Causal control design for wave energy converters with finite stroke

Abstract

Control design is of central importance in the optimization of power generation from ocean wave energy converters (WECs). The problem is made challenging by the fact that the resource is vibratory and stochastic, with a low quality factor. It has recently been shown that when constrained to causality, the optimal feedback controller for a WEC is solvable in closed-form as a sign-indefinite LQG problem, for the case in which the WEC exhibits linear dynamics and quadratic power transmission dissipation. However, most WECs exhibit stroke limits, which must be explicitly accounted for in control design to avoid end-stop collisions. This is important because such collisions lead to damage, and also because the introduction of unmodeled stroke limits can actually destabilize the otherwise-optimal closed loop. We illustrate a control design technique to address this issue, which consists of two design steps. In the first step, LMI techniques are used to optimize the mean power harvested from waves with a known power spectral density, subject to several competing objectives. In the second step, the controller is augmented via a nonlinear passivity-based outer-loop design which guarantees to prevent stroke saturation while also guaranteeing to preserve closed-loop stability. The technique is illustrated using a model of a simple heaving point absorber, and verified in simulation.