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Journal of Dynamic Systems, Measurement, and Control | Volume 138 | Issue 12 | research-article
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
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Citing Articles

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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References

1
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2
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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]
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Figures

Grahic Jump Location
Fig. 1

Schematic of conceptual design

+Schematic of conceptual design
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Schematic of conceptual design
Grahic Jump Location
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.

+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
Grahic Jump Location
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.

+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
Grahic Jump Location
Fig. 2

Block diagram of the whole model

+Block diagram of the whole model
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Block diagram of the whole model
Grahic Jump Location
Fig. 3

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

+Design of spring-damper systems is equal to determine the feedback controller K
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Design of spring-damper systems is equal to determine the feedback controller K
Grahic Jump Location
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.

+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
Grahic Jump Location
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.

+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.
Grahic Jump Location
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.

+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.
View Large  |  Save Figure  |  Download Slide (.ppt)
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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