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Technical Brief

Control of Three Degrees-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, MI 49931
e-mail: ooabdelk@mtu.edu

Shangyan Zou, Rush Robinett

Department of Mechanical Engineering and Engineering,
Mechanics Michigan Tech University,
Houghton, MI 49931

Giorgio Bacelli, David Wilson, Ryan Coe

Water Power Technologies and
Electrical Sciences & Experiments,
Departments Sandia National Labs,
Albuquerque, NM 87185

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received December 7, 2016; final manuscript received December 20, 2017; published online January 19, 2018. Assoc. Editor: Yang Shi.

J. Dyn. Sys., Meas., Control 140(7), 074501 (Jan 19, 2018) (9 pages) Paper No: DS-16-1584; doi: 10.1115/1.4038860 History: Received December 07, 2016; Revised December 20, 2017

This paper 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.

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References

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Figures

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Fig. 2

Simulation environment diagram

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Fig. 7

Velocity of surge motion (m/s)

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Fig. 6

Velocity of pitch motion (rad/s)

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Fig. 1

Geometry of a 3DOF cylindrical Buoy; MWL is the mean water level

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Fig. 18

Control force in surge (U1) and pitch (U2) directions

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Fig. 19

Energy harvested in each of the three modes when buoy motion is constrained

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Fig. 20

The pitch motion in rad when the buoy is constrained

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Fig. 12

The Bretschneider wave amplitude

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Fig. 8

Energy extracted in pitch and surge compared to heave extracted energy

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Fig. 9

Control force (N) in pitch (U2) and surge (U1)

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Fig. 10

Velocity of pitch motion (rad/s)

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Fig. 11

Velocity of surge motion (m/s)

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Fig. 5

Control force (N) in pitch (U2) and surge (U1)

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Fig. 13

The total energy is more than six times the energy harvested in heave mode only, for a parametric excited WEC in a Bretschneider wave

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Fig. 3

The general overview of 1:17 scaled T3R2 WEC of Sandia National

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Fig. 14

Surge position in a Bretschneider wave

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Fig. 15

Pitch rotation in a Bretschneider wave

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Fig. 16

Surge velocity in a Bretschneider wave

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Fig. 17

Pitch angular velocity in a Bretschneider wave

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Fig. 4

Energy extracted in pitch and surge compared to heave extracted energy

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Fig. 21

Nonparametric excited WEC in a regular wave: Energy harvested using PS and NMPC controllers

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Fig. 22

Parametric excited WEC in a regular wave: Energy harvested using PS and NMPC controllers

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Fig. 23

Parametric excited WEC in an irregular wave: Energy harvested using PS and NMPC controllers

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Fig. 24

The approximation error for surge velocity with different constraint

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