Multi-resonant feedback control of a single degree-of-freedom wave energy converter
A multi-resonant wide band controller decomposes the wave energy converter control problem into sub-problems; an independent single-frequency controller is used for each sub-problem. Thus, each sub-problem controller can be optimized independently. The feedback control enables actual time-domain realization of multi-frequency complex conjugate control. The feedback strategy requires only measurements of the buoy position and velocity. No knowledge of excitation force, wave measurements, nor wave prediction is needed. As an example, the feedback signal processing can be carried out using Fast Fourier Transform with Hanning windows and optimization of amplitudes and phases. Given that the output signal is decomposed into individual frequencies, the implementation of the control is very simple, yet generates energy similar to the complex conjugate control.
1. A multi-resonant single degree-of-freedom wave energy converter, comprising:
a buoy in a water environment having wave motion, wherein the waves impacting the buoy exert an excitation force with a plurality of excitation frequencies that causes a buoy motion in a heave direction relative to a reference,
a sensor for measuring a position or velocity of the buoy relative to the reference for a sample period,
a power take-off that is configured to apply a control force in the heave direction to the buoy and harvest the energy of the buoy motion, and
a feedback controller that uses a signal processor to extracts a plurality of frequencies, amplitudes, and phases of the measured position or velocity of the buoy, computes a proportional-derivative control for each of the plurality of extracted frequencies, amplitudes, and phases, adds up each of the proportional-derivative controls to provide a computed control force, and causes the power take-off to apply the computed control force to the buoy to put the buoy heave motion in resonance with the excitation force.
2. The wave energy converter of claim 1 , wherein the signal processor comprises a Fast Fourier Transform, Kalman filter, or least-squares processor.
3. The wave energy converter of claim 1 , wherein the plurality of frequencies comprises at least three frequencies having the most significant amplitudes.
4. The wave energy converter of claim 1 , wherein the sample period is 6 to 8 periods of one of the plurality of frequencies.
5. A method for proportional-derivate complex conjugate control of a wave energy converter, comprising:
providing a multi-resonant single degree-of-freedom wave energy converter comprising a buoy in a water environment having wave motion, wherein the waves impacting the buoy exert an excitation force with a plurality of excitation frequencies that causes a buoy motion in a heave direction relative to a reference, a sensor for measuring a position or velocity of the buoy relative to the reference for a sample period, a power take-off that is configured to apply a control force in the heave direction to the buoy, and a feedback controller comprising a signal processor;
measuring the position and velocity of the buoy relative to the reference over a sample period with the sensor;
extracting a plurality of frequencies, amplitudes, and phases of the measured position or velocity of the buoy using the signal processor,
computing a proportional-derivative control for each of the plurality of frequencies, amplitudes, and phases;
adding up each of the proportional-derivative controls to provide a computed control force; and
causing the power take-off to apply the computed control force to the buoy to put the buoy heave motion in resonance with the excitation force.
6. The method of claim 5 , wherein the signal processor comprises a Fast Fourier Transform, Kalman filter, or least-squares processor.
7. The method of claim 5 , wherein the plurality of frequencies comprises at least three frequencies having the most significant amplitudes.
8. The method of claim 5 , wherein the sample period comprises 6 to 8 periods of one of the plurality of frequencies.