Sliding Mode Control of a Nonlinear Wave Energy Converter Model

Gonzalez, Tania Demonte; Parker, Gordon G.; Anderlini, Enrico; Weaver, Wayne W.

doi:10.3390/jmse9090951

Cited by 17 publications

(7 citation statements)

References 23 publications

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“…The control law was organized into a subsystem. The incident regular wave elevation of Equation ( 2) was A = 0.5 m with a period of six seconds, ω = π 3 matching the conditions of [30]. The reference displacement, ζ r of Equation ( 27), used by the tracking control law, had the same period but with an amplitude of two meters shown in Equation (27).…”

Section: Resultsmentioning

confidence: 99%

“…Although not entirely consistent with the large motion assumption mentioned earlier, a linear radiation force model is used here to keep the focus on the effect of the FK forces. The radiation forces are split into two components, one related to velocity and the other to acceleration, shown in Equation ( 9) [30],…”

Section: Radiation Forcementioning

confidence: 99%

“…In Section 6, the energy extraction results of applying the control law of Section 4 to the hourglass buoy and the spherical buoy of [30] are discussed. A brief description of the spherical buoy model is provided here.…”

Section: Spherical Buoy Modelmentioning

confidence: 99%

“…Researchers have proposed various control strategies that incorporate the analytical nonlinear FK forces. The authors in [30,31] developed a sliding mode controller for a heaving point absorber that demonstrated the robustness and energy maximization of the WEC. In [32], an optimal model-based control was developed for a data-based modeled heaving point absorber.…”

Section: Introductionmentioning

confidence: 99%

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Effect of the Dynamic Froude–Krylov Force on Energy Extraction from a Point Absorber Wave Energy Converter with an Hourglass-Shaped Buoy

et al. 2023

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Point absorber wave energy converter (WEC) control strategies often require accurate models for maximum energy extraction. While linear models are suitable for small motions, the focus is on the nonlinear model of an hour-glass shaped buoy undergoing large vertical displacements. Closed-form expressions for the static and dynamic Froude–Krylov forces are developed. It is shown that, in general, the dynamic and static forces are of similar magnitude, which is not the case for a spherical buoy. While the dynamic force reduces the amplitude of the net buoy force, its shape predicts a larger buoy response than if neglected, causing the nonlinear terms to have an even more significant effect. An input-state feedback linearizing controller is developed to show how the nonlinear model can be used in a control law. A 2.5 m buoy example is simulated to illustrate the approach of tracking an arbitrary displacement reference. For the case considered, the extracted power is 30% larger when the nonlinear dynamic FK force is used in the control law. The hourglass buoy is also compared to a spherical buoy to illustrate differences in their response to regular waves and energy extraction when using the same control laws. A spherical buoy diameter of 7.5 m was required to obtain the same power output as a 5 m tall hourglass buoy. A power-force-amplitude (PFA) metric is introduced to compare energy extraction performance and power take-off requirements. The hourglass buoy’s PFA was 13% larger than the spherical buoy implying that it can produce similar power but with less control effort.

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Section: Resultsmentioning

confidence: 99%

Section: Radiation Forcementioning

confidence: 99%

Section: Spherical Buoy Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effect of the Dynamic Froude–Krylov Force on Energy Extraction from a Point Absorber Wave Energy Converter with an Hourglass-Shaped Buoy

et al. 2023

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“…Put another way, given a model-based control strategy, a family of buoy shapes and power take-off technologies likely exist that permit maximum energy extraction. Recent control algorithm development has focused on large buoy motions to exploit the buoy's nonlinear dynamic response, further motivating the need for accurate models for control-system implementation and buoy-shape optimization [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Free-Decay Heave Motion of a Spherical Buoy

Colling

Kang

Dehdashti

et al. 2022

Fluids

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We examined the heave motion of a spherical buoy during a free-decay drop test. A comprehensive approach was adopted to study the oscillations of the buoy involving experimental measurements and complementary numerical simulations. The experiments were performed in a wave tank equipped with an array of high-speed motion-capture cameras and a set of high-precision wave gauges. The simulations included three sets of calculations with varying levels of sophistication. Specifically, in one set, the volume-of-fluid (VOF) method was used to solve the incompressible, two-phase, Navier–Stokes equations on an overset grid, whereas the calculations in other sets were based on Cummins and mass-spring-damper models that are both rooted in the linear potential flow theory. Excellent agreements were observed between the experimental data and the results of VOF simulations. Although less accurate, the predictions of the two reduced-order models were found to be quite credible, too. Regarding the motion of the buoy, the obtained results indicate that, after being released from a height approximately equal to its draft at static equilibrium (which is about 60% of its radius), the buoy underwent nearly harmonic damped oscillations. The conducted analysis reveals that the draft length of the buoy has a profound effect on the frequency and attenuation rate of the oscillations. For example, compared to a spherical buoy of the same size that is half submerged at equilibrium (i.e., the draft is equal to the radius), the tested buoy oscillated with a period that was roughly 20% shorter, and its amplitude of oscillations decayed almost twice faster per period. Overall, the presented study provides additional insights into the motion response of a floating sphere that can be used for optimal buoy design for energy extraction.

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Optimal control of wave energy systems considering nonlinear Froude–Krylov effects: control-oriented modelling and moment-based control

et al. 2022

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Motivated by the relevance of so-called nonlinear Froude–Krylov (FK) hydrodynamic effects in the accurate dynamical description of wave energy converters (WECs) under controlled conditions, and the apparent lack of a suitable control framework effectively capable of optimally harvesting ocean wave energy in such circumstances, we present, in this paper, an integrated framework to achieve such a control objective, by means of two main contributions. We first propose a data-based, control-oriented, modelling procedure, able to compute a suitable mathematical representation for nonlinear FK effects, fully compatible with state-of-the-art control procedures. Secondly, we propose a moment-based optimal control solution, capable of transcribing the energy-maximising optimal control problem for WECs subject to nonlinear FK effects, by incorporating the corresponding data-based FK model via moment-based theory, with real-time capabilities. We illustrate the application of the proposed framework, including energy absorption performance, by means of a comprehensive case study, comprising both the data-based modelling, and the optimal moment-based control of a heaving point absorber WEC subject to nonlinear FK forces.

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Sliding Mode Control of a Nonlinear Wave Energy Converter Model

Cited by 17 publications

References 23 publications

Effect of the Dynamic Froude–Krylov Force on Energy Extraction from a Point Absorber Wave Energy Converter with an Hourglass-Shaped Buoy

Effect of the Dynamic Froude–Krylov Force on Energy Extraction from a Point Absorber Wave Energy Converter with an Hourglass-Shaped Buoy

Free-Decay Heave Motion of a Spherical Buoy

Optimal control of wave energy systems considering nonlinear Froude–Krylov effects: control-oriented modelling and moment-based control

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