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Technical Brief

Control of Three-Degree-of-Freedom Wave Energy Converters Using Pseudo-Spectral Methods

[+] Author and Article Information
Ossama Abdelkhalik

Department of Mechanical Engineering and Engineering Mechanics, Michigan Tech University, Houghton, Michigan 49931
ooabdelk@mtu.edu

Shangyan Zou

Department of Mechanical Engineering and Engineering Mechanics, Michigan Tech University, Houghton, Michigan 49931
szou2@mtu.edu

Rush Robinett

Department of Mechanical Engineering and Engineering Mechanics, Michigan Tech University, Houghton, Michigan 49931
rdrobine@mtu.edu

Giorgio Bacelli

Water Power Technologies and Electrical Sciences & Experiments Departments, Sandia National Labs, Albuquerque, New Mexico 87185
gbacell@sandia.gov

David G. Wilson

Water Power Technologies and Electrical Sciences & Experiments Departments, Sandia National Labs, Albuquerque, New Mexico 87185
dwilso@sandia.gov

Ryan Coe

Water Power Technologies and Electrical Sciences & Experiments Departments, Sandia National Labs, Albuquerque, New Mexico 87185
rcoe@sandia.gov

1Corresponding author.

ASME doi:10.1115/1.4038860 History: Received December 07, 2016; Revised December 20, 2017

Abstract

This paper presents a solution to the optimal control problem of a three-degree-of-freedom wave energy converter. 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 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.

Sandia National Laboratories (SNL)
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