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At least 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Helios Prototype Vehicle Mishap: Technical Findings, Recommendations, and Lessons Learned

Instability associated with the Helios Prototype HPO3-2 vehicle was a nonlinear stability and control problem involving complex interactions among the flexible structure, the unsteady aerodynamics, the flight control system, the environmental conditions, and vehicle flight dynamics. Analysis tools and solution techniques were constrained by conventional and segmented linear methodologies that did not provide the proper level of complexity to understand the technology interactions on the vehicle s stability and control characteristics. More advanced, multidisciplinary (structures, aeroelastic, aerodynamics, atmospheric, materials, propulsion, controls, etc) "time-domain" analysis methods appropriate to highly flexible, "morphing" vehicles are required. Ground-test procedures and techniques appropriate to this class of vehicle are needed to validate new analysis methods and predictions

DelFrate, John H.↗
NASA NTRS2009

Control of Systems With Slow Actuators Using Time Scale Separation

This paper addresses the problem of controlling a nonlinear plant with a slow actuator using singular perturbation method. For the known plant-actuator cascaded system the proposed scheme achieves tracking of a given reference model with considerably less control demand than would otherwise result when using conventional design techniques. This is the consequence of excluding the small parameter from the actuator dynamics via time scale separation. The resulting tracking error is within the order of this small parameter. For the unknown system the adaptive counterpart is developed based on the prediction model, which is driven towards the reference model by the control design. It is proven that the prediction model tracks the reference model with an error proportional to the small parameter, while the prediction error converges to zero. The resulting closed-loop system with all prediction models and adaptive laws remains stable. The benefits of the approach are demonstrated in simulation studies and compared to conventional control approaches.

Stepanyan, Vehram↗
NASA NTRS1988

Does the resistive tearing instability nonlinearly evolve to a fast reconnection mode

A fundamental problem in applying linear tearing instability theory to the rapid processes (particle acceleration, heating) in flares was the characteristically slow rate of reconnection. This problem can be at least partially overcome if the tearin mode nonlinearly evolves to a regime in which the reconnection rate is substantially enhanced, such as that for the Petschek configuration. This possibility was often suggested, and some numerical simulations appear to provide support for such a view. Numerical simulation are used to study the nonlinear evolution of the tearing stability and show that a fast Petschek-like regime may not be achieved. This conclusion follows when there are sufficient grid points within the diffusion region to completely resolve the nonlinear dynamic interactions in the diffusion layer. When the numerical resolution is not adequate, the solution does appear to approach a Petschek configuration. The resolved solution contains reverse flow vortices and current sheets, terminated with a current reversal, similar to those obtained by Syrovatsky (JEPT, 33, 933, 1971).

Steinolfson, R. S.↗
NASA NTRS1990

Buoyancy-driven instabilities and the nonlinear breakup of a sheared magnetic layer

Motivated by problems concerning the storage and subsequent escape of the solar magnetic field, a study has been made of how a magnetic layer embedded in a convectively stable atmosphere evolves due to axisymmetric instabilities driven by magnetic buoyancy. The initial equilibrium consists of a toroidal field sheared by a weaker poloidal component. The linear stability problem is investigated for both ideal and resistive MHD, and the nonlinear evolution is followed by numerical integration of the equations of motion. In all cases, the instability is greatly affected by the distribution and strength of the poloidal field. In particular, both the horizontal and vertical scales of the motions are controlled by the location of the surface on which the poloidal field vanishes: the resonant surface. In the nonlinear regime, a resonant surface close to the interface between the magnetized and field-free fluid leads to the localization of the instability, so that only a fraction of the magnetic region is disrupted by the motions. By contrast, a deeply seated resonant surface leads to the complete disruption of the layer and to the formation of large, helical magnetic fragments whose identity is preserved for the entire simulation.

Cattaneo, Fausto↗
NASA NTRS1991

Exact and explicit optimal solutions for trajectory planning and control of single-link flexible-joint manipulators

An optimal trajectory planning problem for a single-link, flexible joint manipulator is studied. A global feedback-linearization is first applied to formulate the nonlinear inequality-constrained optimization problem in a suitable way. Then, an exact and explicit structural formula for the optimal solution of the problem is derived and the solution is shown to be unique. It turns out that the optimal trajectory planning and control can be done off-line, so that the proposed method is applicable to both theoretical analysis and real time tele-robotics control engineering.

Chen, Guanrong↗
NASA NTRS1978

A high order accurate finite element algorithm for high Reynolds number flow prediction

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

Baker, A. J.↗
NASA NTRS2003

On the Hilbert-Huang Transform Data Processing System Development

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). The Fourier view of nonlinear mechanics that had existed for a long time, and the associated FFT (fairly recent development), carry strong a-priori assumptions about the source data, such as linearity and of being stationary. Natural phenomena measurements are essentially nonlinear and nonstationary. A very recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT) proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using the Empirical Mode Decomposition (EMD) followed by the Hilbert Transform of the empirical decomposition data (HT), the HHT allows spectrum analysis of nonlinear and nonstationary data by using an engineering a-posteriori data processing, based on the EMD algorithm. This results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF) that can be further analyzed for spectrum interpretation by the classical Hilbert Transform. This paper describes phase one of the development of a new engineering tool, the HHT Data Processing System (HHTDPS). The HHTDPS allows applying the "T to a data vector in a fashion similar to the heritage FFT. It is a generic, low cost, high performance personal computer (PC) based system that implements the HHT computational algorithms in a user friendly, file driven environment. This paper also presents a quantitative analysis for a complex waveform data sample, a summary of technology commercialization efforts and the lessons learned from this new technology development.

Kizhner, Semion↗
NASA NTRS1993

Nonlinear evolution of the first mode supersonic oblique waves in compressible boundary layers. Part 1: Heated/cooled walls

The nonlinear stability of an oblique mode propagating in a two-dimensional compressible boundary layer is considered under the long wave-length approximation. The growth rate of the wave is assumed to be small so that the concept of unsteady nonlinear critical layers can be used. It is shown that the spatial/temporal evolution of the mode is governed by a pair of coupled unsteady nonlinear equations for the disturbance vorticity and density. Expressions for the linear growth rate show clearly the effects of wall heating and cooling and in particular how heating destabilizes the boundary layer for these long wavelength inviscid modes at O(1) Mach numbers. A generalized expression for the linear growth rate is obtained and is shown to compare very well for a range of frequencies and wave-angles at moderate Mach numbers with full numerical solutions of the linear stability problem. The numerical solution of the nonlinear unsteady critical layer problem using a novel method based on Fourier decomposition and Chebychev collocation is discussed and some results are presented.

Gajjar, J. S. B.↗
NASA NTRS1974

System design optimization for a Mars-roving vehicle and perturbed-optimal solutions in nonlinear programming

Work in two somewhat distinct areas is presented. First, the optimal system design problem for a Mars-roving vehicle is attacked by creating static system models and a system evaluation function and optimizing via nonlinear programming techniques. The second area concerns the problem of perturbed-optimal solutions. Given an initial perturbation in an element of the solution to a nonlinear programming problem, a linear method is determined to approximate the optimal readjustments of the other elements of the solution. Then, the sensitivity of the Mars rover designs is described by application of this method.

Pavarini, C.↗
NASA NTRS1969

Towards an optimal inversion method for remote atmospheric sensing

The inference of atmospheric structure from satellite radiometric observations requires an inversion algorithm. A variety of techniques was spawned to meet these demands. One class, the nonlinear inversion methods, copes with the problem of data noise. Unlike linear techniques which require a priori data smoothing, the nonlinear method can be applied directly to raw data. The algorithm discriminates the noise input by resolving the inferences into two types of solution, associating the real roots with atmospheric structure while ascribing the imaginary roots to noise.

King, J. I. F.↗
NASA NTRS1998

Numerical Experiment with Time and Spatial Accuracy of Navier-Stokes Computation For Helicopter Problems

Helicopter flowfields are highly unsteady, nonlinear and three-dimensional. In forward flight and in hover, the rotor blades interact with the tip vortex and wake sheet developed by either itself or the other blades. This interaction, known as blade-vortex interactions (BVI), results in unsteady loading of the blades and can cause a distinctive acoustic signature. Accurate and cost-effective computational fluid dynamic solutions that capture blade-vortex interactions can help rotor designers and engineers to predict rotor performance and to develop designs for low acoustic signature. Such a predictive method must preserve a blade's shed vortex for several blade revolutions before being dissipated. A number of researchers have explored the requirements for this task. This paper will outline some new capabilities that have been added to the NASA Ames' OVERFLOW code to improve its overall accuracy for both vortex capturing and unsteady flows. To highlight these improvements, a number of case studies will be presented. These case studies consist of free convection of a 2-dimensional vortex, dynamically pitching 2-D airfoil including light-stall, and a full 3-D unsteady viscous solution of a helicopter rotor in forward flight In this study both central and upwind difference schemes are modified to be more accurate. Central difference scheme is chosen for this simulation because the flowfield is not dominated by strong shocks. The feature of shock-vortex interaction in such a flow is less important than the dominant blade-vortex interaction. The scheme is second-order accurate in time and solves the thin-layer Navier-Stokes equations in fully-implicit manner at each time-step. The spatial accuracy is either second and fourth-order central difference or third-order upwind difference using Roe-flux and MUSCLE scheme. This paper will highlight and demonstrate the methods for several sample cases and for a helicopter rotor. Preliminary computations on a rotor were performed by using this method and are in the process of documentation.

Ahmad, Jasim↗
NASA NTRS1957

On the Use of the Harmonic Linearizaiton Method in the Automatic Control Theory

The method of harmonic linearization (harmonic balance), first proposed by N. M. Krylov and N. N. Bogolyubov for the approximate investigation of nonlinear vibrations, has been developed and received wide practical application to problems in the theory of automatic control. Recently, some doubt has been expressed on the legitimacy of application of the method to these problems, and assertions were made on the absence in them of a small parameter of any kind. Nevertheless, the method gives practical, acceptable results and is a simple and powerful means in engineering computations. Hence, the importance of questions arises as to its justification. The underlying principle of the method is the replacement of the given nonlinear equation by a linear equation. In establishing the method, a small parameter is considered whose presence makes it possible to speak, with some degree of approximation, of the solution of this new equation to the solution of the given nonlinear equation. In an article by the author, certain considerations were given on the presence of the small parameter, but this question has not as yet received a final answer. In the present report, a somewhat different approach to the problem is applied that permits: (a) establishing, in the clearest manner, the form of the presence of the small parameter in nonlinear problems of control theory, solvable by the method of harmonic linearization; (b) connecting it with previous intuitive physical concepts (with the "filter property") and extending the class of problems possessing this property; and (c) discussing various generalizations of the method.

Popov, E. P.↗
NASA NTRS2013

Mixed Integer Programming and Heuristic Scheduling for Space Communication

Optimal planning and scheduling for a communication network was created where the nodes within the network are communicating at the highest possible rates while meeting the mission requirements and operational constraints. The planning and scheduling problem was formulated in the framework of Mixed Integer Programming (MIP) to introduce a special penalty function to convert the MIP problem into a continuous optimization problem, and to solve the constrained optimization problem using heuristic optimization. The communication network consists of space and ground assets with the link dynamics between any two assets varying with respect to time, distance, and telecom configurations. One asset could be communicating with another at very high data rates at one time, and at other times, communication is impossible, as the asset could be inaccessible from the network due to planetary occultation. Based on the network's geometric dynamics and link capabilities, the start time, end time, and link configuration of each view period are selected to maximize the communication efficiency within the network. Mathematical formulations for the constrained mixed integer optimization problem were derived, and efficient analytical and numerical techniques were developed to find the optimal solution. By setting up the problem using MIP, the search space for the optimization problem is reduced significantly, thereby speeding up the solution process. The ratio of the dimension of the traditional method over the proposed formulation is approximately an order N (single) to 2*N (arraying), where N is the number of receiving antennas of a node. By introducing a special penalty function, the MIP problem with non-differentiable cost function and nonlinear constraints can be converted into a continuous variable problem, whose solution is possible.

Lee, Charles H.↗
NASA NTRS1978

A critical evaluation of the minimization techniques as applied to nonlinear structural analyses

This paper identifies the potential for unconstrained minimization algorithms of mathematical programming to be cost-effective with other conventional techniques of transient nonlinear structural analysis. With this in mind the authors have attempted to critically evaluate a few of the most commonly used algorithms for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth order, first order and second order depending upon the order of the derivative of the function called for by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives derived on the basis of finite difference operations clearly suggest using analytically derived derivatives to obtain better control on the number of minimizations required for convergence to the exact solution.

Kamat, M. P.↗
NASA NTRS2001

Volterra Series Approach for Nonlinear Aeroelastic Response of 2-D Lifting Surfaces

The problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via Volterra series approach is addressed. The related aeroelastic governing equations are based upon the inclusion of structural nonlinearities, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of geometric nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

Silva, Walter A.↗