Model Predictive Control Strategy applied to aWave Energy Converter

The incoming menace of global overheating and the exhaustion of fossil fuels, highlights the needing for alternative, renewable energy sources. In this context, the most interesting ideas appear to be related to solar, wind and wave power conversion. If on one hand solar and wind power extraction techniques are already well-established technologies, on the other hand the wave field is still setting its point, both in terms of used tools and of actual potential. The wave source offers a huge and untapped potential, thanks to its high superficial power density and its geographical spread. The state of art device to extract power from waves are called Wave Energy Converters (WECs). One of these device is mainly composed by 3 elements. The first one is basically a floating buoy, able to change position according to the wave elevation. The second one is called Power Take Off (PTO): it is an electro-mechanical mechanism in charge of converting the buoy movement in electrical energy. The last macro element of a WEC consists in a mooring system, which must keep the floater in its positioning spot without affecting (too much) the WEC's productivity. In this framework, PTO control strategy appears immediately to be of paramount importance: the better will its effectiveness be, the greater will be the final power absorption. Between the different control concepts, an Economic Model Predictive Control (EMPC) approach has been chosen, for its ability to use the simplified model of the WEC and its current state variables to determine an (almost) optimal control action, and to optimize directly the absorbed power, increasing so that the productivity of the WEC. The main advantage of this approach consists in predicting the system behaviour with the current information over a finite time horizon, then to solve an optimization problem to generate the optimal control action. So that, the computed control action will be optimal, under certain a-priori conditions, for the solved problem. To build the control law, first an third part toolbox (YALMIP) has been used to formulate the original problem, which was not guaranteed to be convex, then a direct convexification of the MPC cost function allowed to get rid of YALMIP to directly formulate the problem by means of matrices and solving it with a tailored optimization algorithm. Building the MPC, also the problem of the optimization algorithm arose, leading to an analisys of the categories for the quadratic programming solvers. As final choice, a Gauss-Seidel like iterative algorithm, developed by Hildreth, has been chosen. Since there are no cheap and reliable sensors for the estimation of the wave incoming force, the wave evaluation and prediction problem has been tackled, to build the entire control loop. For the estimation problem, several approaches have been reviewed, leading to he choice of a novel estimation approach developed by professor Nicolas Faédo. For what concerns the prediction, an ARX model has been used in order to feed the MPC with a fictitious forecast of the wave excitation force. After developing the entire control loop for a benchmark problem, a structural design stage has been carried out to build a heaving spherical point absorber, on which the controller has been fitted and tested. As final stage, the results have been compared with optimal proportional-derivative parameters for different sea states, showing the potential of the MPC application.