Abstract
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.
Highlights
One of the challenges in wave energy harvesting is the motion control
We investigate the impact of having nonlinear terms in the equation of motion whether they appear due to nonlinear hydrodynamics, nonlinear hydrostatics, nonlinear damping, nonlinear control forces, or all of the above
This would be of interest in wave energy conversion especially in the case of regular waves since the wave repeats itself at a regular rate; and it is intuitive that a control system that brings the Wave Energy Converters (WECs) to some initial state at the same rate would be suitable
Summary
One of the challenges in wave energy harvesting is the motion control. There has been significant developments for different control methods for WECs [1]. Where z is the heave displacement, m is the buoy mass, k is the hydrostatic stiffness due to buoyancy, ais the added mass, Fex is the excitation force, u is the control force, Bv is a viscous damping coefficient, and hr is the radiation impulse response function (radiation kernel). The work in [6] presented a numerical implementation for nonlinear hydrodynamic forces at different levels from a full nonlinear model using Computational Fluid Dynamics (CFD) tools, linear models corrected by nonlinear Froude–Krylov force, as well as nonlinear viscous and hydrostatic forces. In the case of heaving point absorbers, the nonlinear Froude–Krylov force is essential, while the nonlinear diffraction and radiation can be neglected. The nonlinear viscous effects are weak as well for point absorbers [8], and the nonlinear PTO and mooring effects seem to be significant
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