Publications

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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.

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. 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.

For a heave-pitch-surge three-degrees-of-freedom wave energy converter, the heave mode is usually decoupled from the pitch-surge modes for small motions. The pitch-surge modes are usually coupled and are parametrically excited by the heave mode, depending on the buoy geometry. In this paper, a Model Predictive Control is applied to the parametric excited pitch-surge motion, while the heave motion is optimized independently. The optimality conditions are derived, and a gradient-based numerical optimization algorithm is used to search for the optimal control. Numerical tests are conducted for regular and Bretschneider waves. The results demonstrate that the proposed control can be implemented to harvest more than three times the energy that can be harvested using a heave-only wave energy converter. The energy harvested using a parametrically excited model is higher than that is harvested when using a linear model.

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Optimal control theory is applied to compute control for a single-degree-of-freedom heave wave energy converter. The goal is to maximize the energy extraction per cycle. Both constrained and unconstrained optimal control problems are presented. Both periodic and non-periodic excitation forces are considered. In contrast to prior work, it is shown that for this non-autonomous system, the optimal control, in general, includes both singular arc and bang-bang modes. Conditions that determine the switching times to/from the singular arc are derived. Simulation results show that the proposed optimal control solution matches the solution obtained using the complex conjugate control. A generic linear dynamic model is used in the simulations. The main advantage of the proposed control is that it finds the optimal control without the need for wave prediction; it only requires the knowledge of the excitation force and its derivatives at the current time.

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This report gives a brief discussion and examples on the topic of state estimation for wave energy converters (WECs). These methods are intended for use to enable real-time closed loop control of WECs.

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A linear dynamic model for a wave energy converter (WEC) has been developed based on the results of experimental wave tank testing. Based on this model, a model predictive control (MPC) strategy has been designed and implemented. To assess the performance of this control strategy, a deployment environment off the coast of Newport, OR has been selected and the controller has been used to simulate the WEC response in a set of irregular sea states. To better understand the influence of model accuracy on control performance, an uncertainty analysis has been performed by varying the parameters of the model used for the design of the controller (i.e. the control model), while keeping the WEC dynamic model employed in these simulations (i.e. the plant model) unaltered. The results of this study indicate a relative low sensitivity of the MPC control strategy to uncertainties in the controller model for the specific case studied here.

A study was performed to optimize the geometry of a point absorber style wave energy converter (WEC). An axisymmetric single-body device, moving in heave only, was considered. Design geometries, generated using a parametric definition, were optimized using genetic algorithms. Each geometry was analyzed using a boundary element model (BEM) tool to obtain corresponding frequency domain models. Based on these models, a pseudo-spectral method was applied to develop a control methodology for each geometry. The performance of each design was assessed using a Bretschneider sea state. The objective of optimization is to maximize harvested energy. In this preliminary investigation, a constraint is imposed on the the geometry to guarantee a linear dynamic model would be valid for all geometries generated by the optimization tool. Numerical results are presented for axisymmetric buoy shapes.

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Many of the control strategies for wave energy converters (WECs) that have been studied in the literature rely on the availability of estimates for either the wave elevation or the exciting force caused by the incoming wave; with the objective of addressing this issue, this paper presents the design of a state estimator for a WEC. In particular, the work described in this paper is based on an extended Kalman filter that uses measurements from pressure sensors located on the hull of the WEC to estimate the wave exciting force. Simulation results conducted on a heaving point absorber WEC shows that the extended Kalman filter provides a good estimation of the exciting force in the presence of measurement noise combined with a simplified model of the system, thus making it a suitable candidate for the implementation in an experimental set-up.

A model-scale wave tank test was conducted in the interest of improving control systems design of wave energy converters (WECs). The success of most control strategies is based directly upon the availability of a reduced-order model with the ability to capture the dynamics of the system with sufficient accuracy. For this reason, the test described in this report, which is the first in a series of planned tests on WEC controls, focused on system identification (system ID) and model validation.

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