Model predictive control of parametric excited pitch-surge modes in wave energy converters
A parametric excitation dynamic model is used for a three degrees-of-freedom (3-DOF) wave energy converter. Since the heave motion is uncoupled from the pitch and surge modes, the pitch-surge equations of motion can be treated as a linear time varying system, or a linear system with parametric excitation. In such case the parametric exciting frequency can be tuned to twice the natural frequency of the system for higher energy harvesting. A parametric excited 3-DOF wave energy converter can harvest more power, for both regular and irregular waves, compared to the linear 3-DOF. For example, in a Bretschneider wave, the harvested energy in the three modes is about 3.8 times the energy harvested in the heave mode alone; while the same device produces about 3.1 times the heave mode energy when using a linear 3-DOF model.
1. A multi-resonant multiple degree-of-freedom wave energy converter, comprising:
a buoy in a water environment having a wave motion, wherein the waves impacting the buoy exert an excitation force with a plurality of excitation frequencies that causes a buoy motion in heave, surge, and pitch directions relative to a reference,
a power take-off that is configured to apply control forces in the heave, surge, and pitch directions to the buoy and harvest mechanical energy of the buoy motion,
a predictor that is configured to predict the excitation force of the wave impacting the buoy in a future time horizon, and
a controller that causes the power take-off to apply a force to the buoy to put the heave motion in resonance with the predicted wave excitation force in the heave direction and wherein the control forces in the surge and pitch directions are optimized using a model predictive control method to maximize parametric excitation of the surge-pitch motion by the heave motion.
2. The wave energy converter of claim 1 , wherein a natural frequency of the pitch-surge motion of the wave enemy converter is tuned to be approximately half of the heave motion frequency.
3. The wave energy converter of claim 1 , wherein the force in the heave direction is computed using a singular-arc control method.