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.

## References

References
1.
Ishihara
,
T.
,
Phuc
,
P.
,
Sukegawa
,
H.
,
,
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
.
2.
Henderson
,
A. R.
, and
Patel
,
M. H.
,
2003
, “
On the Modelling of a Floating Offshore Wind Turbine
,”
Wind Energy
,
6
(
1
), pp.
53
86
.
3.
Faltinsen
,
O.
,
1993
,
Sea Loads on Ships and Offshore Structures
,
Cambridge University Press
,
Cambridge, UK
.
4.
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).
5.
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
.
6.
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.
7.
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
.
8.
,
M.
, and
Michailides
,
C.
,
2015
, “
V-Shaped Semisubmersible Offshore Wind Turbine: An Alternative Concept for Offshore Wind Technology
,”
Renewable Energy
,
83
, pp.
126
143
.
9.
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
.
10.
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
.
11.
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
.
12.
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
.
13.
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
.
14.
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.
15.
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
.
16.
Cummins
,
W. E.
,
1962
, “
The Impulse Response Function and Ship Motions
,” Schiffstechnik,
Technical Report No. 47
.
17.
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
.
18.
Yu
,
Z.
, and
Falnes
,
J.
,
1995
, “
State-Space Modelling of a Vertical Cylinder in Heave
,”
Appl. Ocean Res.
,
17
(
5
), pp.
265
275
.
19.
Fossen
,
T. I.
,
2011
,
Handbook of Marine Craft Hydrodynamics and Motion Control
,
Wiley
, Chichester,
UK
.
20.
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
.
21.
Kennedy
,
J.
, and
Eberhart
,
R.
,
1995
, “
Particle Swarm Optimization
,”
IEEE International Conference on Neural Networks
, Vol.
4
, pp.
1942
1948
.
22.
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
.
23.
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
.