Control of wave energy converters

Abstract

In this thesis, two types of control problems related to wave energy converters are studied. The first type of control problem is active force control. We propose a simple optimal control problem formulation for which, in theory, there is no convexity guarantee. However, we demonstrate that the discretized large-scale nonlinear programming (NLP) problem can be convex and that the convexity is related only to the system parameters and is independent from the excitation force and current state. This important feature implies that we are always able to choose a set of system parameters off-line so that, for the online closed-loop implementation, all the optimization problems are convex. In practice, for a large range of parameter sets, the resulting optimization problems are convex.

The second one is known to the wave energy community as passive control. In particular, latching, declutching and latching-declutching control. We propose a unified model based on a hybrid system (a mix of discrete event and continuous-time system) for these passive control implementations. With our model, we formulate the latching-declutching control problem as a small dimensional discrete optimization problem, where the only decision variables are the bounds on the latching time and power-take-off (PTO)-active time. Based on the specific problem we have, we propose a coordinate-search algorithm, which is one of the directional direct search algorithm. The algorithm is able to efficiently solve small dimensional problems with discrete decision variables.

We study derivative-free optimization algorithms and reveal a sufficient convergence condition for general directional direct search algorithms. The condition is the formalization of the intuition that: if the search directions intersect the sub-level sets, then any directional direct search algorithm should converge. We illustrate that this is not always true and regularity conditions must be added. Examples are given in order to show some interesting cases.

State constraints are rarely discussed for declutching control. In the last part of the thesis we propose a formulation which is able to incorporate state constraints. The formulation results in a mixed-integer nonlinear optimal control problem, which is very hard to solve. Based on a technique known as variable time transform, we are able to reformulate the mixed-integer nonlinear optimal control problem into a large-scale nonlinear programming (NLP) problem. The transformed NLP problem can be solved efficiently by NLP solvers, such as interior point method used in IPOPT.