New concepts in evolutionary algorithms for systems architecture optimization

This talk will present recent developments in evolutionary algorithms that focus on the systems architecture optimization. One challenge in systems optimization is the variable number of design variables. Three new concepts will be presented in this talk that enable evolutionary algorithms to handle this type of problems more efficiently. The first is the biologically inspired concept of Hidden Genes that implements tags to cover/uncover genes in the variables\u27 code, which enable handling variable number of variables in evolutionary algorithms. The second concept is a structured chromosome approach that transcripts the variables in a multi-layer code as opposed to the standard single-layer coding. Finally, a dynamic population size concept is presented. Application of these methods in aerospace engineering will be presented.https://digitalcommons.mtu.edu/techtalks/1059/thumbnail.jp

Repeated Shadow Track Orbits for Space-SunSetter Missions

This paper introduces a new set of orbits, the “Repeated Shadow Track Orbits.” In these orbits, the shadow of a spacecraft on the Earth visits the same locations periodically every desired number of days. The 2 perturbation is utilized to synchronize the spacecraft shadow motion with both the Earth rotational motion and the Earth-Sun vector rotation. Motivation for the design of new shadow track orbits comes from the need to save energy. The general mathematical model to design a Repeated Shadow Track Orbit (RSTO) is presented within this paper. RSTOs' conditions are formulated and numerically solved. Results show the feasibility of RSTOs. An optimization process is also developed to maximize the shadow duration over a given site. A Genetic Algorithm (GA) technique is utilized for optimization

A control system for a constrained two-body wave energy converter

Wave energy can be used to power oceano-graphic buoys. A new switching control strategy is developed in this paper for a two-body heaving wave energy converter that is composed of a floating cylinder and two rigidly connected submerged hemispheres. This control strategy is designed to prevent excessive displacement of the floating buoy that may occur due to the actuator force. This control strategy switches the control between a multi-resonant controller and a nonlinear damping controller, depending on the state of the system, to account for displacement constraints. This control strategy is developed using a one-degree-of-freedom dynamic model for the relative motion of the two bodies. Estimation of the relative motion, needed for feedback control, is carried out using a Kalman filter. Numerical simulations are conducted to select the proper mooring stiffness. The controller is tested with stochastic models of irregular waves in this paper. The performance of the controller with different sea states is discussed. Annual power production using this control strategy is presented based on real data in 2015 published by Martha’s Vineyard Coastal Observatory

Dynamic modeling of the motions of variable-shape wave energy converters

In the recently introduced Variable-Shape heaving wave energy converters, the buoy changes its shape actively in response to changing incident waves. In this study, a Lagrangian approach for the dynamic modeling of a spherical Variable-Shape Wave Energy Converter is described. The classical bending theory is used to write the stress-strain equations for the flexible body using Love's approximation. The elastic spherical shell is assumed to have an axisymmetric vibrational behavior. The Rayleigh-Ritz discretization method is adopted to find an approximate solution for the vibration model of the spherical shell. A novel equation of motion is presented that serves as a substitute for Cummins equation for flexible buoys. Also, novel hydrodynamic coefficients that account for the buoy mode shapes are proposed. The developed dynamic model is coupled with the open-source boundary element method software NEMOH. Two-way and one-way Fluid-Structure Interaction simulations are performed using MATLAB to study the effect of using a flexible shape buoy in the wave energy converter on its trajectory and power production. Finally, the variable shape buoy was able to harvest more energy for all the tested wave conditions.Comment: 29 pages, 13 figures; Renewable and Sustainable Energy Reviews, v173 (2023) in progress. arXiv admin note: substantial text overlap with arXiv:2201.0894

Dynamic Modeling Of Spherical Variable-Shape Wave Energy Converters

In the recently introduced Variable-Shape heaving wave energy converters, the buoy changes its shape in response to changing incident waves actively. In this study, the dynamic model for a spherical Variable-Shape Wave Energy Converter is developed using the Lagrangian approach. The classical bending theory is used to write the stress-strain equations for the flexible body using Love's first approximation. The elastic spherical shell is assumed to have an axisymmetric vibration behavior. The Rayleigh-Ritz discretization method is adopted to find an approximate solution for the vibration model of the spherical shell. One-way Fluid-Structure Interaction simulations are performed using MATLAB to validate the developed dynamic model and to study the effect of using a flexible buoy in the wave energy converter on its trajectory and power production.Comment: 24 pages, 8 figures, and 2 tables, the paper is currently under review (journal

Power take-off and energy storage system static modeling and sizing for direct drive wave energy converter to support ocean sensing applications

This paper addresses the sizing and design problem of a permanent magnet electrical machine power take-off system for a two-body wave energy converter, which is designed to support ocean sensing applications with sustained power. The design is based upon ground truth ocean data bi-spectrums (swell and wind waves) from Martha’s Vineyard Coastal Observatory in the year 2015. According to the ground truth ocean data, the paper presents the optimal harvesting power time series of the whole year. The electrical machine and energy storage static modeling are introduced in the paper. The paper uses the ground truth ocean data in March to discuss the model integration of the buoy dynamic model, the power take-off model, and the energy storage model. Electrical machine operation constraints are applied to ensure the designed machine can fulfill the buoy control requirements. The electrical machine and energy storage systems operation status is presented as well. Furthermore, rule-based control strategies are applied to the electrical machine for fulfilling specific design demands, such as improving power generating efficiency and downsizing the electrical machine scale. The corresponding required capacities of the energy storage system are discussed. This paper relates results to the wave data sets (different combinations of significant wave heights and periods of both swell and wind waves). In this way, the power take-off system rule-based control strategy determinations can rely on current ocean wave measurements instead of a large historical ocean wave database

Design of Initial Guess Low Thrust Trajectories Using Clohessy-Wiltshire Equations

The commercial interest in producing low-cost space missions by exploiting the superior propellant management of low-thrust propulsion technology has become increasingly popular. Typical to such missions is the design of transfer trajectories between desired targets. This is a complex and computationally expensive process. Additionally, the optimal solvers used to generate these trajectories are extremely sensitive to initial guesses. One way to overcome this challenge is to use a reasonably approximate trajectory as an initial guess on optimal solvers. This paper presents a flexible approach to generating very low thrust trajectories. The initial guess is obtained from a flexible semi-analytic approach that can provide both planar and three-dimensional initial guess trajectories for various design scenarios like orbit raising, orbit insertion, phasing, and rendezvous. NASA's Evolutionary Mission Trajectory Generator (EMTG) and General Mission Analysis Tool (GMAT) are used as optimal solvers in this analysis. Numerical case studies are presented in this paper.Comment: 33rd AAS/AIAA Space Flight Mechanics Meeting, Austin, TX, January 15-19, 202

A Hamiltonian Surface-Shaping approach for control system analysis and the design of nonlinear wave energy converters

The dynamic model of Wave Energy Converters (WECs) may have nonlinearities due to several reasons such as a nonuniform buoy shape and/or nonlinear power takeoff units. This paper presents the Hamiltonian Surface-Shaping (HSS) approach as a tool for the analysis and design of nonlinear control of WECs. The Hamiltonian represents the stored energy in the system and can be constructed as a function of the WEC’s system states, its position, and velocity. The Hamiltonian surface is defined by the energy storage, while the system trajectories are constrained to this surface and determined by the power flows of the applied non-conservative forces. The HSS approach presented in this paper can be used as a tool for the design of nonlinear control systems that are guaranteed to be stable. The optimality of the obtained solutions is not addressed in this paper. The case studies presented here cover regular and irregular waves and demonstrate that a nonlinear control system can result in a multiple fold increase in the harvested energy

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

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