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At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Predictive and Neural Predictive Control of Uncertain Systems

Accomplishments and future work are:(1) Stability analysis: the work completed includes characterization of stability of receding horizon-based MPC in the setting of LQ paradigm. The current work-in-progress includes analyzing local as well as global stability of the closed-loop system under various nonlinearities; for example, actuator nonlinearities; sensor nonlinearities, and other plant nonlinearities. Actuator nonlinearities include three major types of nonlineaxities: saturation, dead-zone, and (0, 00) sector. (2) Robustness analysis: It is shown that receding horizon parameters such as input and output horizon lengths have direct effect on the robustness of the system. (3) Code development: A matlab code has been developed which can simulate various MPC formulations. The current effort is to generalize the code to include ability to handle all plant types and all MPC types. (4) Improved predictor: It is shown that MPC design using better predictors that can minimize prediction errors. It is shown analytically and numerically that Smith predictor can provide closed-loop stability under GPC operation for plants with dead times where standard optimal predictor fails. (5) Neural network predictors: When neural network is used as predictor it can be shown that neural network predicts the plant output within some finite error bound under certain conditions. Our preliminary study shows that with proper choice of update laws and network architectures such bound can be obtained. However, much work needs to be done to obtain a similar result in general case.

Kelkar, Atul G.↗
NASA NTRS1982

The applicability of Lyapunov characteristic numbers in the study of the stability of satellite orbits

It is pointed out that the Lyapunov Characteristic Numbers constitute a new tool for determining stability of trajectories of dynamical systems, or, even more generally, of solutions of systems of ordinary differential equations. In contrast with the characteristic exponents, which apply only to periodic solutions, the Lyapunov Characteristic Numbers apply to arbitrary nonperiodic solutions as well. A description is presented of the numerical experiments which have been made in order to investigate the practical value of the Lyapunov Characteristic Number and the Kolmogorov Entropy for the purpose of estimating the stability of trajectories and/or numerical integration methods in celestial mechanics. It is found that the Lyapunov Characteristic Numbers are extremely useful for the classification of the solutions of nonintegrable dynamical systems, especially in order to distinguish between quasi-periodic and chaotic solutions. However, the Lyapunov Characteristics Numbers do not appear to be useful for the purpose of evaluating numerical integration methods.

Broucke, R.↗
NASA NTRS1987

Numerical simulation of three dimensional transonic flows

The three-dimensional flow over a projectile has been computed using an implicit, approximately factored, partially flux-split algorithm. A simple composite grid scheme has been developed in which a single grid is partitioned into a series of smaller grids for applications which require an external large memory device such as the SSD of the CRAY X-MP/48, or multitasking. The accuracy and stability of the composite grid scheme has been tested by numerically simulating the flow over an ellipsoid at angle of attack and comparing the solution with a single grid solution. The flowfield over a projectile at M = 0.96 and 4 deg angle-of-attack has been computed using a fine grid, and compared with experiment.

Sahu, Jubaraj↗
DOE OSTI2023

Stabilizing a strongly nonlinear structure through shaker dynamics in fixed frequency voltage control tests

Bifurcations are commonly encountered during force controlled swept and stepped sine testing of nonlinear structures, which generally leads to the so-called jump-down or jump-up phenomena between stable solutions. There are various experimental closed-loop control algorithms, such as control-based continuation and phase-locked loop, to stabilize dynamical systems through these bifurcations, but they generally rely on specialized control algorithms that are not readily available with many commercial data acquisition software packages. A recent method was developed to experimentally apply sequential continuation using the shaker voltage that can be readily deployed using commercially available software. By utilizing the stabilizing effects of electrodynamic shakers and the force dropout phenomena in fixed frequency voltage control sine tests, this approach has been demonstrated to stabilize the unstable branch of a nonlinear system with three branches, allowing for three multivalued solutions to be identified within a specific frequency bandwidth near resonance. Recent testing on a strongly nonlinear system with vibro-impact nonlinearity has revealed jumping behavior when performing sequential continuation along the voltage parameter, like the jump phenomena seen during more traditional force controlled swept and stepped sine testing. Here, this paper investigates the stabilizing effects of an electrodynamic shaker on strongly nonlinear structures in fixed frequency voltage control tests using both numerical and experimental methods. The harmonic balance method is applied to the coupled shaker-structure system with an electromechanical model to simulate the fixed voltage control tests and predict the stabilization for different parameters of the model. The simulated results are leveraged to inform the design of a set of experiments to demonstrate the stabilization characteristics on a fixture-pylon assembly with a vibro-impact nonlinearity. Through numerical simulation and experimental testing on two different strongly nonlinear systems, the various parameters that influence the stability of the coupled shaker-structure are revealed to better understand the performance of fixed frequency voltage control tests.

42 ENGINEERING↗
NASA NTRS1999

Melt Stabilization of PbSnTe in a Magnetic Field

Both the experimental observation and numerical simulation indicate that the Bridgman growth of PbSnTe under the microgravity environment in space is still greatly influenced by buoyancy-induced convection. The application of a magnetic field during the semiconductor growth can dampen the convective flow in the metal-like melt. However, for Bridgman growth of PbSnTe on earth (with either vertical or horizontal configuration), both experimental observation and numerical modeling suggest that even with a strong magnetic furnace (5-Tesla constant axial magnetic field), the convective flow in the melt still cannot be sufficiently suppressed to reach the diffusion-controlled level. In order to completely dampen the buoyancy-induced convection on earth, estimates based on scaling analysis indicate that for common experimental conditions, an extremely high magnetic field is required, far beyond the capacity of the experimental apparatus currently available. Therefore, it is proposed that only the combination of microgravity environment and magnetic damping will produce the desired diffusion-controlled growth state for this particular material. The primary objectives of this study are to provide a quantitative understanding of the complex transport phenomena during solidification of non-dilute binarys, to furnish a numerical tool for furnace design and growth condition optimization, to provide estimates of the required magnetic field strength for low gravity growth, and to assess the role of magnetic damping for space and earth control of the double-diffusive convection. As an integral part of a NASA research program, our numerical simulation supports both the flight and ground-based experiments in an effort to bring together a complete picture of the complex physical phenomena involved in the crystal growth process. For Bridgman growth of PbSnTe under microgravity (with both vertical and horizontal configurations), the simulations suggest that a moderate axial magnetic field of only a few kilo-Gauss in strength could effectively eliminate buoyancy-induced convection in the melt and control solute segregation. Therefore, this work confirms the idea that the combination of microgravity environment and the magnetic damping will indeed be sufficient to produce the desired diffusion-controlled growth state for PbSnTe.

Fripp, Archibald L.↗
NASA NTRS2001

Jet Stability and the Generation of Superluminal and Stationary Components

We present a numerical simulation of the response of an expanding relativistic jet to the ejection of a superluminal component. The simulation has been performed with a relativistic time-dependent hydrodynamical code from which simulated radio maps are computed by integrating the transfer equations for synchrotron radiation. The interaction of the superluminal component with the underlying jet results in the formation of multiple conical shocks behind the main perturbation. These trailing components can be easily distinguished because they appear to be released from the primary superluminal component instead of being ejected from the core. Their oblique nature should also result in distinct polarization properties. Those appearing closer to the core show small apparent motions and a very slow secular decrease in brightness and could be identified as stationary components. Those appearing farther downstream are weaker and can reach superluminal apparent motions. The existence of these trailing components indicates that not all observed components necessarily represent major perturbations at the jet inlet; rather, multiple emission components can be generated by a single disturbance in the jet. While the superluminal component associated with the primary perturbation exhibits a rather stable pattern speed, trailing components have velocities that increase with distance from the core but move at less than the jet speed. The trailing components exhibit motion and structure consistent with the triggering of pinch modes by the superluminal component. The increase in velocity of the trailing components is an indirect consequence of the acceleration of the expanding fluid, which is assumed to be relativistically hot; if observed, such accelerations would therefore favor an electron-positron (as opposed to proton rest mass) dominated jet.

Agudo, Ivan↗
NASA NTRS1990

Numerical simulation of three-dimensional transonic flows

The three-dimensional flow over a projectile has been computed using an implicit, approximately factored, partially flux-split algorithm. A simple composite grid scheme has been developed in which a single grid is partitioned into a series of smaller grids for applications which require an external large memory device such as the SSD of the CRAY X-MP/48 or multi-tasking. The accuracy and stability of the composite grid scheme have been tested by numerically simulating the flow over an ellipsoid at an angle of attack and comparing the solution with a single-grid solution. The flow field over a projectile at M = 0.96 and 1.1, and 4-deg angle of attack has been computed using a fine grid and compared with experiment.

Sahu, Jubaraj↗
NASA NTRS1994

On the dynamics of some grid adaption schemes

The dynamics of a one-parameter family of mesh equidistribution schemes coupled with finite difference discretisations of linear and nonlinear convection-diffusion model equations is studied numerically. It is shown that, when time marched to steady state, the grid adaption not only influences the stability and convergence rate of the overall scheme, but can also introduce spurious dynamics to the numerical solution procedure.

Sweby, Peter K.↗
DOE OSTI2025

Simulated annealing of reduced magnetohydrodynamic systems

Theory of simulated annealing (SA), a method for equilibrium and stability analyses for Hamiltonian systems, is reviewed. The SA explained in this review is based on a double bracket formulation that derives from Hamiltonian structure. In addition to general theoretical aspects, the explicit formulation as well as numerical applications are presented. Both finite and infinite degree-of-freedom systems are treated, in particular, the heavy top, a toy model mimicking low-beta reduced magnetohydrodynamics (MHD) and low- and high-beta reduced MHD. Furthermore, the numerical results successfully demonstrate the usefulness of SA for equilibrium and stability analyses. At the same time, the results raise some future issues that are discussed in the paper.

Poisson Bracket↗
NASA NTRS1976

Application of optimal input synthesis to aircraft parameter identification

The Frequency Domain Input Synthesis procedure is used in identifying the stability and control derivatives of an aircraft. By using a frequency-domain approach, one can handle criteria that are not easily handled by the time-domain approaches. Numerical results are presented for optimal elevator deflections to estimate the longitudinal stability and control derivatives subject to root-mean square constraints on the input. The applicability of the steady state optimal inputs to finite duration flight testing is investigated. The steady state approximation of frequency-domain synthesis is good for data lengths greater than two time cycles for the short period mode of the aircraft longitudinal motions. Phase relationships between different frequency components become important for shorter data lengths. The frequency domain inputs are shown to be much better than the conventional doublet inputs.

Gupta, N. K.↗
DOE OSTI2022

Multistage Stabilized Continuation for Indirect Optimal Control of Three-Dimensional Hypersonic Trajectories

This work presents the development of a multistaged stabilized continuation for the three-dimensional unpowered hypersonic trajectory planning problem using indirect optimal control methods. The stabilized continuation method is noniterative and guaranteed to terminate within a finite number of floating point operations, thereby making it well suited for onboard autonomous implementations. Here, we present a multistage formulation of the stabilized continuation scheme that involves starting with a “loose” integration tolerance during the first stage and ramping up toward a “strict” integration tolerance through subsequent stages. An important benefit of this approach is that even when the solution to the underlying optimal control problem is numerically unstable, such as with the hypersonic vehicle footprint generation problem, the stabilized continuation algorithm is shown to be successful in finding a solution while providing some additional insights into the underlying cause of the numerical instability.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1979

Applications of Laplace transform methods to airfoil motion and stability calculations

This paper reviews the development of generalized unsteady aerodynamic theory and presents a derivation of the generalized Possio integral equation. Numerical calculations resolve questions concerning subsonic indicial lift functions and demonstrate the generation of Kutta waves at high values of reduced frequency, subsonic Mach number, or both. The use of rational function approximations of unsteady aerodynamic loads in aeroelastic stability calculations is reviewed, and a reformulation of the matrix Pade approximation technique is given. Numerical examples of flutter boundary calculations for a wing which is to be flight tested are given. Finally, a simplified aerodynamic model of transonic flow is used to study the stability of an airfoil exposed to supersonic and subsonic flow regions.

Edwards, J. W.↗
NASA NTRS1992

Prediction of high frequency combustion instability in liquid propellant rocket engines

The present use of a numerical model developed for the prediction of high-frequency combustion stabilities in liquid propellant rocket engines focuses on (1) the overall behavior of nonlinear combustion instabilities (2) the effects of acoustic oscillations on the fuel-droplet vaporization and combustion process in stable and unstable engine operating conditions, oscillating flowfields, and liquid-fuel trajectories during combustion instability, and (3) the effects of such design parameters as inlet boundary conditions, initial spray conditions, and baffle length. The numerical model has yielded predictions of the tangential-mode combustion instability; baffle length and droplet size variations are noted to have significant effects on engine stability.

Kim, Y. M.↗
DOE OSTI2023

A subdivision-stabilized B-spline mixed material point method

Subjected to external loadings, polymeric materials, e.g., biological tissues, hydrogels, and elastomers, may undergo extreme, nearly incompressible, (self-)contact deformations. For numerical modeling employing mesh-based techniques such as the finite element method (FEM), these deformations pose significant challenges due to large distortions in the deformed geometry, accuracy issues stemming from volumetric locking effects, and increased computational cost from complex contact searches. As an alternative to mesh-based methods, the material point method (MPM), a continuum-based particle technique, is gaining attention for its ability to handle extreme distortions and capture no-slip contact without added cost. For nearly incompressible material behaviors, while mixed formulations can address locking effects by treating displacements and pressure as independent fields, they can suffer from numerical instabilities close to the incompressibility limit due to the violation of the inf-sup condition, leading to inaccurate nodal pressure solutions. Here we propose an efficient and stable mixed B-spline material point method with highest achievable regularity for quasi-compressible polymeric materials. Using the two-scale relation of B-splines, we introduce a subdivision-stabilization for the two-field mixed MPM and obtain numerically stable, oscillation-free nodal solutions with equal-order interpolations with optimal regularity. Building on the Eulerian-Lagrangian nature of MPM, a previously-converged solution framework is adopted to mitigate issues related to cell-crossing and numerical fracture artifact present in standard MPM. We assess the stability and accuracy of the developed mixed MPM at large deformations for soft materials through the benchmark Cook’s membrane problem. Additionally, we test the robustness of the proposed MPM by modeling several examples, including the compression and indentation of a circular block into a quasi-compressible substrate and the twisting deformation of a rectangular block. The findings demonstrate the MPM’s capabilities for modeling practical soft material applications.

36 MATERIALS SCIENCE↗
NASA NTRS2004

Thermal Noise Limit in Frequency Stabilization of Lasers with Rigid Cavities

We evaluated thermal noise (Brownian motion) in a rigid reference cavity used for frequency stabilization of lasers, based on the mechanical loss of cavity materials and the numerical analysis of the mirror-spacer mechanics with t.he direct application of the fluctuation dissipation theorem. This noise sets a fundamental limit for the frequency stability achieved with a rigid frequency- reference cavity of order 1 Hz/square root Hz(0.01 Hz/square root Hz) at 10 mHz (100 Hz) at room temperature. This level coincides with the world-highest level stabilization results.

Numata, Kenji↗