Modelling, control and Pontryagin Maximum Principle for a two-body wave energy device

Abstract

Frequency domain analysis is applied to a wave energy device composed by two coaxial axisymmetric bodies. For each frequency optimal damping coefficient values which maximize absorbed power are obtained. Several displacement amplitude restriction scenarios are considered. A stochastic model to describe the device’s behaviour in irregular waves is developed. Optimal mechanical damping and spring coefficients are computed. Considering different sea state conditions, probability density functions are defined for relevant parameters and time averaged absorbed power values are obtained.A time domain model is also developed for the device. A non-linear power take-off mechanism configuration, consisting in a hydraulic circuit with low-pressure and high-pressure gas accumulators, is devised. Time averaged absorbed power is maximized in terms of characteristic mechanism parameter. A sub-optimal method of phase control by latching is applied to the device in order to improve its performance. Analytical development of Pontryagin Maximum Principle is used to establish an algorithm for device’s control.