This report outlines the development of load-mitigating feedback control for wave energy converters. 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 experiment 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. This controller is demonstrated for two similar, but distinct systems: one described by the identified linear models from physical testing of the WaveBot device, and another based upon a WEC-Sim simulation that expands upon boundary element method data from the WaveBot device. In both cases, because the power surface is consistently fairly flat in the vicinity of control parameters that maximize power capture in contrasting sea-states, it is found to be generally possible to mitigate either fatigue damage or PTO load. However, PTO load is found to conflict 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, this objective transition is too slow to act as a system constraint, and objective thresholds must thus be considered quite conservatively. Improvement of the adjustment strategy is demonstrated through the addition of an integral term. 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.
Interest in wave energy converters to provide autonomous power to various ocean-bound systems, such as autonomous underwater vehicles, sensor systems, and even aquaculture farms, has grown in recent years. The Monterey Bay Aquarium Research Institute has developed and deployed a small two-body point absorber wave energy device suitable to such needs. This paper provides a description of the system to support future open-source access to the device and further the general development of similar wave energy systems. Additionally, to support future control design and system modification efforts, a set of hydrodynamic models are presented and cross-compared. To test the viability of using a linear frequency-domain admittance model for controller tuning, the linear model is compared against four WEC-Sim models of increasing complexity. The linear frequency-domain model is found to be generally adequate for capturing system dynamics, as the model agreement is good and the degree of nonlinearity introduced in the WEC-Sim models is generally less than 2.5%.
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.
A passive yaw implementation is developed, validated, and explored for the WEC-Sim, an open-source wave energy converter modeling tool that works within MATLAB/Simulink. The Reference Model 5 (RM5) is selected for this investigation, and a WEC-Sim model of the device is modified to allow yaw motion. A boundary element method (BEM) code was used to calculate the excitation force coefficients for a range of wave headings. An algorithm was implemented in WEC-Sim to determine the equivalent wave heading from a body's instantaneous yaw angle and interpolate the appropriate excitation coefficients to ensure the correct time-domain excitation force. This approach is able to determine excitation force for a body undergoing large yaw displacement. For the mathematically simple case of regular wave excitation, the dynamic equation was integrated numerically and found to closely approximate the results from this implementation in WEC-Sim. A case study is presented for the same device in irregular waves. In this case, computation time is increased by 32x when this interpolation is performed at every time step. To reduce this expense, a threshold yaw displacement can be set to reduce the number of interpolations performed. A threshold of 0.01o was found to increase computation time by only 22x without significantly affecting time domain results. Similar amplitude spectra for yaw force and displacements are observed for all threshold values less than 1o, for which computation time is only increased by 2.2x.