Pseudo-spectral Control for Wave Energy Converter Modes
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Solution Overview
Problem
Current wave energy converter technologies face challenges in designing effective control strategies for higher energy harvesting, particularly due to limitations in existing theories and practices that assume small motion directions, which are not applicable to the larger heave and pitch motions required for efficient energy extraction.
Innovation Solution
The implementation of a pseudo-spectral control method for three-degree-of-freedom wave energy converters, which accounts for nonlinear parametric excitation between heave, pitch, and surge modes, using Fourier series as basis functions to approximate states and control, and a sequential quadratic programming approach for numerical optimization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If linear dynamic models based on small motion assumptions are used, then the control algorithm is simpler and easier to implement, but the energy harvesting capability is limited because large heave and pitch motions cannot be effectively captured
Solution Approach 1:
The patent transitions from static linear models to dynamic nonlinear models that adapt to large motion conditions. The control algorithm dynamically adjusts to account for parametric excitation and coupling effects that become significant during large heave and pitch motions, enabling effective energy harvesting while maintaining computational tractability through reduced-order modeling techniques
Solution Approach 2:
The patent changes the fundamental parameters of the mathematical model by incorporating nonlinear terms for parametric excitation and mode coupling. This transforms the system from a linear time-invariant model to a nonlinear time-varying model, allowing the controller to accurately represent and exploit large motion dynamics for enhanced energy extraction
2Measurement precision
If nonlinear parametric excitation terms are included in the mathematical model, then the accuracy of energy harvesting prediction improves, but the computational complexity increases making real-time control more difficult
Solution Approach 1:
The patent segments the complex nonlinear control problem into manageable components by separately modeling parametric excitation effects and mode coupling. This decomposition allows the controller to handle each nonlinear effect independently while maintaining overall accuracy, reducing computational burden compared to a fully coupled nonlinear approach
Solution Approach 2:
The patent replaces complex mechanical nonlinearities with equivalent mathematical representations that are computationally efficient. By using analytical solutions for parametric excitation and reduced-order models for coupling effects, the system achieves high prediction accuracy without requiring computationally intensive numerical simulations in real-time control
3Productivity
If three-degree-of-freedom motion (heave, pitch, surge) is utilized, then energy harvesting increases to more than three times that of single-degree-of-freedom systems, but the system complexity and control difficulty increase significantly
Solution Approach 1:
The patent implements a unified control framework that simultaneously manages all three degrees of freedom (heave, pitch, surge) and accounts for their interactions. The controller universally handles parametric excitation in pitch, coupling between pitch-surge, and heave-pitch interactions through a single integrated algorithm, avoiding the need for separate control systems for each mode and reducing overall complexity
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach significantly increases energy harvesting capabilities, with the three-degree-of-freedom system capturing more than three times the energy of a one-degree-of-freedom heave system, and demonstrates computational efficiency for real-time implementations.
Implementation Method 1
wave energy converters
Implementation Method 2
uses Fourier series as basis functions to approximate states and control
Data Source
AI summary
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.