Optimal Control Algorithms for Wave Energy Conversion

Abstract

The aim of this thesis is to design control strategies with the objective of power maximization for point absorber (PA) type of wave energy converter (WEC) devices, considering non-linearities and physical limitations on operational conditions. Novel formulations were developed for control algorithms to address some of the open challenges in wave energy conversion systems. Specifically, the areas of contribution are in the development of multi-resolution control, Linear Matrix Inequal- ities(LMI)-based control, control for nonlinear systems/time-varying systems and observer-based control. Multi-resolution control has only recently been proved successful in engineering but its application in the area of ocean energy is still unexplored. The broadbanded nature of sea waves is a perfect match where such approach and controllers are useful. A wavelet domain linear quadratic regulator has been formulated for WEC in this thesis, which assign appropriate weights emphasis- ing the frequency bands of importance and an optimal solution is sought for control. LMI-based control instead has seen a substantial recent establishment in tackling multi-objective optimization control problems. The design of a WEC presents often many contrasting requirements, which can be effectively addressed by LMI-based control. These constraints can be either bounds on actuator forces or limitation on displacement strokes of Power-Take-Off systems. The feedback controllers designed with this feature in this thesis, enforce the energy harnessing requirement by the mini- mization of a performance index, conveniently represented by an H2 and H∞ norm of a transfer function. Another aspect considered in this dissertation is deveopment of controllers in the pres- ence of WEC non-linearities. Nonlinear effects in modeling a PA are often too computationally demanding with respect to the design of control strategies, as they are to be computed in real time. This is one of the reasons why linear theories are so widely used in literature. Sometimes though, non-linearities can be significant and bring only a small additional computational bur- den, so control theories able to consider them will be successful. A control methodology based on a time-varying state space formulation is proposed which solves the Riccati differential equation forward in time. Remarkable improvements are seen compared to the standard LTI control. A fur- ther improved forward Riccati differential equation based controller in multi-resolution framework is also developed and advances the method. Multi-resolution strategies are seen to enhance the power performance by about 12% with equivalent control forces involved. With the application of constrained LMI-based control a significant boost of over 40% in energy harnessed was achieved for a given site. Application of nonlinear Forward Riccati Equation control demonstrates a three-fold boost in power for a given sea environment, with the application of the same magnitude of control forces.