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

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 force

Energy-maximising moment-based constrained optimal control of ocean wave energy farms

Successful commercialisation of wave energy technology inherently incorporates the concept of an array of wave energy converters (WECs). These devices, which constantly interact via hydrodynamic effects, require optimised control that can guarantee maximum energy extraction from incoming ocean waves while ensuring, at the same time, that any physical limitations associated with device and actuator systems are being consistently respected. This paper presents a moment-based energy-maximising optimal control framework for WECs arrays subject to state and input constraints. The authors develop a framework under which the objective function (and system variables) can be mapped to a finite-dimensional tractable quadratic program (QP), which can be efficiently solved using state-of-the-art solvers. Moreover, the authors show that this QP is always concave, i.e. existence and uniqueness of a globally optimal solution is guaranteed under this moment-based framework. The performance of the proposed strategy is demonstrated through a case study, where (state and input constrained) energy-maximisation for a WEC farm composed of CorPower-like WEC devices is considered

Nonlinear Model Reduction by Moment-Matching for a Point Absorber Wave Energy Conversion System

This paper presents a data-driven model reduction by moment-matching approach to construct control-oriented models for a point absorber device. The methodology chosen and developed generates models which are input-to-state linear, with any nonlinear behaviour confined to the output map. Such a map is the result of a data-driven approximation procedure, where the so-called moment of the point absorber system is estimated via a least-squares procedure. The resulting control-oriented model can inherently preserve steady-state properties of the target WEC system for a user-defined class of input signals of interest, with the computation only dependent upon a suitably defined set of input-output data

Data-driven nonlinear model reduction by moment-matching for the ISWEC system

Given the relevance of control-oriented models in optimal control design for wave energy converters (WECs), this paper presents a data-driven approach to nonlinear model reduction by moment-matching for the ISWEC device, a device originally developed at the Politecnico di Torino. The presented model reduction technique is capable of providing simple WEC models, which inherently preserve steady-state response characteristics from the target nonlinear system, by merely using information on the system outputs, defined for a specific class of operating conditions. We demonstrate that the proposed model reduction by moment-matching procedure is well-posed for the ISWEC, and illustrate the efficacy of this reduction technique under a variety of sea conditions

First principles simulations of liquid Fe-S under Earth's core conditions

First principles electronic structure calculations, based upon density functional theory within the generalized gradient approximation and ultra-soft Vanderbilt pseudopotentials, have been used to simulate a liquid alloy of iron and sulfur at Earth's core conditions. We have used a sulfur concentration of $\approx 12$wt, in line with the maximum recent estimates of the sulfur abundance in the Earth's outer core. The analysis of the structural, dynamical and electronic structure properties has been used to report on the effect of the sulfur impurities on the behavior of the liquid. Although pure sulfur is known to form chains in the liquid phase, we have not found any tendency towards polymerization in our liquid simulation. Rather, a net S-S repulsion is evident, and we propose an explanation for this effect in terms of the electronic structure. The inspection of the dynamical properties of the system suggests that the sulfur impurities have a negligible effect on the viscosity of Earth's liquid core.Comment: 24 pages (including 8 figures

The wave energy converter control competition (WECCCOMP): Wave energy control algorithms compared in both simulation and tank testing

The wave energy control competition established a benchmark problem which was offered as an open challenge to the wave energy system control community. The competition had two stages: In the first stage, competitors used a standard wave energy simulation platform (WEC-Sim) to evaluate their controllers while, in the second stage, competitors were invited to test their controllers in a real-time implementation on a prototype system in a wave tank. The performance function used was based on converted energy across a range of standard sea states, but also included aspects related to economic performance, such as peak/average power, peak force, etc. This paper compares simulated and experimental results and, in particular, examines if the results obtained in a linear system simulation are borne out in reality. Overall, within the scope of the device tested, the range of sea states employed, and the performance metric used, the conclusion is that high-performance WEC controllers work well in practice, with good carry-over from simulation to experimentation. However, the availability of a good WEC mathematical model is deemed to be crucial

Focused wave interactions with floating structures: A blind comparative study

The paper presents results from the Collaborative Computational Project in Wave Structure Interaction (CCP-WSI) Blind Test Series 2. Without prior access to the physical data, participants, with numerical methods ranging from low-fidelity linear models to fully non-linear Navier-Stokes (NS) solvers, simulate the interaction between focused wave events and two separate, taut-moored, floating structures: a hemispherical-bottomed cylinder and a cylinder with a moonpool. The 'blind' numerical predictions for heave, surge, pitch and mooring load, are compared against physical measurements. Dynamic time warping is used to quantify the predictive capability of participating methods. In general, NS solvers and hybrid methods give more accurate predictions; however, heave amplitude is predicted reasonably well by all methods; and a WEC-Sim implementation, with CFD-informed viscous terms, demonstrates comparable predictive capability to even the stronger NS solvers. Large variations in the solutions are observed (even among similar methods), highlighting a need for standardisation in the numerical modelling of WSI problems

Quantization of the Closed Mini-Superspace Models as Bound States

Wheeler-DeWitt equation is applied to $k > 0$ Friedmann Robertson Walker metric with various types of matter. It is shown that if the Universe ends in the matter dominated era (e.g., radiation or pressureless gas) with zero cosmological constant, then the resulting Wheeler-DeWitt equation describes a bound state problem. As solutions of a non-degenerate bound state system, the eigen-wave functions are real (Hartle-Hawking) and the usual issue associated with the ambiguity in the boundary conditions for the wave functions is resolved. Furthermore, as a bound state problem, there exists a quantization condition that relates the curvature of the three space with the energy density of the Universe. Incorporating a cosmological constant in the early Universe (inflation) is given as a natural explanation for the large quantum number associated with our Universe, which resulted from the quantization condition. It is also shown that if there is a cosmological constant $\Lambda > 0$ in our Universe that persists for all time, then the resulting Wheeler-DeWitt equation describes a non-bound state system, regardless of the magnitude of the cosmological constant. As a consequence, the wave functions are in general complex (Vilenkin) and the initial conditions for wave functions are a free parameters not determined by the formalism.Comment: 20

Mechanical ventilation modulates TLR4 and IRAK-3 in a non-infectious, ventilator-induced lung injury model

<p>Abstract</p> <p>Background</p> <p>Previous experimental studies have shown that injurious mechanical ventilation has a direct effect on pulmonary and systemic immune responses. How these responses are propagated or attenuated is a matter of speculation. The goal of this study was to determine the contribution of mechanical ventilation in the regulation of Toll-like receptor (TLR) signaling and interleukin-1 receptor associated kinase-3 (IRAK-3) during experimental ventilator-induced lung injury.</p> <p>Methods</p> <p>Prospective, randomized, controlled animal study using male, healthy adults Sprague-Dawley rats weighing 300-350 g. Animals were anesthetized and randomized to spontaneous breathing and to two different mechanical ventilation strategies for 4 hours: high tidal volume (V_T) (20 ml/kg) and low V_T(6 ml/kg). Histological evaluation, TLR2, TLR4, <it>IRAK3 </it>gene expression, IRAK-3 protein levels, inhibitory kappa B alpha (IκBα), tumor necrosis factor-alpha (<it>TNF-α</it>) and interleukin-6 (<it>IL6</it>) gene expression in the lungs and TNF-α and IL-6 protein serum concentrations were analyzed.</p> <p>Results</p> <p>High V_Tmechanical ventilation for 4 hours was associated with a significant increase of TLR4 but not TLR2, a significant decrease of <it>IRAK3 </it>lung gene expression and protein levels, a significant decrease of IκBα, and a higher lung expression and serum concentrations of pro-inflammatory cytokines.</p> <p>Conclusions</p> <p>The current study supports an interaction between TLR4 and IRAK-3 signaling pathway for the over-expression and release of pro-inflammatory cytokines during ventilator-induced lung injury. Our study also suggests that injurious mechanical ventilation may elicit an immune response that is similar to that observed during infections.</p