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Consideration of the problem of optimal ascent from an initial circular planetary orbit to some specified final energy level by a spacecraft equipped with a low-thrust engine. Optimal is defined as minimum time. An accurate small parameter perturbation solution is presented, and the optimal trajectory is analyzed and compared with a tangential thrust trajectory.
Proton-conducting electrochemical cells (PCECs) are promising for efficient hydrogen production, but achieving dense, uniform, thin electrolyte layers remains a key challenge, particularly for scalable fabrication. Here, we present a solution-processed deposition approach with a mechanistically optimized slurry for uniform electrolyte formation. By tailoring particle size distribution, solid loading, and solvent/additive balance, we regulated wetting behavior and evaporation kinetics of the electrolyte slurry to promote homogeneous electrolyte particle packing. These features facilitate tight grain boundary contact and early stage neck growth during sintering, eliminating residual porosity, and improving mechanical integrity. The resulting ∼15 μm thick electrolyte shows high density, strong electrode adhesion, and stable interfaces outperforming the previously reported spray-based fabricated electrolyte by about 31% at 600 °C in FC mode. Single cells deliver 0.962 W cm –2 at 600 °C in fuel cell mode and 1.31 A cm –2 at 1.3 V in electrolysis mode, maintaining robust performance over 100 h with negligible degradation (≤0.02% h –1 ) in each mode. Scale-up to 2.5 cm diameter substrates confirmed reproducible densification and geometric stability. This work demonstrates a cost-effective, scalable route where control over particle-fluid interactions and drying dynamics enables a superior electrolyte microstructure and high PCEC performance.
Second-order solution for motion of satellite about oblate earth, including second, third, and fourth zonal harmonics - celestial mechanics
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The Oxygen Generating Assembly (OGA) on-board the International Space Station (ISS) employs a polymer electrolyte membrane (PEM) water electrolysis cell stack to electrochemically dissociate water into its two components – oxygen and hydrogen. Oxygen is provided to the cabin atmosphere for crew respiration while the hydrogen is delivered to a carbon dioxide reduction system to recover oxygen as water. The design of the OGA evolved over a number of years to arrive at the system solution that is currently operational on ISS. Future manned missions to space will require advanced technologies that eliminate the need for resupply from earth and feature in-situ resource utilization to sustain crew life and to provide useful materials to the crew. The architects planning such missions should consider all potential solutions at their disposal to arrive at an optimal vehicle solution that minimizes crew maintenance time, launch weight, installed volume and energy consumption demands. Skyre is developing new technologies through funding from NASA, the Department of Energy, and internal investment based on PEM technology that could become an integral part of these new vehicle solutions. At varying stages of Technology Readiness Level (TRL) are: an oxygen concentrator and compressor that can separate oxygen from an air stream and provide an enriched oxygen resource for crew medical use and space suit recharge without any moving parts in the pure oxygen stream; a regenerative carbon dioxide removal system featuring a PEM-based sorbent regenerator; a carbon dioxide reduction system that electrochemically produces organic compounds that could serve as fuels or as a useful intermediary to more beneficial compounds; and an electrochemical hydrogen separator and compressor for hydrogen recycle. The technical maturity of these projects is presented along with pertinent performance test data that could be beneficial in future study efforts.
The purpose of this research effort was to begin the study of the application of hp-version finite elements to the numerical solution of optimal control problems. Under NAG-939, the hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element. One possible drawback is the increased computational effort within each element required in implementing hp-version finite elements. We are trying to determine whether this computational effort is sufficiently offset by the reduction in the number of time elements used and improved Newton-Raphson convergence so as to be useful in solving optimal control problems in real time. Because certain of the element interior unknowns can be eliminated at the element level by solving a small set of nonlinear algebraic equations in which the nodal values are taken as given, the scheme may turn out to be especially powerful in a parallel computing environment. A different processor could be assigned to each element. The number of processors, strictly speaking, is not required to be any larger than the number of sub-regions which are free of discontinuities of any kind.
The activity of aqueous-based carbon dioxide reduction (CO 2 R) reactions is often limited by the solubility of CO 2 . The addition of amines can increase the total dissolved carbon in water through the formation of bicarbonate and carbamate species, which has been used to a great effect to capture CO 2 from dilute streams. Here, in this study, we explore the effect of 12 primary and secondary amines of varying Brønsted basicity, steric profile, and hydrogen-bonding capabilities on the aqueous CO 2 R to CO activity of a molecular Ni(cyclam)Cl 2 catalyst with a Hg electrode. Addition of some of the amines results in greater activity and selectivity for CO production compared to equivalent aqueous solutions without added amines. Under optimal conditions (0.4 M 3-amino-propionitrile), there is an over sevenfold increase in partial current density and greater selectivity for CO compared to equivalent conditions with no amine. Interestingly, the increase in activity did not correlate to any single property across the 12 amines. To elucidate the effect of the amine additives on catalysis, we used vapor–liquid equilibrium modeling (VLE), 13 C NMR spectroscopy, and computational analysis to determine the carbon speciation of the solutions. These results indicate that for amines without ethylalcohol functionalities, CO 2 R activity correlates with carbamate concentration, which is in turn governed by amine basicity and steric effects. However, this correlation does not persist for amines with ethylalcohol functionalities, which can form more stable carbamates through intramolecular-hydrogen bonding. These studies demonstrate that amine additives can enhance aqueous CO 2 R activity and selectivity and describe amine properties that lead to these higher performance metrics.
Pontryagin maximum principle applied to solution of optimal control problems by hybrid computer, using digital parameter optimizer to solve two- point boundary value problem
The solution of the optimal control problem, even with low order dynamical systems, can usually strain the analytical ability of most engineers. The understanding of this subject matter, therefore, would be greatly enhanced if a software package existed that could simulate simple generic problems. Surprisingly, despite a great abundance of commercially available control software, few, if any, address the part of optimal control in its most generic form. The purpose of this paper is, therefore, to present a simple computer program that will perform simulations of optimal control problems that arise from the first necessary condition and the Pontryagin's maximum principle.
The purpose of this research effort is to develop a means to use, and to ultimately implement, hp-version finite elements in the numerical solution of optimal control problems. The hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element.
Engine failure represents a major safety concern to helicopter operations, especially in the critical flight phases of takeoff and landing from/to small, confined areas. As a result, the JAA and FAA both certificate a transport helicopter as either Category-A or Category-B according to the ability to continue its operations following engine failures. A Category-B helicopter must be able to land safely in the event of one or all engine failures. There is no requirement, however, for continued flight capability. In contrast, Category-A certification, which applies to multi-engine transport helicopters with independent engine systems, requires that they continue the flight with one engine inoperative (OEI). These stringent requirements, while permitting its operations from rooftops and oil rigs and flight to areas where no emergency landing sites are available, restrict the payload of a Category-A transport helicopter to a value safe for continued flight as well as for landing with one engine inoperative. The current certification process involves extensive flight tests, which are potentially dangerous, costly, and time consuming. These tests require the pilot to simulate engine failures at increasingly critical conditions, Flight manuals based on these tests tend to provide very conservative recommendations with regard to maximum takeoff weight or required runway length. There are very few theoretical studies on this subject to identify the fundamental parameters and tradeoff factors involved. Furthermore, a capability for real-time generation of OEI optimal trajectories is very desirable for providing timely cockpit display guidance to assist the pilot in reducing his workload and to increase safety in a consistent and reliable manner. A joint research program involving NASA Ames Research Center, the FAA, and the University of Minnesota is being conducted to determine OEI optimal control strategies and the associated optimal,trajectories for continued takeoff (CTO), rejected takeoff (RTO), balked landing (BL), and continued landing (CL) for a twin engine helicopter in both VTOL and STOL terminal-area operations. This proposed paper will present the problem formulation, the optimal control solution methods, and the key results of the trajectory optimization studies for both STOL and VTOL OEI operations. In addition, new results concerning the recently developed methodology, which enable a real-time generation of optimal OEI trajectories, will be presented in the paper. This new real-time capability was developed to support the second piloted simulator investigation on cockpit displays for Category-A operations being scheduled for the NASA Ames Vertical Motion Simulator in June-August of 1995. The first VMS simulation was conducted in 1994 and reported.
A set of necessary and sufficient conditions under which a general H2-optimal control problem has a unique solution is derived. It is shown that the solution for an H2-optimal control problem, if it exists, is unique if and only if (1) the transfer function from the control input to the controlled output is left invertible, and (2) the transfer function from the disturbance to the measurement output is right invertible.
Transformation of Lagrange multipliers and Euler equations to obtain control angle solutions by variational calculus
Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer from high numerical cost associated with the combinatorial nature of integer programming. Hence, such methods are often limited to small and medium-sized problems. We propose a globally convergent, coordinate descent–inspired algorithm that allows tractable subproblem solutions restricted to a partition of the domain. Our decomposition method solves relatively small trust-region subproblems that modify the control variable on a subdomain only. Given nontrivial subdomain overlap, we prove that a global first-order necessary optimality condition is equivalent to a first-order necessary optimality condition per subdomain. We additionally show that a sufficient decrease is achieved on a single subdomain by way of a trust-region subproblem solver using geometric measure–theoretic arguments, which we integrate with a greedy patch selection to prove convergence of our algorithm. In conclusion, we demonstrate the practicality of our algorithm on a benchmark large-scale, PDE-constrained integer optimal control problem and find that our method is faster than the state of the art.
This guide instructs users in the operation of a Proximity Operations Planning System. This system uses an interactive graphical method for planning fuel-efficient rendezvous trajectories in the multi-spacecraft environment of the space station and allows the operator to compose a multi-burn transfer trajectory between orbit initial chaser and target trajectories. The available task time (window) of the mission is predetermined and the maneuver is subject to various operational constraints, such as departure, arrival, spatial, plume impingement, and en route passage constraints. The maneuvers are described in terms of the relative motion experienced in a space station centered coordinate system. Both in-orbital plane as well as out-of-orbital plane maneuvering is considered. A number of visual optimization aids are used for assisting the operator in reaching fuel-efficient solutions. These optimization aids are based on the Primer Vector theory. The visual feedback of trajectory shapes, operational constraints, and optimization functions, provided by user-transparent and continuously active background computations, allows the operator to make fast, iterative design changes that rapidly converge to fuel-efficient solutions. The planning tool is an example of operator-assisted optimization of nonlinear cost functions.
The following will outline the methodology and results of validating a coupled Method of Characteristics (MOC) and Direct Simulation Monte Carlo (DSMC) method. This research focused specifically on modeling plume impingement, induced by Reaction Control System (RCS) thrusters that flew on the National Aeronautics and Space Administration’s (NASA’s) space shuttle Discovery. For each simulation, the continuum portion of the RCS thruster was simulated using MOC for solving hyperbolic Partial Differential Equations (PDEs) and computed with the NASA code, Reacting and Multi-phase Program (RAMP). The solution was then implemented as a starting condition into the NASA DSMC code, Direct Simulation and Monte Carlo Analysis Code (DAC). Typically, DSMC models rely on code-to-code validation for fidelity. The significance of this research is in its ability to validate its models against empirical data. Prior to computing solutions for these simulations, the mesh size and structure were optimized and many variants of DSMC input parameters were iterated on in order to acquire a reliable, mesh-independent, fully optimized numerical solution. This research will discuss the mathematical formulation of MOC for nozzle flow and DSMC for rarefied gases. Additionally, it will provide an explanation of how to implement these mathematical concepts into the two solvers: RAMP and DAC. Ultimately, this research will demonstrate that the overall process illustrated produces results in good agreement with empirical data. As a consequence, the methodology presented is granted an increased level of confidence and will greatly contribute to the aerospace industry and its effort in understanding and predicting rarefied flow fields.