Wave-energy converters of the point-absorbing type (i.e., having small extension compared with the wavelength) are promising for achieving cost reductions and design improvements because of a high power-to-volume ratio and better possibilities for mass production of components and devices as compared with larger converter units. However, their frequency response tends to be narrow banded, which means that the performance in real seas (irregular waves) will be poor unless their motion is actively controlled. Only then the invested equipment can be fully exploited, bringing down the overall energy cost. In this work various control methods for point-absorbing devices are reviewed, and a representative selection of methods is investigated by numerical simulation in irregular waves, based on an idealized example of a heaving semisubmerged sphere. Methods include velocity-proportional control, approximate complex conjugated control, approximate optimal velocity tracking, phase control by latching and clutching, and model-predictive control, all assuming a wave pressure measurement as the only external input to the controller. The methods are applied for a single-degree-of-freedom heaving buoy. Suggestions are given on how to implement the controllers, including how to tune control parameters and handle amplitude constraints. Based on simulation results, comparisons are made on absorbed power, reactive power flow, peak-to-average power ratios, and implementation complexity. Identified strengths and weaknesses of each method are highlighted and explored. It is found that overall improvements in average absorbed power of about 100–330% are achieved for the investigated controllers as compared with a control strategy with velocity-proportional machinery force. One interesting finding is the low peak-to-average ratios resulting from clutching control for wave periods about 1.5 times the resonance period and above.

1.
Evans
,
D. V.
, 1981, “
Power From Water Waves
,”
Annu. Rev. Fluid Mech.
0066-4189,
13
, pp.
157
187
.
2.
Falnes
,
J.
, 2002, “
Optimum Control of Oscillation of Wave-Energy Converters
,”
Int. J. Offshore Polar Eng.
1053-5381,
12
(
2
), pp.
147
155
.
3.
Falnes
,
J.
, 2002,
Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction
,
Cambridge University Press
,
Cambridge
.
4.
Price
,
A. A. E.
,
Forehand
,
D. I. M.
, and
Wallace
,
A. R.
, 2009, “
Time-Span of Future Information Necessary for Theoretical Acausal Optimal Control of Wave Energy Converters
,”
Proceedings of the European Control Conference 2009
, Budapest, Hungary, pp.
3761
3766
.
5.
Perdigão
,
J. N. B. A.
, and
Sarmento
,
A. J. N. A.
, 1989, “
A Phase Control Strategy for OWC Devices in Irregular Seas
,”
The Fourth International Workshop on Water Waves and Floating Bodies
,
J.
Grue
, ed., Department of Mathematics, University of Oslo, pp.
205
209
.
6.
Beirão
,
P. J. B. F. N.
, 2007, “
Modelling and Control of a Wave Energy Converter: Archimedes Wave Swing
,” Ph.D. thesis, Universidade Tecnica de Lisboa, Delft.
7.
Gieske
,
P.
, 2007, “
Model Predictive Control of a Wave Energy Converter: Archimedes Wave Swing
,” MS thesis, Delft University of Technology, Delft.
8.
Eidsmoen
,
H.
, 1995, “
On the Theory and Simulation of Heaving-Buoy Wave-Energy Converters With Control
,” Ph.D. thesis, NTH (now NTNU), Trondheim.
9.
Hals
,
J.
,
Falnes
,
J.
, and
Moan
,
T.
, 2011, “
Constrained Optimal Control of a Heaving Buoy Wave-Energy Converter
,”
ASME J. Offshore Mech. Arct. Eng.
0892-7219,
133
(
1
), p.
011401
.
10.
Kamenský
,
M.
, and
Guglielmi
,
M.
, 2007, “
Optimal Control of Power Take-Off From Mass Spring-Damper System
,”
16th International on Process Control 2007
.
11.
Nolan
,
G.
,
Ringwood
,
J.
,
Leithead
,
W.
, and
Butler
,
S.
, 2005, “
Optimal Damping Profiles for a Heaving Buoy Wave Energy Converter
,”
Proceedings of the 15th International Offshore and Polar Engineering Conference
, ISOPE, Seoul, Korea.
12.
Hoskin
,
R. E.
, and
Nichols
,
N. K.
, 1987, “
Optimal Strategies For Phase Control Of Wave Energy Devices
,” in
Utilization of Ocean Waves—Wave to Energy Conversion
,
M. E.
McCormick
and
Y. C.
Kim
, ed.,
American Society of Civil Engineering
,
New York
, pp.
184
199
.
13.
Naidu
,
D. S.
, 2003,
Optimal Control Systems
,
CRC
,
Boca Raton, FL
.
14.
Budal
,
K.
, and
Falnes
,
J.
, 1980, “
Interacting Point Absorbers With Controlled Motion
,”
Power from Sea Waves
,
B.
Count
, ed.,
Academic
,
London
, pp.
381
399
.
15.
Budal
,
K.
,
Falnes
,
J.
,
Iversen
,
L. C.
,
Lillebekken
,
P. M.
,
Oltedal
,
G.
,
Hals
,
T.
,
Onshus
,
T.
, and
Høy
,
A. S.
, 1982, “
The Norwegian Wave-Power Buoy Project
,”
Proceedings of the Second International Symposium on Wave Energy Utilization
,
H.
Berge
, ed., Tapir, Trondheim, Norway, pp.
323
344
.
16.
Babarit
,
A.
, 2005, “
Optimisation hydrodynamique et contrôle optimal d’un récupérateur de l’énergie des vagues
,” Ph.D. thesis, Ecole Centrale de Nantes, Nantes.
17.
Hals
,
J.
,
Taghipour
,
R.
, and
Moan
,
T.
, 2007, “
Dynamics of a Force-Compensated Two Body Wave Energy Converter in Heave With Hydraulic Power Take-Off Subject to Phase Control
,”
Proceedings of the 7th European Wave and Tidal Energy Conference
, Porto, Portugal.
18.
Falnes
,
J.
, 1999, “
Wave-Energy Conversion Through Relative Motion Between Two Single Mode Oscillating Bodies
,”
ASME J. Offshore Mech. Arct. Eng.
0892-7219,
121
, pp.
32
38
.
19.
Falcão
,
A. F. O.
, 2007, “
Phase Control Through Load Control of Oscillating-Body Wave Energy Converters With Hydraulic PTO System
,”
Proceedings of the Seventh European Wave and Tidal Energy Conference
, Porto, Portugal.
20.
Lopes
,
M.
,
Hals
,
J.
,
Gomes
,
R.
,
Moan
,
T.
,
Gato
,
L.
, and
Falcao
,
A. O.
, 2009, “
Experimental and Numerical Investigation of Non-Predictive Phase-Control Strategies for a Point-Absorbing Wave Energy Converter
,”
Ocean Eng.
0029-8018,
36
(
5
), pp.
386
402
.
21.
Salter
,
S. H.
,
Taylor
,
J. R. M.
, and
Caldwell
,
N. J.
, 2002, “
Power Conversion Mechanisms for Wave Energy
,”
Proceedings of Institute of Mechanical Engineers, Part M, Engineering for the Maritime Environment
,
216
, pp.
1
27
.
22.
Babarit
,
A.
,
Guglielmi
,
M.
, and
Clement
,
A. H.
, 2009, “
Declutching Control of a Wave Energy Converter
,”
Ocean Eng.
0029-8018,
36
(
12–13
), pp.
1015
1024
.
23.
Evans
,
D. V.
, 1981, “
Maximum Wave-Power Absorption Under Motion Constraints
,”
Appl. Ocean. Res.
0141-1187,
3
(
4
), pp.
200
203
.
24.
Pizer
,
D.
, 1993, “
Maximum Wave-Power Absorption of Point-Absorbers Under Motion Constraints
,”
Appl. Ocean. Res.
0141-1187,
15
(
4
), pp.
227
234
.
25.
Falnes
,
J.
, 2000, “
Maximum Wave-Energy Absorption by Oscillating Systems Consisting of Bodie and Water Columns With Restricted or Unrestricted Amplitudes
,”
Proceedings of the International Offshore and Polar Engineering Conference
, Vol.
1
, pp.
420
426
.
26.
Leijon
,
M.
,
Danielsson
,
O.
,
Eriksson
,
M.
,
Thorburn
,
K.
,
Bernhoff
,
H.
,
Isberg
,
J.
,
Sundberg
,
J.
,
Ivanova
,
I.
,
Sjöstedt
,
E.
,
Agren
,
O.
,
Karlsson
,
K.
, and
Wolfbrandt
,
A.
, 2006, “
An Electrical Approach to Wave Energy Conversion
,”
Renewable Energy
0960-1481,
31
(
9
), pp.
1309
1319
.
27.
de Sousa Prado
,
M.
,
Gardner
,
F.
,
Damen
,
M.
, and
Polinder
,
H.
, 2006, “
Modelling and Test Results of the Archimedes Wave Swing
,”
Proc. Inst. Mech. Eng., Part A
0957-6509,
220
(
8
), pp.
855
868
.
28.
Brown
,
R. G.
, and
Hwang
,
P. Y. C.
, 1997,
Introduction to Random Signals and Applied Kalman Filtering
,
3rd ed.
,
Wiley
,
New York
.
29.
Astrom
,
K. J.
, and
Wittenmark
,
B.
, 2008,
Adaptive Control
,
Dover
,
New York
.
30.
Ariyur
,
K. B.
, and
Krstic
,
M.
, 2003,
Real-Time Optimization by Extremum-Seeking Control
,
Wiley
,
New York
.
31.
Cummins
,
W. E.
, 1962, “
The Impulse Response Function and Ship Motions
,”
Schiffstechnik
0937-7255,
9
, pp.
101
109
.
32.
Jefferys
,
E. R.
, 1984, “
Simulation of Wave Power Devices
,”
Appl. Ocean. Res.
0141-1187,
6
(
1
), pp.
31
39
.
33.
Taghipour
,
R.
,
Perez
,
T.
, and
Moan
,
T.
, 2008, “
Hybrid Frequency-Time Domain Models for Dynamic Response Analysis of Marine Structures
,”
Ocean Eng.
0029-8018,
35
(
7
), pp.
685
705
.
34.
Hals
,
J.
,
Bjarte-Larsson
,
T.
, and
Falnes
,
J.
, 2002, “
Optimum Reactive Control and Control by Latching of a Wave-Absorbing Semisubmerged Heaving Sphere
,”
Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering—OMAE
, Vol.
4
, pp.
415
423
.
35.
Nebel
,
P.
, 1992, “
Maximizing the Efficiency of Wave-Energy Plants Using Complex Conjugate Control
,”
Proceedings of the Institution of Mechanical Engineers. Part I Journal of Systems and Control Engineering
,
206
(
4
), pp.
225
236
.
36.
Budal
,
K.
,
Falnes
,
J.
,
Hals
,
T.
,
Iversen
,
L. C.
, and
Onshus
,
T.
, 1981, “
Model Experiment with a Phase Controlled Point Absorber
,”
Proceedings of the Second International Symposium on Wave and Tidal Energy
,
H. S.
Stephens
and
C. A.
Stapleton
, eds., BHRA Fluid Engineering (Cranford, Bedford), Cambridge, UK, pp.
191
206
.
37.
Babarit
,
A.
,
Duclos
,
G.
, and
Clement
,
A. H.
, 2004, “
Comparison of Latching Control Strategies for a Heaving Wave Energy Device in Random Sea
,”
Appl. Ocean. Res.
,
26
(
5
), pp.
227
238
.
38.
Killingsworth
,
N.
, and
Krstic
,
M.
, 2005, “
Auto-Tuning of PID Controllers via Extremum Seeking
,”
Proceedings of the American Control Conference
, Vol.
4
, pp.
2251
2256
.
39.
Spong
,
M. W.
, 2006,
Robot Modeling and Control
,
Wiley
,
Hoboken, NJ
.
40.
Edwards
,
C.
, and
Spurgeon
,
S. K.
, 1998,
Sliding Mode Control
,
CRC
,
Boca Raton, FL
.
41.
The Mathworks Inc.
, 2006, MATLAB, version 7.2, URL: http://www.mathworks.com/http://www.mathworks.com/
42.
WAMIT
, 2006, WAMIT User Manual, version 6.3, http://www.wamit.comhttp://www.wamit.com
43.
Falnes
,
J.
, 2007, “
A Review of Wave-Energy Extraction
,”
Mar. Struct.
,
20
(
4
), pp.
185
201
.
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