Time-varying linear quadratic Gaussian optimal control for three-degree-of-freedom wave energy converters

Document Type


Publication Date



Department of Mechanical Engineering-Engineering Mechanics


This paper presents a time-varying linear quadratic control for a three-degree-of-freedom (3-DoF) wave energy converter (WEC). The dynamic model for a heave-surge-pitch WEC has a linear coupling between pitch and surge modes, as well as a nonlinear coupling between the heave and pitch modes that affect the pitch motion. It is observed, however, that the heave motion is decoupled from the other two modes, and that the heave effect on the pitch motion can be recognized as a time-varying stiffness. Hence it is proposed in this paper to design a time-varying linear quadratic control for the coupled pitch-surge modes. The goal is to maximize the energy harvested over a receding time horizon. Prediction of the excitation forces is needed and is obtained based an estimate of the excitation force at the current time. The latter is obtained using an extended Kalman filter. The WEC motion is assumed constrained in this study. The results show that the energy harvested using this 3-DoF WEC is about three-fold higher than the energy extracted in heave mode, depending on the sea state. The paper also shows, with proper design of the control, it is possible to exploit this coupling to harvest more energy.

Publication Title

Renewable Energy