Model-predictive control (MPC) has shown its strong potential in maximizing energy extraction for wave-energy converters (WECs) while handling hard constraints. However, the computational demand is known to be a primary concern for applying MPC in real time. In this work, we develop a cost function in which a penalty term on the slew rate of the machinery force is introduced and used to ensure the convexity of the cost function. Constraints on states and the input are incorporated. Such a constrained optimization problem is cast into a Quadratic Programming (QP) form and efficiently solved by a standard QP solver. The current MPC is found to have good energy-capture capability in both regular and irregular wave conditions, and is able to broaden favorably the bandwidth for capturing wave energy compared to other controllers in the literature. Reactive power required by the power-take-off (PTO) system is presented. The effects of the additional penalty term are discussed.

References

References
1.
Bacelli
,
G.
,
Coe
,
R.
,
Wilson
,
D.
,
Abdelkhalik
,
O.
,
Korde
,
U.
,
Robinett
,
R.
, and
Bull
,
D.
,
2016
, “
A Comparison of WEC Control Strategies for a Linear WEC Model
,” Sandia National Laboratories, Albuquerque, NM, Report No.
SAND2016-4293
http://energy.sandia.gov/wp-content/uploads/dlm_uploads/2016/06/SAND2016-4293.pdf.
2.
Hals
,
J.
,
Falnes
,
J.
, and
Moan
,
T.
,
2011
, “
A Comparison of Selected Strategies for Adaptive Control of Wave Energy Converters
,”
ASME J. Offshore Mech. Arct. Eng.
,
133
(
3
), p.
031101
.
3.
Eidsmoen
,
H.
,
1996
, “
Optimum Control of a Floating Wave-Energy Converter With Restricted Amplitude
,”
ASME J. Offshore Mech. Arct. Eng.
,
118
(
2
), pp.
96
101
.
4.
Evans
,
D.
,
1981
, “
Maximum Wave-Power Absorption Under Motion Constraints
,”
Appl. Ocean Res.
,
3
(
4
), pp.
200
203
.
5.
Mayne
,
D.
,
Rawlings
,
J.
,
Rao
,
C.
, and
Scokaert
,
P.
,
2000
, “
Constrained Model Predictive Control: Stability and Optimality
,”
Automatica
,
36
(
6
), pp.
789
814
.
6.
Belmont
,
M.
,
Horwood
,
J.
,
Thurley
,
R.
, and
Baker
,
J.
,
2006
, “
Filters for Linear Sea-Wave Prediction
,”
Ocean Eng.
,
33
(
17
), pp.
2332
2351
.
7.
Fusco
,
F.
, and
Ringwood
,
J.
,
2012
, “
A Study of the Prediction Requirements in Real-Time Control of Wave Energy Converters
,”
IEEE Trans. Sustainable Energy
,
3
(
1
), pp.
176
184
.
8.
Morris
,
E.
,
Zienkiewicz
,
H.
, and
Belmont
,
M.
,
1998
, “
Short Term Forecasting of the Sea Surface Shape
,”
Int. Shipbuilding Prog.
,
45
(
444
), pp.
383
400
.
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.
,
133
(
1
), p.
011401
.
10.
Li
,
G.
, and
Belmont
,
M.
,
2014
, “
Model Predictive Control of Sea Wave Energy Converters—Part I: A Convex Approach for the Case of a Single Device
,”
Renewable Energy
,
69
, pp.
453
463
.
11.
Cretel
,
J.
,
Lightbody
,
G.
,
Thomas
,
G.
, and
Lewis
,
A.
,
2011
, “
Maximisation of Energy Capture by a Wave-Energy Point Absorber Using Model Predictive Control
,”
IFAC Proc.
,
44
(
1
), pp.
3714
3721
.
12.
Tom
,
N.
, and
Yeung
,
R.
,
2014
, “
Nonlinear Model Predictive Control Applied to a Generic Ocean-Wave Energy Extractor
,”
ASME J. Offshore Mech. Arct. Eng.
,
136
(
4
), p.
041901
.
13.
Son
,
D.
, and
Yeung
,
R.
,
2017
, “
Optimizing Ocean-Wave Energy Extraction of a Dual Coaxial-Cylinder WEC Using Nonlinear Model Predictive Control
,”
Appl. Energy
,
187
, pp.
746
757
.
14.
Tom
,
N.
, and
Yeung
,
R.
,
2016
, “
Experimental Confirmation of Nonlinear-Model-Predictive Control Applied Offline to a Permanent Magnet Linear Generator for Ocean-Wave Energy Conversion
,”
IEEE J. Oceanic Eng.
,
41
(
2
), pp.
281
295
.
15.
Son
,
D.
,
2016
, “
Performance Evaluation and Optimization of a Dual Coaxial-Cylinder System as an Ocean-Wave Energy Converter
,” Ph.D. thesis, University of California at Berkeley, Berkeley, CA.
16.
Bacelli
,
G.
,
Coe
,
R.
,
Patterson
,
D.
, and
Wilson
,
D.
,
2017
, “
System Identification of a Heaving Point Absorber: Design of Experiment and Device Modeling
,”
Energies
,
10
(4), p.472.
17.
Wehausen
,
J.
,
1971
, “
The Motion of Floating Bodies
,”
Annu. Rev. Fluid Mech.
,
3
(
1
), pp.
237
268
.
18.
Yeung
,
R.
,
1981
, “
Added Mass and Damping of a Vertical Cylinder in Finite-Depth Waters
,”
Appl. Ocean Res.
,
3
(
3
), pp.
119
133
.
19.
Falnes
,
J.
,
2002
,
Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction
,
Cambridge University Press
, Cambridge, UK.
20.
Chau
,
F.
, and
Yeung
,
R.
,
2012
, “
Inertia, Damping, and Wave Excitation of Heaving Coaxial Cylinders
,”
ASME
Paper No. OMAE2012-83987.
21.
Wächter
,
A.
, and
Biegler
,
L. T.
,
2006
, “
On the Implementation of an Interior-Point Filter Line-Search Algorithm for Large-Scale Nonlinear Programming
,”
Math. Program.
,
106
(
1
), pp.
25
57
.
22.
Herceg
,
M.
,
Kvasnica
,
M.
,
Jones
,
C.
, and
Morari
,
M.
,
2013
, “
Multi-Parametric Toolbox 3.0
,”
European Control Conference
(
ECC
), Zurich, Switzerland, July 17–19, pp.
502
510
.http://ieeexplore.ieee.org/document/6669862/
23.
Currie
,
J.
, and
Wilson
,
D. I.
,
2012
, “
OPTI: Lowering the Barrier Between Open Source Optimizers and the Industrial MATLAB User
,”
Foundations of Computer-Aided Process, Operations
,
N.
Sahinidis
and
J.
Pinto
, eds., Elsevier, Savannah, GA.
24.
Zhong
,
Q.
, and
Yeung
,
R.
,
2016
, “
Wave-Body Interactions Among an Array of Truncated Vertical Cylinders
,”
ASME
Paper No. OMAE2016-55055.
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