Wave-by-wave control in irregular waves for a wave energy converter with approximate parameters

This paper investigates wave-by-wave control of a single-mode wave energy converter driven to operate such that the oscillation velocity closely matches the hydrodynamically optimum velocity for best power absorption. Such control typically requires prediction of the incident wave profile, which, for realistic wave spectra may be obtained using up-wave measurements over a duration and at a distance based on a deterministic propagation model and the device dynamics. This work investigates how such control may be attempted when the device inertia, viscous damping, hydrostatic stiffness, frequency-dependent hydrodynamic coefficients, and exciting force are quantified approximately. In particular, this paper studies an implementation of adaptive trajectory-tracking control using on-line estimation of the mechanical and hydrodynamic parameters (i.e. inertia, viscous damping, hydrostatic stiffness, frequency-dependent added mass, frequency-dependent radiation damping, and the exciting force), where a hydrodynamically optimum velocity variation based on approximate parameter estimates provides the reference trajectory. In this study, the rest mass, infinite-frequency added mass, hydrostatic stiffness, a linearized viscous damping coefficient, and two parameters representing the uncertainties in the radiation impulse-response function and the exciting force impulse-response function are estimated on line. The present method relies on feedback and feedforward forces derived using a Lyapunov function comprised of a system Hamiltonian that combines the mechanical and information exergy functions. Energy capture results under oscillation constraints show that, while the present implementation leaves significant room for improvement relative to near-optimal wave-by-wave control with exact parameters, considerable improvement is still observed relative to resistive control with exact parameters.