A Hamiltonian surface-shaping approach for control system analysis and the design of nonlinear wave energy converters

Shadi Darani, Michigan Technological University
Ossama Abdelkhalik, Michigan Technological University
Rush D. Robinett III, Michigan Technological University
David Wilson, Sandia National Laboratories

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Publisher’s version of record: https://doi.org/10.3390/JMSE7020048


The dynamic model of Wave Energy Converters (WECs) may have nonlinearities due to several reasons such as a nonuniform buoy shape and/or nonlinear power takeoff units. This paper presents the Hamiltonian Surface-Shaping (HSS) approach as a tool for the analysis and design of nonlinear control of WECs. The Hamiltonian represents the stored energy in the system and can be constructed as a function of the WEC’s system states, its position, and velocity. The Hamiltonian surface is defined by the energy storage, while the system trajectories are constrained to this surface and determined by the power flows of the applied non-conservative forces. The HSS approach presented in this paper can be used as a tool for the design of nonlinear control systems that are guaranteed to be stable. The optimality of the obtained solutions is not addressed in this paper. The case studies presented here cover regular and irregular waves and demonstrate that a nonlinear control system can result in a multiple fold increase in the harvested energy.