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Title: Control of Three Degrees-of-Freedom Wave Energy Converters Using Pseudo-Spectral Methods

Abstract

This study presents a solution to the optimal control problem of a three degrees-of-freedom (3DOF) wave energy converter (WEC). The three modes are the heave, pitch, and surge. The dynamic model is characterized by a coupling between the pitch and surge modes, while the heave is decoupled. The heave, however, excites the pitch motion through nonlinear parametric excitation in the pitch mode. This paper uses Fourier series (FS) as basis functions to approximate the states and the control. A simplified model is first used where the parametric excitation term is neglected and a closed-form solution for the optimal control is developed. For the parametrically excited case, a sequential quadratic programming approach is implemented to solve for the optimal control numerically. Numerical results show that the harvested energy from three modes is greater than three times the harvested energy from the heave mode alone. Moreover, the harvested energy using a control that accounts for the parametric excitation is significantly higher than the energy harvested when neglecting this nonlinear parametric excitation term.

Authors:
 [1];  [1];  [1];  [2];  [2];  [2]
  1. Michigan Tech Univ., Houghton, MI (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Energy Efficiency and Renewable Energy (EERE), Wind and Water Technologies Office (EE-4W)
OSTI Identifier:
1485469
Report Number(s):
SAND-2018-12263J
Journal ID: ISSN 0022-0434; 669160
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Dynamic Systems, Measurement, and Control
Additional Journal Information:
Journal Volume: 140; Journal Issue: 7; Journal ID: ISSN 0022-0434
Publisher:
ASME
Country of Publication:
United States
Language:
English
Subject:
16 TIDAL AND WAVE POWER; Waves; Degrees of freedom; Optimization; Surges; Wave energy converters; Excitation; Optimal control; Fourier series; Dynamic models

Citation Formats

Abdelkhalik, Ossama, Zou, Shangyan, Robinett, III, Rush D., Bacelli, Giorgio, Wilson, David G., and Coe, Ryan Geoffrey. Control of Three Degrees-of-Freedom Wave Energy Converters Using Pseudo-Spectral Methods. United States: N. p., 2018. Web. doi:10.1115/1.4038860.
Abdelkhalik, Ossama, Zou, Shangyan, Robinett, III, Rush D., Bacelli, Giorgio, Wilson, David G., & Coe, Ryan Geoffrey. Control of Three Degrees-of-Freedom Wave Energy Converters Using Pseudo-Spectral Methods. United States. doi:10.1115/1.4038860.
Abdelkhalik, Ossama, Zou, Shangyan, Robinett, III, Rush D., Bacelli, Giorgio, Wilson, David G., and Coe, Ryan Geoffrey. Fri . "Control of Three Degrees-of-Freedom Wave Energy Converters Using Pseudo-Spectral Methods". United States. doi:10.1115/1.4038860. https://www.osti.gov/servlets/purl/1485469.
@article{osti_1485469,
title = {Control of Three Degrees-of-Freedom Wave Energy Converters Using Pseudo-Spectral Methods},
author = {Abdelkhalik, Ossama and Zou, Shangyan and Robinett, III, Rush D. and Bacelli, Giorgio and Wilson, David G. and Coe, Ryan Geoffrey},
abstractNote = {This study presents a solution to the optimal control problem of a three degrees-of-freedom (3DOF) wave energy converter (WEC). The three modes are the heave, pitch, and surge. The dynamic model is characterized by a coupling between the pitch and surge modes, while the heave is decoupled. The heave, however, excites the pitch motion through nonlinear parametric excitation in the pitch mode. This paper uses Fourier series (FS) as basis functions to approximate the states and the control. A simplified model is first used where the parametric excitation term is neglected and a closed-form solution for the optimal control is developed. For the parametrically excited case, a sequential quadratic programming approach is implemented to solve for the optimal control numerically. Numerical results show that the harvested energy from three modes is greater than three times the harvested energy from the heave mode alone. Moreover, the harvested energy using a control that accounts for the parametric excitation is significantly higher than the energy harvested when neglecting this nonlinear parametric excitation term.},
doi = {10.1115/1.4038860},
journal = {Journal of Dynamic Systems, Measurement, and Control},
number = 7,
volume = 140,
place = {United States},
year = {2018},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 1 work
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Figures / Tables:

Figure 1 Figure 1: Geometry of a 3-DoF cylindrical Buoy; MWL is the mean water level

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Works referenced in this record:

Heaving buoys, point absorbers and arrays
journal, January 2012

  • Falnes, Johannes; Hals, Jørgen
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 370, Issue 1959
  • DOI: 10.1098/rsta.2011.0249

A theory for wave-power absorption by oscillating bodies
journal, September 1976


Multi-resonant feedback control of heave wave energy converters
journal, November 2016


Model Predictive Control of parametric excited pitch-surge modes in wave energy converters
journal, September 2017


On Control of a Pitching and Surging Wave Energy Converter
journal, July 2011


Multiresonant Feedback Control of a Three-Degree-of-Freedom Wave Energy Converter
journal, October 2017

  • Abdelkhalik, Ossama; Zou, Shangyan; Robinett, Rush D.
  • IEEE Transactions on Sustainable Energy, Vol. 8, Issue 4
  • DOI: 10.1109/TSTE.2017.2692647

Comparison of latching control strategies for a heaving wave energy device in random sea
journal, July 2004


Power From Water Waves
journal, January 1981


Direct and indirect methods for trajectory optimization
journal, December 1992

  • von Stryk, O.; Bulirsch, R.
  • Annals of Operations Research, Vol. 37, Issue 1
  • DOI: 10.1007/BF02071065

Numerical Optimal Control of Wave Energy Converters
journal, April 2015

  • Bacelli, Giorgio; Ringwood, John V.
  • IEEE Transactions on Sustainable Energy, Vol. 6, Issue 2
  • DOI: 10.1109/TSTE.2014.2371536

Wave energy converter control by wave prediction and dynamic programming
journal, December 2012


Pseudospectral Methods for Infinite-Horizon Nonlinear Optimal Control Problems
journal, July 2008

  • Fahroo, Fariba; Ross, I. Michael
  • Journal of Guidance, Control, and Dynamics, Vol. 31, Issue 4
  • DOI: 10.2514/1.33117

Pseudospectral Methods for Infinite-Horizon Nonlinear Optimal Control Problems
conference, June 2012

  • Fahroo, Fariba; Ross, I.
  • AIAA Guidance, Navigation, and Control Conference and Exhibit
  • DOI: 10.2514/6.2005-6076

    Works referencing / citing this record:

    Direct and indirect methods for trajectory optimization
    journal, December 1992

    • von Stryk, O.; Bulirsch, R.
    • Annals of Operations Research, Vol. 37, Issue 1
    • DOI: 10.1007/bf02071065

    Comparison of latching control strategies for a heaving wave energy device in random sea
    journal, July 2004


    Model Predictive Control of parametric excited pitch-surge modes in wave energy converters
    journal, September 2017


    Multi-resonant feedback control of heave wave energy converters
    journal, November 2016


    Wave energy converter control by wave prediction and dynamic programming
    journal, December 2012


    A theory for wave-power absorption by oscillating bodies
    journal, September 1976


    On Control of a Pitching and Surging Wave Energy Converter
    journal, July 2011


    Heaving buoys, point absorbers and arrays
    journal, January 2012

    • Falnes, Johannes; Hals, Jørgen
    • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 370, Issue 1959
    • DOI: 10.1098/rsta.2011.0249

    Numerical Optimal Control of Wave Energy Converters
    journal, April 2015

    • Bacelli, Giorgio; Ringwood, John V.
    • IEEE Transactions on Sustainable Energy, Vol. 6, Issue 2
    • DOI: 10.1109/tste.2014.2371536

    Multiresonant Feedback Control of a Three-Degree-of-Freedom Wave Energy Converter
    journal, October 2017

    • Abdelkhalik, Ossama; Zou, Shangyan; Robinett, Rush D.
    • IEEE Transactions on Sustainable Energy, Vol. 8, Issue 4
    • DOI: 10.1109/tste.2017.2692647

    Power From Water Waves
    journal, January 1981


    Pseudospectral Methods for Infinite-Horizon Nonlinear Optimal Control Problems
    journal, July 2008

    • Fahroo, Fariba; Ross, I. Michael
    • Journal of Guidance, Control, and Dynamics, Vol. 31, Issue 4
    • DOI: 10.2514/1.33117