Multi-objective optimal causal control of an ocean wave energy converter in random waves

In order to maximize the effectiveness of an ocean wave energy converter, its power output must be explicitly regulated via a feedback control system. It is a classical result that when ocean waves are stochastic and the converter´s response is linear, the physically-maximal power generation is only obtained using an anticausal feedback law; i.e., one which regulates power based on future response quantities. More recently, it has been shown that when constrained to causality, the optimal feedback law may be found using LQG control theory. In this paper, we consider the fact that various aspects of a wave energy converter´s dynamic response (i.e., its displacements, force levels, current and voltage levels, etc.) will have finite extent, beyond which the linear dynamic model is no longer valid. In particular, we consider the use of the power generators to simultaneously harvest energy and also restrain these other response quantities. We illustrate one way of accomplishing this constrained optimization, through the use of Linear Matrix Inequality methods, and illustrate its application on a cylindrical buoy-type wave energy converter with three generators, subject to a stationary JONSWAP sea state. Power generation is optimized subject to constraints on acceptable variances on displacements (both linear and rotational) of the buoy. We show that for the particular example used here, response control and energy harvesting constitute objectives with significant conflict.