# Multiresonant Feedback Control of a Three-Degree-of-Freedom Wave Energy Converter

## Abstract

For a three-degree-of-freedom wave energy converter (heave, pitch, and surge), the equations of motion could be coupled depending on the buoy shape. This paper presents a multiresonant feedback control, in a general framework, for this type of a wave energy converter that is modeled by linear time invariant dynamic systems. The proposed control strategy finds the optimal control in the sense that it computes the control based on the complex conjugate criteria. This control strategy is relatively easy to implement since it is a feedback control in the time domain that requires only measurements of the buoy motion. Numerical tests are presented for two different buoy shapes: a sphere and a cylinder. Regular, Bretschnieder, and Ochi-Hubble waves are tested. Simulation results show that the proposed controller harvests energy in the pitch-surge-heave modes that is about three times the energy that can be harvested using a heave-only device. In conclusion, this multiresonant control can also be used to shift the energy harvesting between the coupled modes, which can be exploited to eliminate one of the actuators while maintaining about the same level of energy harvesting.

- Authors:

- Michigan Technological Univ., Houghton, MI (United States)
- 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 National Nuclear Security Administration (NNSA); USDOE Office of Energy Efficiency and Renewable Energy (EERE)

- OSTI Identifier:
- 1492375

- Report Number(s):
- SAND-2018-12236J

Journal ID: ISSN 1949-3029; 669145

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- IEEE Transactions on Sustainable Energy

- Additional Journal Information:
- Journal Volume: 8; Journal Issue: 4; Journal ID: ISSN 1949-3029

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; multi resonant control; three degrees of freedom WEC; wave energy conversion

### Citation Formats

```
Abdelkhalik, Ossama, Zou, Shangyan, Robinett, Rush D., Bacelli, Giorgio, Wilson, David G., Coe, Ryan, and Korde, Umesh. Multiresonant Feedback Control of a Three-Degree-of-Freedom Wave Energy Converter. United States: N. p., 2017.
Web. doi:10.1109/TSTE.2017.2692647.
```

```
Abdelkhalik, Ossama, Zou, Shangyan, Robinett, Rush D., Bacelli, Giorgio, Wilson, David G., Coe, Ryan, & Korde, Umesh. Multiresonant Feedback Control of a Three-Degree-of-Freedom Wave Energy Converter. United States. doi:10.1109/TSTE.2017.2692647.
```

```
Abdelkhalik, Ossama, Zou, Shangyan, Robinett, Rush D., Bacelli, Giorgio, Wilson, David G., Coe, Ryan, and Korde, Umesh. Mon .
"Multiresonant Feedback Control of a Three-Degree-of-Freedom Wave Energy Converter". United States. doi:10.1109/TSTE.2017.2692647. https://www.osti.gov/servlets/purl/1492375.
```

```
@article{osti_1492375,
```

title = {Multiresonant Feedback Control of a Three-Degree-of-Freedom Wave Energy Converter},

author = {Abdelkhalik, Ossama and Zou, Shangyan and Robinett, Rush D. and Bacelli, Giorgio and Wilson, David G. and Coe, Ryan and Korde, Umesh},

abstractNote = {For a three-degree-of-freedom wave energy converter (heave, pitch, and surge), the equations of motion could be coupled depending on the buoy shape. This paper presents a multiresonant feedback control, in a general framework, for this type of a wave energy converter that is modeled by linear time invariant dynamic systems. The proposed control strategy finds the optimal control in the sense that it computes the control based on the complex conjugate criteria. This control strategy is relatively easy to implement since it is a feedback control in the time domain that requires only measurements of the buoy motion. Numerical tests are presented for two different buoy shapes: a sphere and a cylinder. Regular, Bretschnieder, and Ochi-Hubble waves are tested. Simulation results show that the proposed controller harvests energy in the pitch-surge-heave modes that is about three times the energy that can be harvested using a heave-only device. In conclusion, this multiresonant control can also be used to shift the energy harvesting between the coupled modes, which can be exploited to eliminate one of the actuators while maintaining about the same level of energy harvesting.},

doi = {10.1109/TSTE.2017.2692647},

journal = {IEEE Transactions on Sustainable Energy},

number = 4,

volume = 8,

place = {United States},

year = {2017},

month = {4}

}

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Web of Science

#### Figures / Tables:

Works referencing / citing this record:

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

journal, January 2018

- Abdelkhalik, Ossama; Zou, Shangyan; Robinett, Rush
- Journal of Dynamic Systems, Measurement, and Control, Vol. 140, Issue 7

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*