Publications

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This report details the background, design, and initial results for wave energy converter design optimization tool. This tool is intended to provide researchers and developers with a means of optimizing existing wave energy converter designs by including realistic dynamics and control algorithms early in the design cycle.

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.

This report describes the set up, execution, and some initial results from a series of wave tank tests of a model-scale wave energy converter (WEC) completed in May 2018 at the Navy's Maneuvering and Sea Keeping (MASK) basin. The purpose of these tests was to investigate the implementation and performance of a series of closed-loop WEC power take-off (PTO) controllers, intended to increase energy absorption/generation.

The idea of acausality for control of a wave energy converter (WEC) is a concept that has been popular since the birth of modern wave energy research in the 1970s. This concept has led to considerable research into wave prediction and feedforward WEC control algorithms. However, the findings in this report mostly negate the need for wave prediction to improve WEC energy absorption, and favor instead feedback driven control strategies. Feedback control is shown to provide performance that rivals a prediction-based controller, which has been unrealistically assumed to have perfect prediction.

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Through the use of advanced control techniques, wave energy converters have significantly improved energy absorption. The motion of the WEC device is a significant contribution to the energy absorbed by the device. Reactive control (complex conjugate control) maximizes the energy absorption due to the impedance matching. The issue with complex conjugate control is that the controller is non-causal, which requires prediction into the oncoming waves to the device. This paper explores the potential of using system identification (SID) techniques to build a causal transfer function that approximates the complex conjugate controller over a specific frequency band of interest. The resulting controller is stable, and the average efficiency of the power captured by the causal controller is 99%, when compared to the non-causal complex conjugate.

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This paper discusses the optimal output feedback control problem of linear time-invariant systems with additional restrictions on the structure of the optimal feedback control gain. These restrictions include setting individual elements of the optimal gain matrix to zero and making the sum of certain rows of the gain matrix equal to desired values. The paper proposes a method that modifies the standard quadratic cost function to include soft constraints ensuring the satisfaction of these restrictions on the structure of the optimal gain. Necessary conditions for optimality with these soft constraints are derived, and an algorithm to solve the resulting optimal output feedback control problem is given. Finally, a power systems example is presented to illustrate the usefulness of proposed approach.

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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The idea of acausality for control of a wave energy converter (WEC) is a concept that has been popular since the birth of modern wave energy research in the 1970s. This concept has led to considerable research into wave prediction and feedforward WEC control algorithms. However, the findings in this report mostly negate the need for wave prediction to improve WEC energy absorption, and favor instead feedback driven control strategies. Feedback control is shown to provide performance that rivals a prediction-based controller, which has been unrealistically assumed to have perfect prediction. It is well known in classical control engineering that perfect knowledge of past and future events will always lead to higher performing systems. However, it is also well known that the underlying system must be well-designed; control cannot fix a bad design. Additionally, one must consider the practical application of a control design, which relies on measurements and actuation systems. There are major implications to cost and reliability when relying on remote sensors requiring real-time data-streaming (e.g., remote wave buoys). This report shows that for a well-designed WEC, in which closed loop dynamics is considered since early stages of design, a suboptimal controller using no prediction can achieve more than 90% of the theoretical maximum. A predictionless feedback resonating (FBR) controller performs within 0.1% percent of a controller with perfect future knowledge (something which is not practically attainable). Given the major challenges with accurate and robust wave prediction, this result provides a major argument and incentive for utilizing feedback for WEC control. Implementation of these feedback strategies is readily attainable, while the strategy requiring perfect wave prediction will demand an unknown number of additional years to research and develop, all in the service of a marginal 1% benefit.

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