Results for “nonlinear dynamical system” — Page 42

NASA NTRS1994

CFD Optimization on Network-Based Parallel Computer System

Combining multiple engineering workstations into a network-based heterogeneous parallel computer allows application of aerodynamic optimization with advance computational fluid dynamics codes, which is computationally expensive in mainframe supercomputer. This paper introduces a nonlinear quasi-Newton optimizer designed for this network-based heterogeneous parallel computer on a software called Parallel Virtual Machine. This paper will introduce the methodology behind coupling a Parabolized Navier-Stokes flow solver to the nonlinear optimizer. This parallel optimization package has been applied to reduce the wave drag of a body of revolution and a wing/body configuration with results of 5% to 6% drag reduction.

Cheung, Samson H.↗

NASA NTRS1974

Management of analytical redundancy in digital flight control systems for aircraft

This paper presents a design method for optimal redundancy management for nonlinear systems with application to highly maneuvering aircraft. The approach taken is based on selecting the failure states to be covered by the system design and constructing a cost function that represents the cost of making an incorrect decision. The decision logic which minimizes the cost requires a bank of extended Kalman filters running in parallel. This produces a severe computational requirement. To reduce this requirement, a suboptimal logic is developed based on using a nonlinear single-stage prediction algorithm in the filters with filter gains and decision logic selected using steady-state results obtained from a linearization of the vehicle and sensor dynamics. The design process is then applied to designing a redundancy management system for the F8-C aircraft. Results indicate that the system is superior in failure detection to a system using the same structure but using a linear single-stage prediction algorithm in the filters.

Montgomery, R. C.↗

NASA NTRS2003

Aeroservoelastic Model Validation and Test Data Analysis of the F/A-18 Active Aeroelastic Wing

Model validation and flight test data analysis require careful consideration of the effects of uncertainty, noise, and nonlinearity. Uncertainty prevails in the data analysis techniques and results in a composite model uncertainty from unmodeled dynamics, assumptions and mechanics of the estimation procedures, noise, and nonlinearity. A fundamental requirement for reliable and robust model development is an attempt to account for each of these sources of error, in particular, for model validation, robust stability prediction, and flight control system development. This paper is concerned with data processing procedures for uncertainty reduction in model validation for stability estimation and nonlinear identification. F/A-18 Active Aeroelastic Wing (AAW) aircraft data is used to demonstrate signal representation effects on uncertain model development, stability estimation, and nonlinear identification. Data is decomposed using adaptive orthonormal best-basis and wavelet-basis signal decompositions for signal denoising into linear and nonlinear identification algorithms. Nonlinear identification from a wavelet-based Volterra kernel procedure is used to extract nonlinear dynamics from aeroelastic responses, and to assist model development and uncertainty reduction for model validation and stability prediction by removing a class of nonlinearity from the uncertainty.

Brenner, Martin J.↗

NASA NTRS2024

Nonlinear Dynamic Analyses of STS-1 Forward RCS Oxidizer Tank Structural Failure

At liftoff of the first Space Shuttle mission, a strong ignition overpressure pulse excited the stack. The frequency of the experienced pressure wave exceeded pre-launch predictions, and resulted in high, alternating normal accelerations along the length of the vehicle. As result of this unexpected loading, an oxidizer tank support strut in the orbiter’s forward reaction control system module failed in buckling under axial compression, which could have led to loss of the mission, crew, and vehicle. This incident is investigated in more detail using linear and nonlinear finite element analyses, complementing previous analyses with classical structural mechanics. The results of these analyses are examined to provide additional insight into the accident and to better inform future design decisions for modern space vehicle systems and structures.

Space Shuttle↗

NASA NTRS2024

Nonlinear Dynamic Analyses of STS-1 Forward RCS Oxidizer Tank Structural Failure

At liftoff of the first Space Shuttle mission, a strong ignition overpressure pulse excited the stack. The frequency of the experienced pressure wave exceeded pre-launch predictions, and resulted in high, alternating normal accelerations along the length of the vehicle. As result of this unexpected loading, an oxidizer tank support strut in the orbiter’s forward reaction control system module failed in buckling under axial compression, which could have led to loss of the mission, crew, and vehicle. This incident is investigated in more detail using linear and nonlinear finite element analyses, complementing previous analyses with classical structural mechanics. The results of these analyses are examined to provide additional insight into the accident and to better inform future design decisions for modern space vehicle systems and structures.

Space Shuttle↗

NASA NTRS1984

Dynamics of dendritic pattern formation

This paper is a brief review of recent and ongoing developments in the theory of dendritic pattern formation. A marginal stability hypothesis has achieved some success in predicting dendritic growth rates, but a fully nonlinear dynamic theory of the dendritic growth mechanism has yet to be developed. A possible clue for the construction of such a theory is the existence of a class of one-dimensional models in which a pattern is found to spread into an unstable region by propagating at the slowest stable speed. This mathematical realization of the marginal stability mechanism has led to the development of a boundary layer model which describes localized dynamics of fully two- or three-dimensional solidification fronts and which retains some of the mathematical features of the propagating systems. Preliminary results of numerical calculations using the boundary layer model indicate that it is capable of probing fully nonlinear features of dendritic pattern formation.

Langer, J. S.↗

NASA NTRS2016

Wave Amplitude Dependent Engineering Model of Propellant Slosh in Spherical Tanks

Liquid propellant slosh is often a concern for the controllability of flight vehicles. Anti-slosh devices are traditionally included in propellant tank designs to limit the amount of sloshing allowed during flight. These devices and any necessary supports can be quite heavy to meet various structural requirements. Some of the burden on anti-slosh devices can be relieved by exploiting the nonlinear behavior of slosh waves in bare smooth wall tanks. A nonlinear regime slosh model for bare spherical tanks was developed through a joint analytical and experimental effort by NASA/MSFC. The developed slosh model accounts for the large damping inherent in nonlinear slosh waves which is more accurate and drives conservatism from vehicle stability analyses that use traditional bare tank slosh models. A more accurate slosh model will result in more realistic predicted slosh forces during flight reducing or removing the need for active controls during a maneuver or baffles in the tank design. Lower control gains and smaller or fewer tank baffles can reduce cost and system complexity while increasing vehicle performance. Both Computational Fluid Dynamics (CFD) simulation and slosh testing of three different spherical tank geometries were performed to develop the proposed slosh model. Several important findings were made during this effort in addition to determining the parameters to the nonlinear regime slosh model. The linear regime slosh damping trend for spherical tanks reported in NASA SP-106 was shown to be inaccurate for certain regions of a tank. Additionally, transition to the nonlinear regime for spherical tanks was only found to occur at very large wave amplitudes in the lower hemisphere and was a strong function of the propellant fill level in the upper hemisphere. The nonlinear regime damping trend was also found to be a function of the propellant fill level.

Brodnick, Jacob↗

NASA NTRS1994

Dynamic analysis of a magnetic bearing system with flux control

Using measured values of two-dimensional forces in a magnetic actuator, equations of motion for an active magnetic bearing are presented. The presence of geometric coupling between coordinate directions causes the equations of motion to be nonlinear. Two methods are used to examine the unbalance response of the system: simulation by direct integration in time; and determination of approximate steady state solutions by harmonic balance. For relatively large values of the derivative control coefficient, the system behaves in an essentially linear manner, but for lower values of this parameter, or for higher values of the coupling coefficient, the response shows a split of amplitudes in the two principal directions. This bifurcation is sensitive to initial conditions. The harmonic balance solution shows that the separation of amplitudes actually corresponds to a change in stability of multiple coexisting solutions.

Knight, Josiah↗

NASA NTRS1998

Parallel Three-Dimensional Computation of Fluid Dynamics and Fluid-Structure Interactions of Ram-Air Parachutes

This is a final report as far as our work at University of Minnesota is concerned. The report describes our research progress and accomplishments in development of high performance computing methods and tools for 3D finite element computation of aerodynamic characteristics and fluid-structure interactions (FSI) arising in airdrop systems, namely ram-air parachutes and round parachutes. This class of simulations involves complex geometries, flexible structural components, deforming fluid domains, and unsteady flow patterns. The key components of our simulation toolkit are a stabilized finite element flow solver, a nonlinear structural dynamics solver, an automatic mesh moving scheme, and an interface between the fluid and structural solvers; all of these have been developed within a parallel message-passing paradigm.

Tezduyar, Tayfun E.↗

NASA NTRS2014

Statistical Mechanics of Turbulent Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V.↗

NASA NTRS2014

MHD Turbulence and Magnetic Dynamos

Incompressible magnetohydrodynamic (MHD) turbulence and magnetic dynamos, which occur in magnetofluids with large fluid and magnetic Reynolds numbers, will be discussed. When Reynolds numbers are large and energy decays slowly, the distribution of energy with respect to length scale becomes quasi-stationary and MHD turbulence can be described statistically. In the limit of infinite Reynolds numbers, viscosity and resistivity become zero and if these values are used in the MHD equations ab initio, a model system called ideal MHD turbulence results. This model system is typically confined in simple geometries with some form of homogeneous boundary conditions, allowing for velocity and magnetic field to be represented by orthogonal function expansions. One advantage to this is that the coefficients of the expansions form a set of nonlinearly interacting variables whose behavior can be described by equilibrium statistical mechanics, i.e., by a canonical ensemble theory based on the global invariants (energy, cross helicity and magnetic helicity) of ideal MHD turbulence. Another advantage is that truncated expansions provide a finite dynamical system whose time evolution can be numerically simulated to test the predictions of the associated statistical mechanics. If ensemble predictions are the same as time averages, then the system is said to be ergodic; if not, the system is nonergodic. Although it had been implicitly assumed in the early days of ideal MHD statistical theory development that these finite dynamical systems were ergodic, numerical simulations provided sufficient evidence that they were, in fact, nonergodic. Specifically, while canonical ensemble theory predicted that expansion coefficients would be (i) zero-mean random variables with (ii) energy that decreased with length scale, it was found that although (ii) was correct, (i) was not and the expected ergodicity was broken. The exact cause of this broken ergodicity was explained, after much investigation, by greatly extending the statistical theory of ideal MHD turbulence. The mathematical details of broken ergodicity, in fact, give a quantitative explanation of how coherent structure, dynamic alignment and force-free states appear in turbulent magnetofluids. The relevance of these ideal results to real MHD turbulence occurs because broken ergodicity is most manifest in the ideal case at the largest length scales and it is in these largest scales that a real magnetofluid has the least dissipation, i.e., most closely approaches the behavior of an ideal magnetofluid. Furthermore, the effects grow stronger when cross and magnetic helicities grow large with respect to energy, and this is exactly what occurs with time in a real magnetofluid, where it is called selective decay. The relevance of these results found in ideal MHD turbulence theory to the real world is that they provide at least a qualitative explanation of why confined turbulent magnetofluids, such as the liquid iron that fills the Earth's outer core, produce stationary, large-scale magnetic fields, i.e., the geomagnetic field. These results should also apply to other planets as well as to plasma confinement devices on Earth and in space, and the effects should be manifest if Reynolds numbers are high enough and there is enough time for stationarity to occur, at least approximately. In the presentation, details will be given for both theoretical and numerical results, and references will be provided.

Shebalin, John V↗

NASA NTRS2010

A Nonlinear Dynamic Inversion Predictor-Based Model Reference Adaptive Controller for a Generic Transport Model

Presented here is a Predictor-Based Model Reference Adaptive Control (PMRAC) architecture for a generic transport aircraft. At its core, this architecture features a three-axis, non-linear, dynamic-inversion controller. Command inputs for this baseline controller are provided by pilot roll-rate, pitch-rate, and sideslip commands. This paper will first thoroughly present the baseline controller followed by a description of the PMRAC adaptive augmentation to this control system. Results are presented via a full-scale, nonlinear simulation of NASA s Generic Transport Model (GTM).

Campbell, Stefan F.↗

NASA NTRS1977

Robustness of linear quadratic state feedback designs in the presence of system uncertainty

The paper deals with the problem of expressing the robustness (stability) property of a linear quadratic state feedback (LQSF) design quantitatively in terms of bounds on the perturbations (modeling errors or parameter variations) in the system matrices so that the closed-loop system remains stable. Nonlinear time-varying and linear time-invariant perturbations are considered. The only computation required in obtaining a measure of the robustness of an LQSF design is to determine the eigenvalues of two symmetric matrices determined when solving the algebraic Riccati equation corresponding to the LQSF design problem. Results are applied to a complex dynamic system consisting of the flare control of a STOL aircraft. The design of the flare control is formulated as an LQSF tracking problem.

Patel, R. V.↗

NASA NTRS1976

Parameter estimating state reconstruction

Parameter estimation is considered for systems whose entire state cannot be measured. Linear observers are designed to recover the unmeasured states to a sufficient accuracy to permit the estimation process. There are three distinct dynamics that must be accommodated in the system design: the dynamics of the plant, the dynamics of the observer, and the system updating of the parameter estimation. The latter two are designed to minimize interaction of the involved systems. These techniques are extended to weakly nonlinear systems. The application to a simulation of a space shuttle POGO system test is of particular interest. A nonlinear simulation of the system is developed, observers designed, and the parameters estimated.

George, E. B.↗

NASA NTRS1986

Effects of damping on the control dynamics of the space shuttle based on tethered systems

The analysis of the effects of damping on the control dynamics of the space shuttle based on tethered systems suggest that a relatively simple point mass model can provide useful information concering librational dynamics during development and retrieval of the tethered satellites. The results show that a nonlinear tension control strategy in conjunction with a suitable choice of gains and realistic damping can lead to stable retrieval maneuver with amplitudes in pitch and roll limited to acceptable values. Longitudinal and lateral vibrations of the tether are strongly coupled and can lead to the slackening of the tether. Tether vibrations can be controlled quite effectively by speeding up the retrieval at smaller tether length and/or using thruster.

Modi, V. J.↗

NASA NTRS1987

Simple robust control laws for robot manipulators. Part 2: Adaptive case

A new class of asymptotically stable adaptive control laws is introduced for application to the robotic manipulator. Unlike most applications of adaptive control theory to robotic manipulators, this analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and utilizes a parameterization based on physical (time-invariant) quantities. This approach is made possible by using energy-like Lyapunov functions which retain the nonlinear character and structure of the dynamics, rather than simple quadratic forms which are ubiquitous to the adaptive control literature, and which have bound the theory tightly to linear systems with unknown parameters. It is a unique feature of these results that the adaptive forms arise by straightforward certainty equivalence adaptation of their nonadaptive counterparts found in the companion to this paper (i.e., by replacing unknown quantities by their estimates) and that this simple approach leads to asymptotically stable closed-loop adaptive systems. Furthermore, it is emphasized that this approach does not require convergence of the parameter estimates (i.e., via persistent excitation), invertibility of the mass matrix estimate, or measurement of the joint accelerations.

Bayard, D. S.↗

NASA NTRS1990

The dynamics of orbital maneuvering: Design and evaluation of a visual display aid for human controllers

An interactive proximity operations planning system, which allows on-site planning of fuel-efficient, multi-burn maneuvers in a potential multi-spacecraft environment was developed and tested. Though this display system most directly assists planning by providing visual feedback to aid visualization of the trajectories and constraints, its most significant features include an inverse dynamics algorithm that removes control nonlinearities facing the operator and a trajectory planning technique that reduces the order of control and creates, through a geometric spread-sheet the illusion of an inertially stable environment. This synthetic environment provides the user with control of relevant static and dynamic properties of way-points during small orbital changes allowing independent solutions to the normally coupled problems of orbital maneuvering. An experiment was carried out in which experienced operators were required to plan a trajectory to retrieve an object accidently separated from a dual-keel space station. The time required to plan these maneuvers was found to be predicted by the direction of the insertion thrust and did not depend on the point of separation from the space station.

Ellis, Stephen R.↗

NASA NTRS1989

Advanced development of BEM for elastic and inelastic dynamic analysis of solids

Direct Boundary Element formulations and their numerical implementation for periodic and transient elastic as well as inelastic transient dynamic analyses of two-dimensional, axisymmetric and three-dimensional solids are presented. The inelastic formulation is based on an initial stress approach and is the first of its kind in the field of Boundary Element Methods. This formulation employs the Navier-Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution, and the divergence theorem, together with kinematical and constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of the small displacement theory of elastoplasticity. The dynamic (periodic, transient as well as nonlinear transient) formulations have been applied to a range of problems. The numerical formulations presented here are included in the BEST3D and GPBEST systems.

Banerjee, P. K.↗