Nonlinear controller for nonlinear wave energy converters

The present invention is directed to a nonlinear controller for nonlinear wave energy converters (WECs). As an example of the invention, a nonlinear dynamic model is developed for a geometrically right-circular cylinder WEC design for the heave-only motion, or a single degree-of-freedom (DOF). The linear stiffness term is replaced by a nonlinear cubic hardening spring term to demonstrate the performance of a nonlinear WEC as compared to an optimized linear WEC. By exploiting the nonlinear physics in the nonlinear controller, equivalent power and energy capture, as well as simplified operational performance is observed for the nonlinear cubic hardening spring controller when compared to an optimized linear controller.https://digitalcommons.mtu.edu/patents/1151/thumbnail.jp

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.https://digitalcommons.mtu.edu/patents/1148/thumbnail.jp

Pseudo-spectral method to control three-degree-of-freedom wave energy converters

The invention provides optimal control of a three-degree-of-freedom wave energy converter using a pseudo-spectral control method. The three modes are the heave, pitch and surge. A dynamic model is characterized by a coupling between the pitch and surge modes, while the heave is decoupled. The heave, however, excites the pitch motion through nonlinear parametric excitation in the pitch mode. The invention can use a Fourier series as basis functions to approximate the states and the control. For the parametric excited case, a sequential quadratic programming approach can be implemented to numerically solve for the optimal control. The numerical results show that the harvested energy from three modes is greater than three times the harvested energy from the heave mode alone. Moreover, the harvested energy using a control that accounts for the parametric excitation is significantly higher than the energy harvested when neglecting this nonlinear parametric excitation term.https://digitalcommons.mtu.edu/patents/1143/thumbnail.jp

Extending complex conjugate control to nonlinear wave energy converters

This paper extends the concept of Complex Conjugate Control (CCC) of linear wave energy converters (WECs) to nonlinear WECs by designing optimal limit cycles with Hamiltonian Surface Shaping and Power Flow Control (HSSPFC). It will be shown that CCC for a regular wave is equivalent to a power factor of one in electrical power networks, equivalent to mechanical resonance in a mass-spring-damper (MSD) system, and equivalent to a linear limit cycle constrained to a Hamiltonian surface defined in HSSPFC. Specifically, the optimal linear limit cycle is defined as a second-order center in the phase plane projection of the constant energy orbit across the Hamiltonian surface. This concept of CCC described by a linear limit cycle constrained to a Hamiltonian surface will be extended to nonlinear limit cycles constrained to a Hamiltonian surface for maximum energy harvesting by the nonlinear WEC. The case studies presented confirm increased energy harvesting which utilizes nonlinear geometry realization for reactive power generation

Nonlinear Hydrostatic Control Of A Wave Energy Converter

Increased energy harvesting is realized using a nonlinear buoy geometry for reactive power generation. By exploiting the nonlinear dynamic coupling between the buoy geometry and the potential wideband frequency spectrum of incoming waves in the controller/buoy design, increased power can be captured in comparison to conventional wave energy converter designs. In particular, the reactive power and energy storage system requirements are inherently embedded in the nonlinear buoy geometry, therefore requiring only simple rate-feedback control.https://digitalcommons.mtu.edu/patents/1159/thumbnail.jp

Optimal control of wave energy converters

A wave energy converter and method for extracting energy from water waves maximizes the energy extraction per cycle by estimating an excitation force of heave wave motion on the buoy, computing a control force from the estimated excitation force using a dynamic model, and applying the computed control force to the buoy to extract energy from the heave wave motion. Analysis and numerical simulations demonstrate that the optimal control of a heave wave energy converter is, in general, in the form of a bang-singular-bang control; in which the optimal control at a given time can be either in the singular arc mode or in the bang-bang mode. The excitation force and its derivatives at the current time can be obtained through an estimator, for example, using measurements of pressures on the surface of the buoy in addition to measurements of the buoy position. A main advantage of this approximation method is the ease of obtaining accurate measurements for pressure on the buoy surface and for buoy position, compared to wave elevation measurements.https://digitalcommons.mtu.edu/patents/1146/thumbnail.jp

Multi-resonant feedback control of multiple degree-of-freedom wave energy converters

Multi-resonant control of a 3 degree-of-freedom (heave-pitch-surge) wave energy converter enables energy capture that can be in the order of three times the energy capture of a heave-only wave energy converter. The invention uses a time domain feedback control strategy that is optimal based on the criteria of complex conjugate control. The multi-resonant control can also be used to shift the harvested energy from one of the coupled modes to another, enabling the elimination of one of the actuators otherwise required in a 3 degree-of-freedom wave energy converter. This feedback control strategy does not require wave prediction; it only requires the measurement of the buoy position and velocity.https://digitalcommons.mtu.edu/patents/1149/thumbnail.jp

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.https://digitalcommons.mtu.edu/patents/1147/thumbnail.jp

A Self-Tuning WEC Controller for Changing Sea States

A self-tuning proportional-integral control law prescribing motor torques was tested in experiment on a three degree-of-freedom wave energy converter. The control objective was to maximize electrical power. The control law relied upon an identified model of device intrinsic impedance to generate a frequency-domain estimate of the wave-induced excitation force and measurements of device velocities. The control law was tested in irregular sea-states that evolved over hours (a rapid, but realistic time-scale) and that changed instantly (an unrealistic scenario to evaluate controller response). For both cases, the controller converges to gains that closely approximate the postcalculated optimal gains for all degrees of freedom in a sufficiently short-time for realistic sea states. In addition, electrical power was found to be relatively insensitive to gain tuning over a broad range of gains, implying that an imperfectly tuned controller does not result in a large penalty to electrical power capture. Because the controller relies on an identified model of device intrinsic impedance, the sensitivity of power capture was evaluated with respect to uncertainty in the constituent terms of intrinsic impedance. Power capture is found to be relatively insensitive to uncertainty of 20% in constituent terms of the identified intrinsic impedance model. An extension of this control law that allows for adaptation to a changing device impedance model over time is proposed for long-term deployments, as well as an approach to explicitly handle constraints within this architecture

The wave energy converter control competition (WECCCOMP): Wave energy control algorithms compared in both simulation and tank testing

The wave energy control competition established a benchmark problem which was offered as an open challenge to the wave energy system control community. The competition had two stages: In the first stage, competitors used a standard wave energy simulation platform (WEC-Sim) to evaluate their controllers while, in the second stage, competitors were invited to test their controllers in a real-time implementation on a prototype system in a wave tank. The performance function used was based on converted energy across a range of standard sea states, but also included aspects related to economic performance, such as peak/average power, peak force, etc. This paper compares simulated and experimental results and, in particular, examines if the results obtained in a linear system simulation are borne out in reality. Overall, within the scope of the device tested, the range of sea states employed, and the performance metric used, the conclusion is that high-performance WEC controllers work well in practice, with good carry-over from simulation to experimentation. However, the availability of a good WEC mathematical model is deemed to be crucial