WaveBot

2025

1. System identification techniques applied to a laboratory scale WEC point absorber

   Bret Bosma, Courtney Beringer, Ryan Coe, Giorgio Bacelli, Daniel Gaebele, Dominic Forbush, and Bryson Robertson

   In Proceedings of the European Wave and Tidal Energy Conference (EWTEC2025), Oct 2025

   Abs DOI Bib HTML

   Control is a necessary and challenging task in maximizing the energy harvesting from WECs. Tuning controllers using a brute force method can be time consuming and inefficient. This paper describes a system identification technique for impedance matching used to inform a proportional integral (PI) control methodology implemented on the Lab Upgrade Point Absorber (LUPA) WEC. Testing at the O.H. Hinsdale Wave Research Laboratory at Oregon State University with LUPA is detailed outlining the identification procedure using multisine bandlimited white noise to generate an intrinsic impedance model of the WEC. Validation tests are then described applying the resulting control strategy. Results summarize the average power output for four regular wave cases with a matrix of damping and stiffness values centered on the impedance matching results. The proposed control methodology and tuning process has the potential to streamline the maximum power generation from WECs. The paper also gives more insight into the characterization of the LUPA device and will help researchers better take advantage of the open-source experimental model for future research.

   @inproceedings{Bosma:2025aa,
     address = {Madeira, Portugla},
     author = {Bosma, Bret and Beringer, Courtney and Coe, Ryan and Bacelli, Giorgio and Gaebele, Daniel and Forbush, Dominic and Robertson, Bryson},
     booktitle = {{Proceedings of the European Wave and Tidal Energy Conference (EWTEC2025)}},
     date-added = {2025-10-24 09:37:57 -0600},
     date-modified = {2025-10-24 09:41:47 -0600},
     doi = {10.36688/ewtec-2025-826},
     month = oct,
     title = {System identification techniques applied to a laboratory scale WEC point absorber},
     url = {https://doi.org/10.36688/ewtec-2025-826},
     volume = {16},
     year = {2025},
     bdsk-url-1 = {https://doi.org/10.36688/ewtec-2025-826}
   }

2. Streamlined Experimental Approach to System Identification of WEC Dynamics and Excitation Characteristics

   Daniel Gaebele, Ryan Coe, Giorgio Bacelli, Dominic Forbush, Bret Bosma, Courtney Beringer, Bryson Robertson, and Pedro Lomonaco

   In International Conference on Ocean, Offshore and Arctic Engineering (OMAE2025), Jun 2025

   Abs DOI Bib HTML

   Understanding the dynamics of wave energy converters (WECs) is crucial for optimizing their design and performance. Empirically-based modeling can capture complex dynamics that are otherwise difficult to model with first principles, however collecting empirical test data typically involves long, costly testing campaigns. In this study we present the system identification and validation of a multi-input, single-output model of the Lab Upgrade Point Absorber (LUPA). The total testing duration of approximately 2 hours demonstrates significant efficiency compared to traditional week-long testing campaigns. We use a single experimental dataset to derive both the excitation transfer function and intrinsic admittance transfer function, which we express in a non-parametric form relative to the power take off (PTO) degree of freedom (DOF). The dataset contains a series of six trials, with two distinct power levels in the multisine excitation signals for each input. The inputs are the PTO force signal for active actuation and the concurrently generated irregular waves, implemented with white noise (WN) and pink noise (PN) spectra, respectively. For each power level we implemented the input signals with three different phase vectors. Validation experiments showed good agreement (approx. 70% goodness-of-fit) with the identified models, indicating the effectiveness of the approach.

   @inproceedings{Gaebele:2025ab,
     address = {Vancouver, British Columbia, Canada},
     author = {Gaebele, Daniel and Coe, Ryan and Bacelli, Giorgio and Forbush, Dominic and Bosma, Bret and Beringer, Courtney and Robertson, Bryson and Lomonaco, Pedro},
     bibtex_show = true,
     booktitle = {International Conference on Ocean, Offshore and Arctic Engineering (OMAE2025)},
     date-added = {2025-01-14 10:06:04 -0700},
     date-modified = {2025-10-02 07:37:41 -0600},
     doi = {10.1115/OMAE2025-156997},
     eprint = {https://asmedigitalcollection.asme.org/OMAE/proceedings-pdf/OMAE2025/88940/V005T09A055/7531858/v005t09a055-omae2025-156997.pdf},
     month = jun,
     pages = {V005T09A055},
     publisher = {ASME},
     series = {International Conference on Offshore Mechanics and Arctic Engineering},
     title = {Streamlined Experimental Approach to System Identification of WEC Dynamics and Excitation Characteristics},
     url = {https://doi.org/10.1115/OMAE2025-156997},
     volume = {Volume 5: Ocean Renewable Energy},
     year = {2025},
     bdsk-url-1 = {https://doi.org/10.1115/OMAE2025-156997}
   }

3. Real-Time Sea State Estimation for Wave Energy Converter Control via Machine Learning

   Tanvir Alam Shifat, Ryan Coe, Giorgio Bacelli, and Ted Brekken

   Applied Sciences, Jun 2025

   Abs DOI Bib HTML

   Wave energy converters (WECs) harness the untapped power of ocean waves to generate renewable energy, offering a promising solution to sustainable energy. An optimal WEC control strategy is essential to maximize power capture that dynamically adjusts system parameters in response to rapidly changing sea states. This study presents a novel control approach that leverages neural networks to estimate sea states from onboard WEC measurements such as position, velocity, and force. Using a point absorber WEC device as a test platform, our proposed approach estimates sea states in real-time and subsequently adjusts PID controller gains to maximize energy extraction. Simulation results across diverse sea conditions demonstrate that our strategy eliminates the need for external wave monitoring equipment while maintaining power capture efficiency. The results show that our neural network-based control technique can improve power capture by 25.6% while significantly reducing system complexity. This approach offers a practical alternative for WEC deployments where direct wave measurements are either infeasible or cost prohibitive.

   @article{Shifat:2025aa,
     article-number = {5772},
     author = {Shifat, Tanvir Alam and Coe, Ryan and Bacelli, Giorgio and Brekken, Ted},
     date-added = {2025-10-24 09:46:28 -0600},
     date-modified = {2025-10-24 09:47:05 -0600},
     doi = {10.3390/app15105772},
     issn = {2076-3417},
     journal = {Applied Sciences},
     number = {10},
     title = {Real-Time Sea State Estimation for Wave Energy Converter Control via Machine Learning},
     url = {https://www.mdpi.com/2076-3417/15/10/5772},
     volume = {15},
     year = {2025},
     bdsk-url-1 = {https://www.mdpi.com/2076-3417/15/10/5772},
     bdsk-url-2 = {https://doi.org/10.3390/app15105772}
   }

2023

1. Useful power maximization for wave energy converters

   Ryan G. Coe, and Giorgio Bacelli

   Energies, Jun 2023

   Abs DOI Bib HTML

   Wave energy converters (WECs) have enormous potential in providing clean renewable energy with high levels of predictability [...]

   @article{Coe:2023ac,
     article-number = {529},
     author = {Coe, Ryan G. and Bacelli, Giorgio},
     bibtex_show = true,
     date-added = {2022-11-01 08:14:47 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.3390/en16010529},
     issn = {1996-1073},
     journal = {Energies},
     number = {1},
     title = {Useful power maximization for wave energy converters},
     url = {https://www.mdpi.com/1996-1073/16/1/529},
     volume = {16},
     year = {2023},
     bdsk-url-1 = {https://www.mdpi.com/1996-1073/16/1/529},
     bdsk-url-2 = {https://doi.org/10.3390/en16010529}
   }

2022

1. Self-tuning, load-mitigating feedback control of a 3-DOF point absorber

   Dominic D. Forbush, Giorgio Bacelli, and Ryan G. Coe

   International Marine Energy Journal, Jun 2022

   Abs DOI Bib HTML

   A simple, self-tuning multi-objective controller is demonstrated in simulation for a 3-DOF (surge, heave, pitch) point absorber. In previous work, the proposed control architecture has been shown to be effective in experiments for a variety of device archetypes for the single objective of the maximization of electrical power capture: here this architecture is extended to reduce device loading as well. In particular, PTO actuation forces and the minimization of fatigue damage (determined from the sum of wave-exerted and PTO forces) are considered as additional objectives for the self-tuning controller. Because the power surface is consistently fairly flat in the vicinity of control parameters that maximize power capture in contrasting sea-states (i.e., WECs are often broad banded), it is found to be generally possible to mitigate either fatigue damage or PTO load. However, PTO load is found to contradict with fatigue damage in some sea-states, limiting the efficacy of control objectives that attempt to mitigate both simultaneously. Additionally, coupling between the surge and pitch DOFs also limits the extent to which fatigue damage can be mitigated for both DOFs in some sea-states. Because control objectives can be considered a function of the sea-state (e.g., load mitigation may not be a concern until the sea is sufficiently large) a simple transition strategy is proposed and demonstrated. This transition strategy is found to be effective with some caveats: firstly, it cannot circumvent the aforementioned objective contradictions. Secondly, the thresholds at which objective transitions occur are somewhat exceeded: in this respect they cannot be considered as constraints and must be selected more conservatively. Finally, selection of well-performing transition parameters can be a function of sea-state. While a simple selection procedure is proposed, it is non-optimal, and a more robust selection procedure is suggested for future work.

   @article{Forbush:2022ab,
     author = {Forbush, Dominic D. and Bacelli, Giorgio and Coe, Ryan G.},
     bibtex_show = true,
     date-added = {2021-03-27 14:42:36 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.36688/imej.5.23-35},
     journal = {International Marine Energy Journal},
     month = jun,
     number = {1},
     pages = {23-35},
     title = {Self-tuning, load-mitigating feedback control of a {3-DOF} point absorber},
     url = {https://marineenergyjournal.org/imej/article/view/68},
     volume = {5},
     year = {2022},
     bdsk-url-1 = {https://marineenergyjournal.org/imej/article/view/68},
     bdsk-url-2 = {https://doi.org/10.36688/imej.5.23-35}
   }

2021

1. A practical approach to wave energy modeling and control

   Ryan G. Coe, Giorgio Bacelli, and Dominic Forbush

   Renewable and Sustainable Energy Reviews, Jun 2021

   Abs DOI Bib HTML Code

   The potential for control design to dramatically improve the economic viability of wave energy has generated a great deal of interest and excitement. However, for a number of reasons, the promised benefits from better control designs have yet to be widely realized by wave energy devices and wave energy remains a relatively nascent technology. This brief paper summarizes a simple, yet powerful approach to wave energy dynamics modeling, and subsequent control design based on impedance matching. Our approach leverages the same concepts that are exploited by a simple FM radio to achieve a feedback controller for wave energy devices that approaches optimal power absorption. If fully utilized, this approach can deliver immediate and consequential reductions to the cost of wave energy. Additionally, this approach provides the necessary framework for control co-design of a wave energy converter, in which an understanding of the control logic allows for synchronous design of the device control system and hardware.

   @article{Coe:2021ab,
     author = {Coe, Ryan G. and Bacelli, Giorgio and Forbush, Dominic},
     bibtex_show = true,
     date-added = {2020-10-07 12:35:05 -0600},
     date-modified = {2025-08-20 17:35:16 -0600},
     doi = {10.1016/j.rser.2021.110791},
     issn = {1364-0321},
     journal = {Renewable and Sustainable Energy Reviews},
     keywords = {Wave energy converter (WEC), Impedance matching, Control, Marine renewable energy, Power maximization},
     pages = {110791},
     title = {{A practical approach to wave energy modeling and control}},
     url = {https://www.sciencedirect.com/science/article/pii/S1364032121000861},
     volume = {142},
     year = {2021},
     bdsk-url-1 = {https://www.techrxiv.org/articles/preprint/A_practical_approach_to_wave_energy_modeling_and_control/12939488},
     bdsk-url-2 = {https://doi.org/10.36227/techrxiv.12939488.v1},
     bdsk-url-3 = {https://www.sciencedirect.com/science/article/pii/S1364032121000861},
     bdsk-url-4 = {https://doi.org/10.1016/j.rser.2021.110791}
   }

2020

1. Feedback Resonating Control for a Wave Energy Converter

   Giorgio Bacelli, Victor Nevarez, Ryan G. Coe, and David G. Wilson

   IEEE Transactions on Industry Applications, Mar 2020

   Abs DOI Bib HTML

   Through the use of advanced control techniques, wave energy converters (WECs) can achieve substantial increases in energy absorption. The motion of the WEC device is a significant contribution to the energy absorbed by the device. Reactive (complex conjugate) control maximizes the energy absorption due to the impedance matching. The issue with complex conjugate control is that, in general, the controller is noncausal, which requires prediction of the incoming waves. This article explores the potential of employing system identification techniques to build a causal transfer function that approximates the complex conjugate controller over a finite frequency band of interest. This approach is quite viable given the band-limited nature of ocean waves. The resulting controller is stable, and the average efficiency of the power captured by the causal controller in realistic ocean waves is 99%, when compared to the noncausal complex conjugate.

   @article{Bacelli:2020aa,
     author = {Bacelli, Giorgio and Nevarez, Victor and G. Coe, Ryan and G. Wilson, David},
     bibtex_show = true,
     date-added = {2020-10-07 12:37:21 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.1109/TIA.2019.2958018},
     groups = {AdvWecCntrls Pubs},
     issn = {1939-9367},
     journal = {IEEE Transactions on Industry Applications},
     keywords = {Mathematical model;Impedance;Force;Impedance matching;Iron;Absorption;Transfer functions;Control systems;energy conversion;identifi-cation;impedance matching;resonance},
     month = mar,
     number = {2},
     pages = {{1862-1868}},
     title = {Feedback Resonating Control for a Wave Energy Converter},
     url = {https://ieeexplore.ieee.org/document/8926523},
     volume = {56},
     year = {2020},
     bdsk-url-1 = {https://ieeexplore.ieee.org/document/8926523},
     bdsk-url-2 = {https://doi.org/10.1109/TIA.2019.2958018}
   }

2. A Self-Tuning WEC Controller For Changing Sea States

   Dominic D. Forbush, Giorgio Bacelli, Steven J. Spencer, and Ryan G. Coe

   IFAC-PapersOnLine, Berlin, Germany, Mar 2020

   21th IFAC World Congress

   Abs DOI Bib HTML Slides

   A self-tuning proportional-integral control law prescribing motor torques was tested in experiment on a three degree-of-freedom wave energy converter. The control objective was to maximize electrical power. The control law relied upon an identified model of device intrinsic impedance to generate a frequency-domain estimate of the wave-induced excitation force and measurements of device velocities. The control law was tested in irregular sea-states that evolved over hours (a rapid, but realistic time-scale) and that changed instantly (an unrealistic scenario to evaluate controller response). For both cases, the controller converges to gains that closely approximate the post-calculated optimal gains for all degrees of freedom. Convergence to near-optimal gains occurred reliably over a sufficiently short time for realistic sea states. In addition, electrical power was found to be relatively insensitive to gain tuning over a broad range of gains, implying that an imperfectly tuned controller does not result in a large penalty to electrical power capture. An extension of this control law that allows for adaptation to a changing device impedance model over time is proposed for long-term deployments, as well as an approach to explicitly handle constraints within this architecture.

   @article{Forbush:2020aa,
     address = {Berlin, Germany},
     author = {Forbush, Dominic D. and Bacelli, Giorgio and Spencer, Steven J. and Coe, Ryan G.},
     bibtex_show = true,
     booktitle = {Proceedings of the 21st IFAC World Congress},
     date-added = {2020-10-07 12:35:17 -0600},
     date-modified = {2025-10-02 07:51:20 -0600},
     doi = {10.1016/j.ifacol.2020.12.1185},
     groups = {AdvWecCntrls Pubs},
     issn = {2405-8963},
     journal = {IFAC-PapersOnLine},
     keywords = {Wave energy, linear control, self-tuning control, spectral analysis, feedback control},
     location = {Berlin, Germany},
     note = {21th IFAC World Congress},
     number = {2},
     organization = {International Federation of Automatic Control},
     pages = {12307-12312},
     title = {A Self-Tuning {WEC} Controller For Changing Sea States},
     url = {https://www.sciencedirect.com/science/article/pii/S2405896320315780},
     volume = {53},
     year = {2020},
     bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S2405896320315780},
     bdsk-url-2 = {https://doi.org/10.1016/j.ifacol.2020.12.1185}
   }

2019

1. Wave tank and bench-top control testing of a wave energy converter

   Giorgio Bacelli, Steven J. Spencer, David C. Patterson, and Ryan G. Coe

   Applied Ocean Research, Mar 2019

   Abs DOI Bib HTML

   An increasing number of experiments are being conducted to study the design and performance of wave energy converters. Often in these tests, a real-time realization of prospective control algorithms is applied in order to assess and optimize energy absorption as well as other factors. This paper details the design and execution of an experiment for evaluating the capability of a model-scale WEC to execute basic control algorithms. Model-scale hardware, system, and experimental design are considered, with a focus on providing an experimental setup capable of meeting the dynamic requirements of a control system. To more efficiently execute such tests, a dry bench testing method is proposed and utilized to allow for controller tuning and to give an initial assessment of controller performance; this is followed by wave tank testing. The trends from the dry bench test and wave tank test results show good agreement with theory and confirm the ability of a relatively simple feedback controller to substantially improve energy absorption. Additionally, the dry bench testing approach is shown to be an effective and efficient means of designing and testing both controllers and actuator systems for wave energy converters.

   @article{Bacelli:2019aa,
     author = {Bacelli, Giorgio and Spencer, Steven J. and Patterson, David C. and Coe, Ryan G.},
     bibtex_show = true,
     date-added = {2020-10-07 12:37:21 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.1016/j.apor.2018.09.009},
     file = {:Bacelli2019.pdf:PDF},
     groups = {AdvWecCntrls Pubs},
     issn = {0141-1187},
     journal = {Applied Ocean Research},
     keywords = {Wave energy converter (WEC), Control, Wave tank, Model-scale testing},
     owner = {rcoe},
     pages = {351 - 366},
     timestamp = {2018.12.16},
     title = {Wave tank and bench-top control testing of a wave energy converter},
     url = {http://www.sciencedirect.com/science/article/pii/S0141118717307484},
     volume = {86},
     year = {2019},
     bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0141118717307484},
     bdsk-url-2 = {https://doi.org/10.1016/j.apor.2018.09.009}
   }

2017

1. A comparison of control strategies for wave energy converters

   Ryan G. Coe, Giorgio Bacelli, David G. Wilson, Ossama Abdelkhalik, Umesh A. Korde, and Rush D. Robinett III

   International Journal of Marine Energy, Mar 2017

   Abs DOI Bib HTML

   In this study, we employ a numerical model to compare the performance of a number of wave energy converter control strategies. The controllers selected for evaluation span a wide range in their requirements for implementation. Each control strategy is evaluated using a single numerical model with a set of sea states to represent a deployment site off the coast of Newport, OR. A number of metrics, ranging from power absorption to kinematics, are employed to provide a comparison of each control strategy’s performance that accounts for both relative benefits and costs. The results show a wide range of performances from the different controllers and highlight the need for a holistic design approach which considers control design as a parallel component within the larger process WEC design.

   @article{Coe:2017aa,
     author = {Coe, Ryan G. and Bacelli, Giorgio and Wilson, David G. and Abdelkhalik, Ossama and Korde, Umesh A. and III, Rush D. Robinett},
     bibtex_show = true,
     date-added = {2020-10-07 12:35:05 -0600},
     date-modified = {2025-08-21 12:47:26 -0600},
     doi = {10.1016/j.ijome.2017.11.001},
     groups = {AdvWecCntrls Pubs},
     issn = {2214-1669},
     journal = {International Journal of Marine Energy},
     keywords = {Wave energy, Control, Dynamics},
     number = {Supplement C},
     pages = {45 - 63},
     title = {A comparison of control strategies for wave energy converters},
     url = {http://www.sciencedirect.com/science/article/pii/S2214166917300905},
     volume = {20},
     year = {2017},
     bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S2214166917300905},
     bdsk-url-2 = {https://doi.org/10.1016/j.ijome.2017.11.001}
   }

2. System Identification of a Heaving Point Absorber: Design of Experiment and Device Modeling

   Giorgio Bacelli, Ryan G. Coe, David Patterson, and David Wilson

   Energies, Mar 2017

   Abs DOI Bib HTML

   Empirically based modeling is an essential aspect of design for a wave energy converter. Empirically based models are used in structural, mechanical and control design processes, as well as for performance prediction. Both the design of experiments and methods used in system identification have a strong impact on the quality of the resulting model. This study considers the system identification and model validation process based on data collected from a wave tank test of a model-scale wave energy converter. Experimental design and data processing techniques based on general system identification procedures are discussed and compared with the practices often followed for wave tank testing. The general system identification processes are shown to have a number of advantages, including an increased signal-to-noise ratio, reduced experimental time and higher frequency resolution. The experimental wave tank data is used to produce multiple models using different formulations to represent the dynamics of the wave energy converter. These models are validated and their performance is compared against one another. While most models of wave energy converters use a formulation with surface elevation as an input, this study shows that a model using a hull pressure measurement to incorporate the wave excitation phenomenon has better accuracy.

   @article{Bacelli:2017aa,
     author = {Bacelli, Giorgio and Coe, Ryan G. and Patterson, David and Wilson, David},
     bibtex_show = true,
     date-added = {2020-10-07 12:37:21 -0600},
     date-modified = {2025-06-25 12:01:07 -0600},
     doi = {10.3390/en10040472},
     file = {Bacelli2017a.pdf:pdfs\\Bacelli2017a.pdf:PDF;Bacelli2017a.pdf:.\\pdfs\\Bacelli2017a.pdf:PDF},
     groups = {AdvWecCntrls Pubs, SID},
     issn = {1996-1073},
     issue = {4},
     journal = {Energies},
     number = {10},
     owner = {rcoe},
     pages = {472},
     publisher = {Multidisciplinary Digital Publishing Institute},
     timestamp = {2017.02.19},
     title = {System Identification of a Heaving Point Absorber: Design of Experiment and Device Modeling},
     url = {http://www.mdpi.com/1996-1073/10/4/472},
     volume = {10},
     year = {2017},
     bdsk-url-1 = {http://www.mdpi.com/1996-1073/10/4/472},
     bdsk-url-2 = {https://doi.org/10.3390/en10040472}
   }