Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear operator theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15

Predictions of core plasma performance for the SPARC tokamak

SPARC is designed to be a high-field, medium-size tokamak aimed at achieving net energy gain with ion cyclotron range-of-frequencies (ICRF) as its primary auxiliary heating mechanism. Empirical predictions with conservative physics indicate that SPARC baseline plasmas would reach $\textit{Q}$ ≈ 11, which is well above its mission objective of $\textit{Q}$ > 2. To build confidence that SPARC will be successful, physics-based integrated modelling has also been performed. The TRANSP code coupled with the theory-based trapped gyro-Landau fluid (TGLF) turbulence model and EPED predictions for pedestal stability find that $\textit{Q}$ ≈ 9 is attainable in standard H-mode operation and confirms $\textit{Q}$ > 2 operation is feasible even with adverse assumptions. In this analysis, ion cyclotron waves are simulated with the full wave TORIC code and alpha heating is modelled with the Monte–Carlo fast ion NUBEAM module. Detailed analysis of expected turbulence regimes with linear and nonlinear CGYRO simulations is also presented, demonstrating that profile predictions with the TGLF reduced model are in reasonable agreement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dynamic Ground Effect for a Cranked Arrow Wing Airplane

Flight-determined ground effect characteristics for an F-16XL airplane are presented and correlated with wind tunnel predictions and similar flight results from other aircraft. Maneuvers were conducted at a variety of flightpath angles. Conventional ground effect flight test methods were used, with the exception that space positioning data were obtained using the differential global positioning system (DGPS). Accuracy of the DGPS was similar to that of optical tracking methods, but it was operationally more attractive. The dynamic flight determined lift and drag coefficient increments were measurably lower than steady-state wind-tunnel predictions. This relationship is consistent with the results of other aircraft for which similar data are available. Trends in the flight measured lift increments caused by ground effect as a function of flightpath angle were evident but weakly correlated. An engineering model of dynamic ground effect was developed based on linear aerodynamic theory and super-positioning of flows. This model was applied to the F-16XL data set and to previously published data for an F-15 airplane. In both cases, the model provided an engineering estimate of the ratio between the steady-state and dynamic data sets.

Curry, Robert E.↗

He II Liquid/Vapor Phase Separator for Large Dynamic Range Operation

A phase separator, which separates helium vapor from liquid superfluid helium (He II), is an indispensable device for space cryogenics. The most recent approach to the Space Infrared Telescope Facility (SIRTF) uses a new design concept in which only the detector package is cold at launch, the remainder of the telescope being subsequently cooled to operating temperature on orbit. Therefore, a large dynamic operational range is required of the cryogen system. This is a report of initial laboratory test results with candidate porous plugs as phase separators. Mass flow rates and pressure and temperature differences across a porous plug were measured in this experiment. Relatively large mass flow rates were observed even at small pressure differences. In the high mass flow rate region, a hysteresis was observed with increases and decreases of the pressure difference. A linear theory is proposed and compared with experimental data to explain several phenomena observed in this system.

Phase Separator, Space Cryogenics↗

Electron dynamics and energy conversion in O-type linear-beam devices.

A general nonlinear interaction theory is used to investigate the effects of transverse fields (i.e., radial circuit fields and radial space-charge fields) in traveling-wave amplifiers for a variety of beam-focusing conditions. Magnetic focusing fields which are periodic or tapered (increased) with distance along the device are considered in addition to uniform magnetic fields. Results are presented for Brillouin flow and near-Brillouin flow, and the minimum magnetic field strength required to effectively constrain the electron beam is determined as a function of the operating parameters for the various focusing systems. Confined flow is also examined for the uniform-field case in order to have a basis of comparison from which the effects of radial motion of the beam electrons can be determined. The results indicate the importance of transverse effects and further yield information on the stability of strongly modulated cylindrical electron beams.-

Detweiler, H. K.↗

One-loop matrix elements of effective superstring interactions: α' -expanding loop integrands

In the low-energy effective action of string theories, non-abelian gauge interactions and supergravity are augmented by infinite towers of higher-mass-dimension operators. We propose a new method to construct one-loop matrix elements with insertions of operators D 2k F n and D 2k R n in the tree-level effective action of type-I and type-II superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of moduli-space integrals using string tree-level amplitudes with two extra points, expanded in powers of the inverse string tension α'. Similar to one-loop ambitwistor computations, intermediate steps feature non-standard linearized Feynman propagators which eventually recombine to conventional quadratic propagators. With linearized propagators the loop integrand of the matrix elements obey one-loop versions of the monodromy and KLT relations. We express a variety of four- and five-point examples in terms of quadratic propagators and formulate a criterion on the underlying genus-one correlation functions that should make this recombination possible at all orders in α'. The ultraviolet divergences of the one-loop matrix elements are crosschecked against the non-separating degeneration of genus-one integrals in string amplitudes. Conversely, our results can be used as a constructive method to determine degenerations of elliptic multiple zeta values and modular graph forms at arbitrary weight.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Fabrication and evaluation of polymeric early-warning fire-alarm devices

The electrical resistivities were investigated of some polymers known to be enhanced by the presence of certain gases. This was done to make a device capable of providing early warning to fire through its response with the gases produced in the early phases of combustion. Eight polymers were investigated: poly(phenyl acetylene), poly(p-aminophenyl acetylene), poly(p-nitrophenyl acetylene), poly(p-formamidophenyl acetylene), poly(ethynyl ferrocene), poly(ethynyl carborane), poly(ethynyl pyridine), and the polymer made from 1,2,3,6 tetramethyl pyridazine. A total of 40 usable thin-film sandwich devices and a total of 70 usable interdigitated-electrode lock-and-key devices were fabricated. The sandwich devices were used for measurements of contact linearity, polymer conductivity, and polymer dielectric constant. The lock-and-key devices were used to determine the response of the polymers to a spectrum of gases that included ammonia, carbon nonoxide, carbon dioxide, sulfur dioxide, ethylene, acrolein, water vapor, and normal laboratory air. Strongest responses were to water vapor, ammonia, and acrolein, and depending on the polymer, weaker responses to carbon dioxide, sulfur dioxide, and carbon monoxide were observed. A quantitative theory of device operation, capable of accounting for observed device leakage current and sensitivity, was developed. A prototype detection/alarm system was designed and built for use in demonstrating sensor performance.

Senturia, S. D.↗

Numerical analysis of right-half plane zeros for a single-link manipulator

The purpose of this research is to further develop an understanding of how nonminimum phase zero location is affected by structural link design. As the demand for light-weight robots that can operate in a large workspace increases, the structural flexibility of the links become more of an issue in controls problems. When the objective is to accurately position the tip while the robot is actuated at the base, the system is nonminimum phase. One important characteristic of nonminimum phase systems is system zeros in the right half of the Laplace plane. The ability to pick the location of these nonminimum phase zeros would give the designer a new freedom similar to pole placement. The research targets a single-link manipulator operating in the horizontal plane and modeled as a Euler-Bernoulli beam with pinned-free end conditions. Using transfer matrix theory, one can consider link designs that have variable cross-sections along the length of the beam. A FORTRAN program was developed to determine the location of poles and zeros given the system model. The program was used to confirm previous research on nonminimum phase systems, and develop a relationship for designing linearly tapered links. The method allows the designer to choose the location of the first pole and zero and then defines the appropriate taper to match the desired locations. With the pole and zero location fixes, the designer can independently change the link's moment of inertia about its axis of rotation by adjusting the height of the beam. These results can be applied to inverse dynamic algorithms currently under development at Georgia Tech.

Girvin, Douglas Lynn↗

Numerical analysis of nonminimum phase zero for nonuniform link design

As the demand for light-weight robots that can operate in a large workspace increases, the structural flexibility of the links becomes more of an issue in control. When the objective is to accurately position the tip while the robot is actuated at the base, the system is nonminimum phase. One important characteristic of nonminimum phase systems is system zeros in the right half of the Laplace plane. The ability to pick the location of these nonminimum phase zeros would give the designer a new freedom similar to pole placement. This research targets a single-link manipulator operating in the horizontal plane and modeled as a Euler-Bernoulli beam with pinned-free end conditions. Using transfer matrix theory, one can consider link designs that have variable cross-sections along the length of the beam. A FORTRAN program was developed to determine the location of poles and zeros given the system model. The program was used to confirm previous research on nonminimum phase systems, and develop a relationship for designing linearly tapered links. The method allows the designer to choose the location of the first pole and zero and then defines the appropriate taper to match the desired locations. With the pole and zero location fixed, the designer can independently change the link's moment of inertia about its axis of rotation by adjusting the height of the beam. These results can be applied to the inverse dynamic algorithms that are currently under development.

Girvin, Douglas L.↗

Anomaly Detection in Test Equipment via Sliding Mode Observers

Nonlinear observers were originally developed based on the ideas of variable structure control, and for the purpose of detecting disturbances in complex systems. In this anomaly detection application, these observers were designed for estimating the distributed state of fluid flow in a pipe described by a class of advection equations. The observer algorithm uses collected data in a piping system to estimate the distributed system state (pressure and velocity along a pipe containing liquid gas propellant flow) using only boundary measurements. These estimates are then used to further estimate and localize possible anomalies such as leaks or foreign objects, and instrumentation metering problems such as incorrect flow meter orifice plate size. The observer algorithm has the following parts: a mathematical model of the fluid flow, observer control algorithm, and an anomaly identification algorithm. The main functional operation of the algorithm is in creating the sliding mode in the observer system implemented as software. Once the sliding mode starts in the system, the equivalent value of the discontinuous function in sliding mode can be obtained by filtering out the high-frequency chattering component. In control theory, "observers" are dynamic algorithms for the online estimation of the current state of a dynamic system by measurements of an output of the system. Classical linear observers can provide optimal estimates of a system state in case of uncertainty modeled by white noise. For nonlinear cases, the theory of nonlinear observers has been developed and its success is mainly due to the sliding mode approach. Using the mathematical theory of variable structure systems with sliding modes, the observer algorithm is designed in such a way that it steers the output of the model to the output of the system obtained via a variety of sensors, in spite of possible mismatches between the assumed model and actual system. The unique properties of sliding mode control allow not only control of the model internal states to the states of the real-life system, but also identification of the disturbance or anomaly that may occur.

Solano, Wanda M.↗

A Threshold Theory for Phase-Locked Loops

A model of a phase-locked loop has been developed which is valid for all signal-to-noise ratios. The model is in the form of a nonlinear feedback system with randomly time-varying parameters. The analysis considers two operating regions. In low signal-to-noise ratio regions, the important consideration is stability. We want to study the asymptotic stability in the mean of a nonlinear system. It follows directly that a necessary condition for asymptotic stability of any nonlinear system is that a linearized model about some equilibrium point be asymptotically stable. By considering all possible equilibrium points, we can find an upper bound on the value of noise density which makes the system unstable. This upper bound represents a threshold value for system operation. In high signal-to-noise ratio regions, our results provide an exact statistical. description of system behavior. Therefore, knowledge of the spectrum of the signal and noise may be used to optimize the system configuration.

Van Trees, H. L.↗

ASCEND: Asymptotically compatible strong form foundations for nonlocal discretization

Nonlocal models naturally handle a range of physics of interest to SNL, but discretization of their underlying integral operators poses mathematical challenges to realize the accuracy and robustness commonplace in discretization of local counterparts. This project focuses on the concept of asymptotic compatibility, namely preservation of the limit of the discrete nonlocal model to a corresponding well-understood local solution. We address challenges that have traditionally troubled nonlocal mechanics models primarily related to consistency guarantees and boundary conditions. For simple problems such as diffusion and linear elasticity we have developed complete error analysis theory providing consistency guarantees. We then take these foundational tools to develop new state-of-the-art capabilities for: lithiation-induced failure in batteries, ductile failure of problems driven by contact, blast-on-structure induced failure, brittle/ductile failure of thin structures. We also summarize ongoing efforts using these frameworks in data-driven modeling contexts. This report provides a high-level summary of all publications which followed from these efforts.

97 MATHEMATICS AND COMPUTING↗

A Koopman-based residual modeling approach for the control of a soft robot arm

Soft robots are challenging to model and control due to their poorly defined kinematics and nonlinear dynamics. Recently, Koopman operator theory has been shown capable of constructing control-oriented soft robot models from data. However, building these models requires extensive data collection and they do not necessarily generalize well outside of the training observations. This paper presents a more data-efficient and generalizable approach to soft robot modeling that first identifies a physics-based Koopman model then supplements it with a data-driven residual Koopman model. The resulting combined model is linear and thus compatible with real-time model-based control techniques such as Model Predictive Control (MPC). The efficacy of the approach is demonstrated on several simulated systems and on a real soft robot arm, where it is shown to generate models that are more accurate than purely physics-based models and require less data to construct than purely data-driven models. Using a model-based controller, the soft arm is able to successfully track end effector trajectories, perform a pick-and-place task, and write on a dry-erase board, showcasing the applicability of this framework to increase the capabilities of soft robotic systems.

Daniel Bruder↗

Time-dependent density functional theory with the orthogonal projector augmented wave method

The projector augmented wave (PAW) method of Blöchl linearly maps smooth pseudo wavefunctions to the highly oscillatory all-electron DFT orbitals. Compared to norm-conserving pseudopotentials (NCPP), PAW has the advantage of lower kinetic energy cutoffs and larger grid spacing at the cost of having to solve for non-orthogonal wavefunctions. We earlier developed orthogonal PAW (OPAW) to allow the use of PAW when orthogonal wavefunctions are required. In OPAW, the pseudo wavefunctions are transformed through the efficient application of powers of the PAW overlap operator with essentially no extra cost compared to NCPP methods. Previously, we applied OPAW to DFT. Here, we take the first step to make OPAW viable for post-DFT methods by implementing it in real-time time-dependent (TD) DFT. Using fourth-order Runge–Kutta for the time-propagation, we compare calculations of absorption spectra for various organic and biological molecules and show that very large grid spacings are sufficient, 0.6–0.7 bohr in OPAW-TDDFT rather than the 0.4–0.5 bohr used in traditional NCPP-TDDFT calculations. This reduces the memory and propagation costs by around a factor of 3. Our method would be directly applicable to any post-DFT methods that require time-dependent propagations such as the GW approximation and the Bethe–Salpeter equation.

Chemistry↗

A flight-dynamic helicopter mathematical model with a single flap-lag-torsion main rotor

A mathematical model of a helicopter system with a single main rotor that includes rigid, hinge-restrained rotor blades with flap, lag, and torsion degrees of freedom is described. The model allows several hinge sequences and two offsets in the hinges. Quasi-steady Greenberg theory is used to calculate the blade-section aerodynamic forces, and inflow effects are accounted for by using three-state nonlinear dynamic inflow model. The motion of the rigid fuselage is defined by six degrees of freedom, and an optional rotor rpm degree of freedom is available. Empennage surfaces and the tail rotor are modeled, and the effect of main-rotor downwash on these elements is included. Model trim linearization, and time-integration operations are described and can be applied to a subset of the model in the rotating or nonrotating coordinate frame. A preliminary validation of the model is made by comparing its results with those of other analytical and experimental studies. This publication presents the results of research compiled in November 1989.

Takahashi, Marc D.↗

Recent Development in the Analytical Investigation of Shipboard Rotorcraft Engage and Disengage Operations

This paper presents an overview of recent developments in an effort to predict transient aeroelastic rotor response during shipboard engage and disengage sequences. The blade is modeled as an elastic beam undergoing in flap, lag, extension and torsion. The blade equations of motion are formulated using Hamilton's principle and they are spatially discretized using the finite element method. The discretized blade equations of motion are integrated for a specified rotor speed run-up or run-down profile. Blade element theory is used to calculate quasi-steady or unsteady aerodynamic loads in linear and nonlinear regimes. The analysis is capable of simulating both articulated, hingeless, and gimballed rotor systems. Validation of the rotor code is discussed, including correlation with droop stop impact tests and wind tunnel experiments. Predictions of safe engagement and disengagement envelopes, limited by excessive blade tip deflections or hub moments, are presented. Future directions of study are also discussed.

Smith, Edward C.↗

Boundary Corrections for Kernel Approximation to Differential Operators

The kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same computational cost as an explicit finite difference scheme but can exhibit order reduction at boundaries. In previous work on periodic domains, order reduction was addressed, yielding high-order accuracy. The issue addressed in this work is the elimination of order reduction of the kernel-based approach for a more general set of boundary conditions. Further, we consider the case of both first and second order operators. To demonstrate the theory, we provide not only the mathematical proofs but also experimental results by applying various boundary conditions to different types of equations. The results agree with the theory, demonstrating a systematic path to high order for kernel-based methods on bounded domains.

97 MATHEMATICS AND COMPUTING↗

The role of modern control theory in the design of controls for aircraft turbine engines

The development, applications, and current research in modern control theory (MCT) are reviewed, noting the importance for fuel-efficient operation of turbines with variable inlet guide vanes, compressor stators, and exhaust nozzle area. The evolution of multivariable propulsion control design is examined, noting a basis in a matrix formulation of the differential equations defining the process, leading to state space formulations. Reports and papers which appeared from 1970-1982 which dealt with problems in MCT applications to turbine engine control design are outlined, including works on linear quadratic regulator methods, frequency domain methods, identification, estimation, and model reduction, detection, isolation, and accommodation, and state space control, adaptive control, and optimization approaches. Finally, NASA programs in frequency domain design, sensor failure detection, computer-aided control design, and plant modeling are explored

Zeller, J.↗

Tilt-rotor flutter control in cruise flight

Tilt-rotor flutter control under cruising operation is analyzed. The rotor model consists of a straight fixed wing, a pylon attached to the wingtip, and a three-blade rotor. The wing is cantilevered to the fuselage and is allowed to bend forward and upward. It also has a torsional degree of freedom about the elastic axis. Each rotor blade has two bending degrees of freedom. Feedback of wingtip velocity and acceleration to cyclic pitch is investigated for flutter control, using strip theory and linearized equations of motion. To determine the feedback gain, an eigenvalue analysis is performed. A second, independent, timewise calculation is conducted to evaluate the control law while employing more sophisticated aerodynamics. The effectiveness of flutter control by cyclic pitch change was confirmed.

Nasu, Ken-Ichi↗