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NASA NTRS1989

An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPs

The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain.

Warming, Robert F.↗

NASA NTRS1990

An eigenvalue analysis of finite-difference approximations for hyperbolic IBVPs

Warming, Robert F.↗

NASA NTRS2011

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

Nguyen, Nhan T.↗

NASA NTRS1975

Stability and transient motion of a plain journal mounted in flexible damped supports

Results are presented for an extensive study of the influence of damped flexible supports on the stability-threshold speed of a symmetric rotor mounted in nonlinear fluid-film bearings. A stability analysis is conducted by applying the Routh criteria and calculating the damped eigenvalues of the system. Stability maps are given in dimensionless form for a range of support stiffness, damping, and mass ratios. The effect of rotor imbalance on the stability of rotor systems is examined, and it is shown that time transient orbits of shaft and support motions clearly indicate their dynamic behavior for both stable and unstable operating speeds. Simple design criteria are proposed for choosing the support stiffness and damping on the basis of rotor weight and journal clearance to promote optimum stability. It is concluded that the use of a flexible damped support system may increase the stability threshold of a plain journal bearing and that damper supports should promote smoother and quieter machine operation by suppressing oil whirl and attenuating unbalanced rotational forces.

Kirk, R. G.↗

NASA NTRS1982

Simultaneous stabilization and simultaneous pole placement by nonswitching dynamic compensation

The 'simultaneous stabilization problem' is defined and theorems are proposed for its solution. The problem consists in answering the question: given an r-tuple G sub 1(s), G sub r(s) of p x m proper transfer functions, does there exist a compensator K(s) such that the closed loop systems G sub 1(s) (I+K(s)G sub 1(s)) (-1), G sub r(s) (I+K(s) G sub r(s)) (-1) are (internally) stable. This question arises in reliability theory, where G sub 2(s), G sub r(s) represents a plant G sub 1(s) operating in various modes of failure and K(s) is a nonswitching stabilizing compensator. It is important in the stability analysis and design of a plant which can be switched into various operating modes. The simultaneous stabilization problem can also apply to the stabilization of a nonlinear system which is linearized at several equilibria. Conditions are defined for pole placement and the generalized Sylvestor matrix is discussed.

Ghosh, B. K.↗

NASA NTRS1983

Simultaneous stabilization and simultaneous pole-placement by nonswitching dynamic compensation

Ghosh, B. K.↗

DOE OSTI2022

A Reversed Impedance-Based Stability Criterion for IBR Grids: Preprint

The existing impedance-based stability criterion is effective for analyzing local control interactions; however, it is difficult to scale the existing criterion to analyze wide-area control interactions among numerous IBRs through a complex power system network. The scaled version of the existing criterion requires the impedance response of each IBR in the system as well as of the network looking from all the IBRs. It is quite challenging to obtain all these impedance responses because of the computational effort and the requirement of separately scanning the impedance of the network and the IBRs. We propose a reversed criterion for the impedance-based stability analysis to address these problems. In contrast to the existing criterion, the reversed criterion analyzes the stability of a power system when an IBR is disconnected from the system. The reversed criterion estimates the impact of an IBR on the frequency and damping of power system oscillation modes using the impedance scans of only the IBR and the grid at its terminal. It can be sequentially applied at different IBRs to evaluate their impact on the power system stability. In addition to scalability, the reversed criterion gives flexibility to focus only on a few selected IBRs, depending on their rating, the magnitude of oscillations observed at their terminals, and the vendor support available for implementing stabilizing control system updates. The reversed criterion is demonstrated on a 14-bus power system with 100% IBRs.

control interactions↗

DOE OSTI2024

Discrete-Element and Material-Point Method (DEM and MPM) Based Solvers for Sustainable Technologies

We present the use of discrete element method (DEM) and material point method (MPM) in three relevant green technology applications that include biomass feedstock handling, lithium-ion battery manufacturing, and high-pressure reverse osmosis. Our open-source DEM and MPM solvers are developed using performance portable grid and particle management library, AMReX, thus enabling superior performance on NVIDIA and AMD GPUs with > 100 million particles. Our DEM solver resolves the motion of individual particles in a granular system and includes a bonded sphere method for modeling non-spherical particles along with Hertzian and liquid bridge-based contact models. We simulate highly variable biomass feedstock flows in large-scale hoppers for biofuel production and electrode calendering in battery manufacturing using DEM. Our simulations predict flow blockage in large scale biomass hoppers and electrode microstructure variations, thus providing valuable information for biofuel and battery manufacturers, respectively. The second half of the talk will be on MPM and its application towards pore resolved simulations of reverse osmosis membranes under compressive loads. We present a validation study of our MPM simulations with membrane microscopy imaging thus providing useful insights on membrane stability under high pressure conditions. We also present a spectral stability analysis of using linear hat, quadratic and cubic spline basis in MPM indicating regions of numerical stability.

BIOMASS FUELS,MATHEMATICS AND COMPUTING↗

NASA NTRS2004

Refinement of the ICRF

Since the ICRF was generated in 1995, VLBI modeling and estimation, data quality: source position stability analysis, and supporting observational programs have improved markedly. There are developing and potential applications in the areas of space navigation Earth orientation monitoring and optical astrometry from space that would benefit from a refined ICRF with enhanced accuracy, stability and spatial distribution. The convergence of analysis, focused observations, and astrometric needs should drive the production of a new realization in the next few years.

Ma, Chopo↗

NASA NTRS1991

Interface behavior of a multi-layer fluid configuration subject to acceleration in a microgravity environment, supplement 1

With the increasing opportunities for research in a microgravity environment, there arises a need for understanding fluid mechanics under such conditions. In particular, a number of material processing configurations involve fluid-fluid interfaces which may experience instabilities in the presence of external forcing. In a microgravity environment, these accelerations may be periodic or impulse-type in nature. This research investigates the behavior of a multi-layer idealized fluid configuration which is infinite in extent. The analysis is linear, and each fluid region is considered inviscid, incompressible, and immiscible. An initial parametric study of confiquration stability in the presence of a constant acceleration field is performed. The zero mean gravity limit case serves as the base state for the subsequent time-dependent forcing cases. A stability analysis of the multi-layer fluid system in the presence of periodic forcing is investigated. Floquet theory is utilized. A parameter study is performed, and regions of stability are identified. For the impulse-type forcing case, asymptotic stability is established for the configuration. Using numerical integration, the time response of the interfaces is determined.

Lyell, M. J.↗

DOE OSTI2026

Characterization of ELM pacing via vertical jogs on DIII-D

Edge localized mode (ELM) pacing via vertical plasma oscillations or jogging has been successfully demonstrated on DIII-D. Rapid vertical movement of the plasma toward the X-point has been shown to effectively trigger ELMs. By vertically oscillating the plasma at a rate of 10 Hz, the ELM frequency increased from ~5 Hz, the natural ELM frequency in similar DIII-D discharges, to 20 Hz. Downward jogs have been observed to trigger multiple ELMs in one cycle. ELMs triggered at higher than natural frequencies lead to smaller decreases in stored energy, from 8% to as little as below 1%. As a consequence, the peak heat flux to the divertor has been observed to be reduced by a factor of ~2. In addition, a reduction in the carbon impurity concentration has been observed. During downward jogs in the lower single null (LSN) configuration, the X-point movement is slower and smaller than the top of the plasma. As a result, a reduction in the plasma cross-section and hence volume has been observed. To understand the mechanism of ELM triggering by jogging, a toy model of the edge toroidal current has been built and tested with DIII-D experiment data. The experimental data and model suggest that when the plasma moves down toward the X-point, a net positive toroidal current is locally induced in the edge region. ELITE stability analysis suggests that this current pushes the plasma state across the peeling side of the peeling–ballooning stability boundary into the unstable region triggering ELMs.

ELM pacing↗

DOE OSTI2026

Dynamic Validation of CNN-Based Surrogate Models for Inverter-Based Resources in Open-Source Solvers

Traditionally, distribution system planning has focused on steady-state analyses, with limited consideration of dynamic behavior. However, as large or medium-scale inverter-based resources (IBRs), particularly grid-following (GFL) inverters in commercial or industry buildings, become more prevalent, understanding their dynamic impact is essential for grid planning and operation. This article presents an innovative deep-learning (DL)-approach using convolutional neural networks technique to model the GFL inverters. Developed from real grid-tied commercial IBR transient data, these dynamic DL models overcome proprietary constraints by requiring minimal knowledge of internal converter physics while maintaining high accuracy and flexibility. To demonstrate their applicability, the models were incorporated into GridLAB-D, an open-source, three-phase distribution analysis tool. This integration enables dynamic simulations of large-scale distribution networks with high IBR penetration stability analysis. Rigorous testing and validation, aligned with industry standards, confirmed the reliability and efficiency of this approach, paving the way for enhanced planning and operational assessments of modern power systems.

Deep-learning↗

NASA NTRS1975

Stabilization of large-scale systems - A spinning flexible spacecraft

Stabilization of high-order constant systems by multilevel control is proposed in the framework of the decomposition-aggregation method for stability analysis of large-scale systems. An 11-order linear model of a spinning flexible spacecraft is stabilized by the method using both the passive and the active stabilization devices. The method can take advantage of the special structural features of the model to provide the best estimate of the stability region for an important parameter which couples the wobble and the spin motion of the spacecraft.

Siljak, D. D.↗

NASA NTRS1988

Flight survey of the 757 wing noise field and its effects on laminar boundary layer transition. Volume 3: Extended data analysis

A flight program was completed in June of 1985 using the Boeing 757 flight research aircraft with an NLF glove installed on the right wing just outboard of the engine. The objectives of this program were to measure noise levels on the wing and to investigate the effect of engine noise on the extent of laminar flow on the glove. Details of the flight test program and results are contained in Volume 1 of this document. Tabulations and plots of the measured data are contained in Volume 2. The present volume contains the results of additional engineering analysis of the data. The latter includes analysis of the measured noise data, a comparison of predicted and measured noise data, a boundary layer stability analysis of 21 flight data cases, and an analysis of the effect of noise on boundary layer transition.

Source record↗

NASA NTRS2014

Dual Fan Separator within the Universal Waste Management System

Since NASA's new spacecraft in development for both LEO and Deep Space capability have considerable crew volume reduction in comparison to the Space Shuttle, it is clear that NASA requires a smaller and less expensive commode. The UTAS Universal Waste Management System (UWMS) was designed to address these new constraints, resulting in an 80% volume reduction in the cabin while enhancing performance. Whereas all of the current space commodes use air flow to capture both urine and feces and separate air from the captured air/urine mixture, the UWMS commode and urine fans and the urine separator were combined into a single unit. This unit enables use of a single motor and motor controller, which provides considerable packaging and weight efficiency. In some of the intended platform applications for the UWMS, the urine is pumped to a water reclamation system. The ISS Urine Processor Assembly (UPA) system requires delivered urine to include less than 0.25% air inclusion. Air inclusion in centrifugal urine separators is greatly dependent on its rotational speed. To satisfy this requirement, a gear reducer was included, allowing the fans to rotate at a much higher speed than the separator. This new design, the Dual Fan Separator (DFS) has been designed, prototyped and tested. This paper will outline the studies and analysis performed to develop the design configuration for testing. The studies included a configuration trade study, dynamic stability analysis of the rotating bodies and a performance analysis of included labyrinth seals. NASA is considereing a program to fly the UWMS aboard the ISS as a flight experiment. The goal of the design activity is to elevate the Technical Readiness Level (TRL) of the Dual Fan Separator and determine if the concept is ready to be included in flight experiment deliverable.

Stapleton, Tom↗

NASA NTRSDate not supplied

Eigenvalue Sensitivity Computations for Linear Stability Theory

To realize the drag reduction benefit of boundary-layer transition control strategies, it is crucial to integrate transition prediction into the vehicle design through an optimization process. The integration of transition prediction based on linear stability analysis into adjoint d design optimization requires coupling an adjoint enabled computational fluid dynamics (CFD) solver with an adjoint enabled linear stability code. In particular, the boundary-layer transition location is often predicted using the N-factor method based on linear stability theory (LST). Thus, sensitivity of the linear-stability eigenvalues constitute an essential building block for optimizing the laminar flow performance. The present paper describes an implementation of LST eigenvalue sensitivity analysis that can be easily coupled with a CFD solver. Specifically, we describe a discrete adjoint formulation for the transition location prediction based on the N-factor method. The verification of this formulation is carried out by comparing the adjoint-based sensitivity of the local growth rate of a given instability mode with respect to the disturbance frequency, and the adjoint-based sensitivity of the transition location with respect to spanwise wavenumber with those sensitivities computed using a finite-difference approximation. Finally, the adjoint LST formulation is applied to flat-plate boundary-layer flows at transonic, supersonic, and hypersonic conditions, to determine the behavior and sensitivities of the transition location with respect to a range of disturbance spanwise wavenumbers.

Boundary Layer Transition↗

NASA NTRS1985

Analysis of some fully-discrete algorithms for the one-dimensional heat equation

The present investigation is concerned with a fully discrete accuracy and stability analysis of the one-dimensional heat equation, taking into account the evaluation of two-pass explicit schemes which simultaneously employ lumped and coupled capacity matrices. Schemes of the considered characteristics are not amenable to uncoupled semidiscrete and ordinary differential equation analyses. The obtained results illustrate that superior behavior may be achieved by schemes of the employed type when compared with the performance of the standard one-pass explicit schemes. The key idea in the considered approach is related to the utilization of a reduced-quadrature capacity matrix in the evaluation of the right-hand-side residual.

Hughes, T. J. R.↗

NASA NTRS1974

Asymmetrical booster ascent guidance and control system design study. Volume 1: Summary

Dynamics and control, stability, and guidance analyses are summarized for the asymmetrical booster ascent guidance and control system design studies, performed in conjunction with space shuttle planning. The mathematical models developed for use in rigid body and flexible body versions of the NASA JSC space shuttle functional simulator are briefly discussed, along with information on the following: (1) space shuttle stability analysis using equations of motion for both pitch and lateral axes; (2) the computer program used to obtain stability margin; and (3) the guidance equations developed for the space shuttle powered flight phases.

Williams, F. E.↗