1.4033948 History: Received January 22, 2016; Revised June 13, 2016

With the development of ocean energy exploration, reliable semisubmersible platforms with very small motion are expected to develop. Especially, in a floating offshore wind turbine (FOWT) system, the maximum pitching amplitude is required to be less than a few degrees. To reduce wave-induced pitch motion, a new type semisubmersible with suspensions and a design method of the suspension coefficients are presented. In practical case, an add-on wave energy dissipation device mounted on a floating platform, such as the combined wave-wind energy converter system, could be regarded as the suspension system. In this study, first, the conceptual semisubmersible is described. Then, the hydrodynamic loads to the semisubmersible are linearized so that the whole system is expressed by a state-space model. The suspension design problem is transformed into solving a constrained H optimization problem, which after all is the optimal controller design of a feedback system. Finally, numerical examples are performed to verify the effectiveness of the design. The results illustrate that the pitch motion of the semisubmersible can be remarkably reduced by the designed suspensions.

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Ishihara, T. , Phuc, P. , Sukegawa, H. , Shimada, K. , and Ohyama, T. , 2007, “ A Study on the Dynamic Response of a Semi-Submersible Floating Offshore Wind Turbine System Part 1: A Water Tank Test,” 12th International Conference on Wind Engineering, Cairns, Australia, July 1–6, pp. 2511–2518.
Henderson, A. R. , and Patel, M. H. , 2003, “ On the Modelling of a Floating Offshore Wind Turbine,” Wind Energy, 6(1), pp. 53–86. [CrossRef]
Faltinsen, O. , 1993, Sea Loads on Ships and Offshore Structures, Cambridge University Press, Cambridge, UK.
Sato, A. , and Suzuki, H. , 2006, “ Effect of Motion of Floating Platform on the Strength Design of Floating Wind Turbine,” 28th Symposium on Wind Energy Utilization, pp. 192–195 (in Japanese).
Suzuki, H. , and Sato, A. , 2007, “ Load on Turbine Blade Induced by Motion of Floating Platform and Design Requirement for the Platform,” ASME Paper No. OMAE2007-29500.
Huijs, F. , Mikx, J. , Savenije, F. , and de Ridder, E.-J. , 2013, “ Integrated Design of Floater, Mooring and Control System for a Semi-Submersible Floating Wind Turbine,” EWEA Offshore, Vienna, Austria.
Roddier, D. , Cermelli, C. , Aubault, A. , and Weinstein, A. , 2010, “ Windfloat: A Floating Foundation for Offshore Wind Turbine,” J. Renewable Sustainable Energy, 2(3), p. 033104. [CrossRef]
Karimirad, M. , and Michailides, C. , 2015, “ V-Shaped Semisubmersible Offshore Wind Turbine: An Alternative Concept for Offshore Wind Technology,” Renewable Energy, 83, pp. 126–143. [CrossRef]
Aubault, A. , Cermelli, C. , and Roddier, D. , 2006, “ Structural Design of a Semi-Submersible Platform With Water-Entrapment Plates Based on a Time-Domain Hydrodynamic Algorithm Coupled With Finite-Elements,” 6th International Offshore and Polar Engineering Conference, San Francisco, CA, May 28–June 2, pp. 187–194.
Zhu, H. , Ou, J. , and Zhai, G. , 2012, “ Conceptual Design of a Deep Draft Semi-Submersible Platform With a Movable Heave-Plate,” J. Ocean Univ. China, 11(1), pp. 7–12. [CrossRef]
Roddier, D. , and Cermelli, C. , 2013, “ Column-Stabilized Offshore Platform With Water-Entrapment Plates and Asymmetric Mooring System for Support of Offshore Wind Turbines,” U.S. patent application US008471396B2.
Chandrasekaran, S. , Raphel, D. , and Shree, S. , 2014, “ Deep Ocean Wave Energy Systems (Dowes): Experimental Investigations,” J. Nav. Archit. Mar. Eng., 11(2), pp. 139–146. [CrossRef]
Perez, C. , Greaves, D. , and Iglesias, G. , 2015, “ A Review of Combined Wave and Offshore Wind Energy,” Renewable Sustainable Energy Rev., 42, pp. 141–153. [CrossRef]
Perez, C. , and Iglesias, G. , 2012, “ Integration of Wave Energy Converters and Offshore Windmills,” Fourth International Conference on Ocean Energy (ICOE), Dublin, Ireland, Oct. 16–18.
Kral, R. , and Kreuzer, E. , 1999, “ Multibody Systems and Fluid-Structure Interactions With Application to Floating Structures,” Multibody Syst. Dyn., 3(1), pp. 65–83. [CrossRef]
Cummins, W. E. , 1962, “ The Impulse Response Function and Ship Motions,” Schiffstechnik, Technical Report No. 47.
Perez, T. , and Fossen, T. , 2009, “ Identification of Dynamic Models of Marine Structures From Frequency-Domain Data Enforcing Model Structure and Parameter Constraints,” ARC Centre of Excellence for Complex Dynamic Systems and Control, Technical Report No. 2009-01.0-Marine Systems Simulator.
Yu, Z. , and Falnes, J. , 1995, “ State-Space Modelling of a Vertical Cylinder in Heave,” Appl. Ocean Res., 17(5), pp. 265–275. [CrossRef]
Fossen, T. I. , 2011, Handbook of Marine Craft Hydrodynamics and Motion Control, Wiley, Chichester, UK.
Borg, M. , Collu, M. , and Brennan, F. P. , 2013, “ Use of a Wave Energy Converter as a Motion Suppression Device for Floating Wind Turbines,” Energy Procedia, 35, pp. 223–233. [CrossRef]
Kennedy, J. , and Eberhart, R. , 1995, “ Particle Swarm Optimization,” IEEE International Conference on Neural Networks, Vol. 4, pp. 1942–1948.
Liu, Y. , Iwashita, H. , and Hu, C. , 2015, “ A Calculation Method for Finite Depth Free-Surface Green Function,” Int. J. Nav. Archit. Ocean Eng., 7(2), pp. 375–389.
Perez, T. , and Fossen, T. , 2009, “ A Matlab Toolbox for Parametric Identification of Radiation-Force Models of Ships and Offshore Structures,” Model., Identif. Control, 30(1), pp. 1–15. [CrossRef]


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Fig. 1

Schematic of conceptual design

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Fig. 2

Block diagram of the whole model

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Fig. 3

Design of spring-damper systems is equal to determine the feedback controller K

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Fig. 4

Plot with solid line showing the MPM spectra for Hs = 4.5 m and Tz = 10 s. The linear approximation by Eq. (28) is plotted with dotted line.

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Fig. 5

Memory functions computed from potential theory (solid lines with circle markers) and their linear approximation (solid lines). (a) Memory function of main body in pitching direction Kθr. (b) Memory function of main body in heaving direction Khr. (c) Memory function of column in heaving direction Kcr.

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Fig. 6

Wave excitation loads computed from potential theory (solid lines with circle markers) and their linear approximation (solid lines). (a) Wave excitation loads to main body in pitching direction. (b) Wave excitation loads to main body in heaving direction. (c) Wave excitation loads to column in heaving direction.

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Fig. 7

Frequency characteristics when varying k, c, and a from the optimal values. The magnitude is in decibels by 20 log10|θ(jω)|. (a) Characteristics when c=copt and a=aopt. (b) Characteristics when k=kopt and a=aopt. (c) Characteristics when c=copt and k=kopt.

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Fig. 8

Numerical results when varying k, c, and a. (a) Pitch motion when c=copt and a=aopt. (b) Pitch motion when k=kopt and a=aopt. (c) Pitch motion when c=copt and k=kopt.




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