Abstract
This paper formulates and solves a new problem of inverse optimal control to maximize harvested energy from dynamical systems induced by external excitations. An inverse optimal control law is designed to minimize a cost function penalizing negativeness of the harvested energy and positiveness of the control and system (partial) states, where it does not require to solve a Hamilton–Jacobi–Belman (HJB) equation or a Hamilton–Jacobi–Isaacs (HJI) equation. An application to a point absorber wave energy converter (PAWEC) is included to illustrate the effectiveness of the proposed theory.
Issue Section:
Research Papers
References
1.
Sepulchre
,
R.
,
Jankovic
,
M.
, and
Kokotovic
,
P.
, 1997
, Constructive Nonlinear Control
,
Springer
,
New York
.2.
Deng
,
H.
,
Krstic
,
M.
, and
Williams
,
R.
, 2001
, “
Stabilization of Stochastic Nonlinear Systems Driven by Noise of Unknown Covariance
,” IEEE Trans. Autom. Control
,
46
(8
), pp. 1237
–1253
.10.1109/9.9409273.
Do
,
K. D.
, 2019
, “
Inverse Optimal Control of Stochastic Systems Driven by Lévy Processes
,” Automatica
,
107
, pp. 539
–550
.10.1016/j.automatica.2019.06.0164.
Praly
,
L.
,
Ortega
,
R.
, and
Kaliora
,
G.
, 2001
, “
Stabilization of Nonlinear Systems Via Forwarding
,” IEEE Trans. Autom. Control
,
46
(9
), pp. 1461
–1466
.10.1109/9.9484785.
Hardy
,
G.
,
Littlewood
,
J. E.
, and
Polya
,
G.
, 1989
, Inequalities
, 2nd ed.,
Cambridge University Press
,
Cambridge, UK
.6.
Krstic
,
M.
, and
Deng
,
H.
, 1998
, Stabilization of Nonlinear Uncertain Systems
,
Springer
,
London, UK
.7.
Deng
,
H.
, and
Krstic
,
M.
, 1997
, “
Stochastic Nonlinear Stabilization—Part II: Inverse Optimality
,” Syst. Control Lett.
,
32
(3
), pp. 151
–159
.10.1016/S0167-6911(97)00067-48.
Do
,
K. D.
, 2015
, “
Global Inverse Optimal Stabilization of Stochastic Nonholonomic Systems
,” Syst. Control Lett.
,
75
, pp. 41
–55
.10.1016/j.sysconle.2014.11.0039.
Do
,
K. D.
, 2019
, “
Inverse Optimal Gain Assignment Control of Evolution Systems and Its Application to Boundary Control of Marine Risers
,” Automatica
,
106
, pp. 242
–256
.10.1016/j.automatica.2019.05.02010.
de O. Falcão
,
A. F.
, 2010
, “
Wave Energy Utilization: A Review of the Technologies
,” Renewable Sustainable Energy Rev.
,
14
(3
), pp. 899
–918
.10.1016/j.rser.2009.11.00311.
Fusco
,
F.
, and
Ringwood
,
J. V.
, 2014
, “
Hierarchical Robust Control of Oscillating Wave Energy Converters With Uncertain Dynamics
,” IEEE Trans. Sustainable Energy
,
5
(3
), pp. 958
–966
.10.1109/TSTE.2014.231347912.
Potapenko
,
T.
,
Temiz
,
I.
, and
Leijon
,
M.
, 2018
, “
Optimization of Resistive Load for a Wave Energy Converter With Linear Generator Power Take Off
,” Proceedings of the 4th Asian Wave and Tidal Energy Conference
,
Taipei, Taiwan
, Sept. 9–13, pp. 1
–5
.https://www.researchgate.net/publication/328043662_Optimization_of_resistive_load_for_a_wave_energy_converter_with_linear_generator_power_take_off13.
Nolan
,
G. A.
,
Ringwood
,
J. V.
,
Leithead
,
W. E.
, and
Butler
,
S.
, 2005
, “
Optimal Damping Profiles for a Heaving Buoy Wave Energy Converter
,” Proceedings of the Fifteenth International Offshore and Polar Engineering Conference
,
Seoul, South Korea
, June 19−24, pp. 477
–484
.10.3182/20100915-3-DE-3008.0006714.
Ekström
,
R.
,
Ekergard
,
B.
, and
Leijon
,
M.
, 2015
, “
Electrical Approach to Output Power Control for a Point Absorbing Wave Energy Converter With a Direct Drive Linear Generator Power Take Off
,” Proceedings of the 12th European Wave and Tidal Energy Conference
,
Cork, Ireland
, June 19–24, Vol.
2
, pp. 116
–128
.15.
Dolguntseva
,
I.
,
Eriksson
,
S.
, and
Leijon
,
M.
, 2017
, “
Electrical Approach to Output Power Control for a Point Absorbing Wave Energy Converter With a Direct Drive Linear Generator Power Take Off
,” Proceedings of the 12th European Wave and Tidal Energy Conference
,
Cork, Ireland
, Aug. 27–Sept. 1, p. 878
.https://www.researchgate.net/publication/320100494_Electrical_Approach_to_Output_Power_Control_for_a_Point_Absorbing_Wave_Energy_Converter_with_a_Direct_Drive_Linear_Generator_Power_Take_Off16.
Budal
,
K.
, and
Falnes
,
J.
, 1980
, “
Interacting Point Absorbers With Controlled Motion
,” Power From the Sea Waves
,
B.
Count
, ed.,
Academic Press Limited
,
London, UK
, pp. 381
–399
.17.
Ringwood
,
J. V.
,
Bacelli
,
G.
, and
Fusco
,
F.
, 2014
, “
Energy-Maximizing Control of Wave-Energy Converters: The Development of Control System Technology to Optimize Their Operation
,” IEEE Control Syst. Mag.
,
34
(5
), pp. 30
–55
.10.1109/MCS.2014.233325318.
Korde
,
U. A.
, 2002
, “
Latching Control of Deep Water Wave Energy Devices Using an Active References
,” Ocean Eng.
,
29
(11
), pp. 1343
–1355
.10.1016/S0029-8018(01)00093-219.
Park
,
J. S.
,
Gu
,
B. G.
,
Kim
,
J. R.
,
Cho
,
I. H.
,
Jeong
,
I.
, and
Lee
,
J.
, 2017
, “
Active Phase Control for Maximum Power Point Tracking of a Linear Wave Generator
,” IEEE Trans. Power Electron.
,
32
(10
), pp. 7651
–7662
.10.1109/TPEL.2016.262584320.
Giorgi
,
G.
, and
Ringwood
,
J. V.
, 2016
, “
Implementation of Latching Control in a Numerical Wave Tank With Regular Waves
,” J. Ocean Eng. Mar. Energy
,
2
(2
), pp. 211
–226
.10.1007/s40722-016-0052-821.
Beatty
,
S. J.
,
Hall
,
M.
,
Buckham
,
B. J.
,
Wild
,
P.
, and
Bocking
,
B.
, 2015
, “
Experimental and Numerical Comparisons of Self-Reacting Point Absorber Wave Energy Converters in Regular Waves
,” Ocean Eng.
,
104
, pp. 370
–386
.10.1016/j.oceaneng.2015.05.02722.
Sheng
,
W.
,
Alcorn
,
R.
, and
Lewis
,
A.
, 2015
, “
On Improving Wave Energy Conversion, Part II: Development of Latching Control Technologies
,” Renewable Energy
,
75
, pp. 935
–944
.10.1016/j.renene.2014.09.04923.
Na
,
J.
,
Wang
,
B.
,
Li
,
G.
,
Zhan
,
S.
, and
He
,
W.
, 2019
, “
Nonlinear Constrained Optimal Control of Wave Energy Converters With Adaptive Dynamic Programming
,” IEEE Trans. Ind. Electron.
,
66
(10
), pp. 7904
–7915
.10.1109/TIE.2018.288072824.
Li
,
G.
, 2017
, “
Nonlinear Model Predictive Control of a Wave Energy Converter Based on Differential Flatness Parameterisation
,” Int. J. Control
,
90
(1
), pp. 68
–77
.10.1080/00207179.2015.108817325.
Merigaud
,
A. P. L.
, and
Ringwood
,
J. V.
, 2018
, “
Improving the Computational Performance of Non-Linear Pseudo-Spectral Control of Wave Energy Converters
,” IEEE Trans. Sustainable Energy
,
9
(3
), pp. 1419
–1426
.10.1109/TSTE.2017.278604526.
Li
,
G.
, and
Belmont
,
M. R.
, 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
.10.1016/j.renene.2014.03.07027.
Richter
,
M.
,
Magana
,
M. E.
,
Sawodny
,
O.
, and
Brekken
,
T. K.
, 2013
, “
Nonlinear Model Predictive Control of a Point Absorber Wave Energy Converter
,” IEEE Trans. Sustainable Energy
,
4
(1
), pp. 118
–126
.10.1109/TSTE.2012.220292928.
Nguyen
,
H. N.
,
Sabiron
,
G.
,
Tona
,
P.
,
Kramer
,
M. M.
, and
Sanchez
,
E. V.
, 2016
, “
Experimental Validation of a Nonlinear MPC Strategy for a Wave Energy Converter Prototype
,” ASME
Paper No. OMAE2016-54455.10.1115/OMAE2016-5445529.
Son
,
D.
, and
Yeung
,
R. W.
, 2017
, “
Optimizing Ocean-Wave Energy Extraction of a Dual Coaxial-Cylinder WEC Using Nonlinear Model Predictive Control
,” Appl. Energy
,
187
, pp. 746
–757
.10.1016/j.apenergy.2016.11.06830.
Secord
,
T. W.
,
Louwagie
,
T. R.
, and
Kopas
,
R. J.
, 2020
, “
Design of Discretely Tunable Resonant Actuators Using Additive Inertial Units
,” ASME J. Dyn. Syst., Meas., Control
,
142
(3
), p. 031009
.10.1115/1.404556231.
Yan
,
Z.
,
Yu
,
V.
,
Shaltout
,
M. L.
,
Cheong
,
M. C.
, and
Chen
,
D.
, 2016
, “
Maximizing Wind Energy Capture for Speed-Constrained Wind Turbines During Partial Load Operation
,” ASME J. Dyn. Syst., Meas., Control
,
138
(9
), p. 091014
.10.1115/1.403390632.
Nielsen
,
S. R.
,
Zhou
,
Q.
,
Kramer
,
M. M.
,
Basu
,
B.
, and
Zhang
,
Z.
, 2013
, “
Optimal Control of Nonlinear Wave Energy Point Converters
,” Ocean Eng.
,
72
, pp. 176
–187
.10.1016/j.oceaneng.2013.06.02933.
Bacelli
,
G.
,
Genest
,
R.
, and
Ringwood
,
J. V.
, 2015
, “
Nonlinear Control of Flap-Type Wave Energy Converter With a Non-Ideal Power Take-Off System
,” Annu. Rev. Control
,
40
, pp. 116
–126
.10.1016/j.arcontrol.2015.09.00634.
Faedo
,
N.
,
Scarciotti
,
G.
,
Astolfi
,
A.
, and
Ringwood
,
J. V.
, 2021
, “
Nonlinear Energy-Maximizing Optimal Control of Wave Energy Systems: A Moment-Based Approach
,” IEEE Trans. Control Syst. Technol.
,
29
(6
), pp. 2533
–2547
.10.1109/TCST.2020.304722935.
Moretti
,
G.
,
Zaccarian
,
L.
, and
Blanchini
,
F.
, 2021
, “
Quadratic Constrained Periodic Optimization for Bandlimited Linear Systems Via the Fourier-Based Method
,” ASME J. Dyn. Syst., Meas., Control
,
143
(6
), p. 061005
.10.1115/1.404954136.
La
,
V. D.
, 2021
, “
Upper Bound of Power Harvested by an On-Off Electrical Damping in a State Space System
,” ASME J. Dyn. Syst., Meas., Control
,
143
(8
), p. 084502
.10.1115/1.405040637.
Wang
,
J.
, 2021
, “
Optimal Design for Energy Harvesting Vibration Absorbers
,” ASME J. Dyn. Syst., Meas., Control
,
143
(5
), p. 051008
.10.1115/1.404923538.
Do
,
K. D.
, 2022
, “
Nonlinear Control With Wave Observer to Maximize Harvested Power for Point Absorber Wave Energy Converters
,” Asian J. Control
,
24
(1
), pp. 16
–45
.10.1002/asjc.246139.
Krstic
,
M.
,
Kanellakopoulos
,
I.
, and
Kokotovic
,
P.
, 1995
, Nonlinear and Adaptive Control Design
,
Wiley
,
New York
.40.
Do
,
K. D.
, 2019
, “
Forwarding Control Design for Strict-Feedforward Systems
,” ASME J. Dyn. Syst., Meas., Control
,
141
(8
), p. 081010
.10.1115/1.404288141.
Fusco
,
F.
, and
Ringwood
,
J. V.
, 2014
, “
Robust Control of Wave Energy Converters
,” Proceedings of the 2014 IEEE International Conference on Control Applications
, Juan Les Antibes, France, Oct. 8–10, pp. 292
–297
.10.1109/CCA.2014.698136142.
Falnes
,
J.
, 2002
, Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-Energy Extraction
,
Cambridge University Press
,
Cambridge, UK
.43.
Do
,
K. D.
, 2010
, “
Control of Nonlinear Systems With Output Tracking Error Constraints and Its Application to Magnetic Bearings
,” Int. J. Control
,
83
(6
), pp. 1199
–1216
.10.1080/0020717100366482844.
Krstic
,
M.
, and
Li
,
Z. H.
, 1998
, “
Inverse Optimal Design of Input-to-State Stabilizing Nonlinear Controllers
,” IEEE Trans. Autom. Control
,
43
(3
), pp. 336
–350
.10.1109/9.66158945.
Faltinsen
,
O.
, 1990
, Sea Loads on Ships and Offshore Structures
,
Cambridge University Press
,
Cambridge, UK
.46.
Morison
,
J. R.
,
Johnson
,
J. W.
, and
Schaaf
,
S. A.
, 1950
, “
The Force Exerted by Surface Waves on Piles
,” J. Pet. Technol.
,
2
(5
), pp. 149
–154
.10.2118/950149-G47.
Cummins
,
W. E.
, 1962
, “
The Impulse Response Function and Ship Motions
,” Symposium on Ship Theory
,
Hamburg, Germany
, Jan. 25–27, pp. 101
–109
.http://hdl.handle.net/1721.3/4904948.
Ekergård
,
B.
, 2013
, “
Full Scale Application of Permanent Magnet Electromagnetic Energy Converters: From Nd2Fe14B to Ferrite
,” Ph.D. thesis
,
Uppsala University
,
Uppsala, Sweden
.https://www.divaportal.org/smash/get/diva2:647550/FULLTEXT01.pdf49.
Fossen
,
T. I.
, 1994
, Guidance and Control of Ocean Vehicles
,
Wiley, Hoboken, NJ
.50.
Niedzwecki
,
J. M.
, and
Liagre
,
P. Y. F.
, 2003
, “
System Identification of Distributed-Parameter Marine Riser Models
,” Ocean Eng.
,
30
(11
), pp. 1387
–1415
.10.1016/S0029-8018(02)00110-5Copyright © 2023 by ASME
You do not currently have access to this content.
