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At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Flight evaluation of highly augmented controls and electronic displays for precision approach and landing of powered-lift aircraft

Experiments were conducted on simulators and on the Quiet Short-Haul Research Aircraft to evaluate the effect of highly augmented control modes and electronic displays on the ability of pilots to execute precision approaches and landings on a short runway. It is found that the primary benefits of highly augmented flightpath and airspeed controls and electronic displays are realized when the pilot is required to execute precisely a complex transition and approach under instrument conditions and in the presence of a wide range of wind and turbulence conditions. A flightpath and airspeed command and stabilization system incorporating nonlinear, inverse system concepts produced fully satisfactory flightpath control throughout the aircraft's terminal operating envelope.

Franklin, J. A.↗
NASA NTRS1985

New stability theorems for averaging and their application to the convergence analysis of adaptive identification and control schemes

New stability theorems are developed for the convergence analysis of a class of one and two-time scale time-varying nonlinear systems using averaging theory. These theorems are applied to a class of continuous time adaptive identifiers and model reference adaptive controllers to obtain estimates of the parameter rate of exponential convergence.

Fu, L.-C.↗
NASA NTRS1984

Post and a random-walk search mode

Multidisciplinary analysis often requires optimization of nonlinear systems that are subject to constraints. Trajectory optimization is one example of this situation. The Program to Optimize Simulated Trajectories (POST) was used successfully for a number of problems. The purpose is to describe POST and a new optimization approach that has been incorporated into it. Typical uses of POST will also be illustrated. The projected-gradient approach to optimization is the preferred option in POST and is discussed. A new approach to optimization, the random-walk approach, is described, and results with the random-walk approach are presented.

Martin, J. A.↗
NASA NTRS1987

Upwind and symmetric shock-capturing schemes

The development of numerical methods for hyperbolic conservation laws has been a rapidly growing area for the last ten years. Many of the fundamental concepts and state-of-the-art developments can only be found in meeting proceedings or internal reports. This review paper attempts to give an overview and a unified formulation of a class of shock-capturing methods. Special emphasis is on the construction of the basic nonlinear scalar second-order schemes and the methods of extending these nonlinear scalar schemes to nonlinear systems via the extact Riemann solver, approximate Riemann solvers, and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows is discussed. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas dynamics problems.

Yee, H. C.↗
NASA NTRS1988

Efficient implementation of essentially non-oscillatory shock capturing schemes, 2

Earlier work on the efficient implementation of ENO (essentially non-oscillatory) shock capturing schemes is continued. A new simplified expression is provided for the ENO construction procedure based again on numerical fluxes rather than cell averages. Also considered are two improvements which are labeled ENO-LLF (local Lax-Friedrichs) and ENO-Roe, which yield sharper shock transitions, improved overall efficiency, and lower computational cost than previous implementation of the ENO schemes. Two methods of sharpening contact discontinuities, i.e., the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors used originally in the cell-average framework, are supplied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations. The implementation for nonlinear systems and multi-dimensions is given. Finally, many numerical examples, including a compressible shock turbulence interaction flow calculation, are given.

Shu, Chi-Wang↗
NASA NTRS1988

Development of a computerized analysis for solid propellant combustion instability with turbulence

A multi-dimensional numerical model has been developed for the unsteady state oscillatory combustion of solid propellants subject to acoustic pressure disturbances. Including the gas phase unsteady effects, the assumption of uniform pressure across the flame zone, which has been conventionally used, is relaxed so that a higher frequency response in the long flame of a double-base propellant can be calculated. The formulation is based on a premixed, laminar flame with a one-step overall chemical reaction and the Arrhenius law of decomposition with no condensed phase reaction. In a given geometry, the Galerkin finite element solution shows the strong resonance and damping effect at the lower frequencies, similar to the result of Denison and Baum. Extended studies deal with the higher frequency region where the pressure varies in the flame thickness. The nonlinear system behavior is investigated by carrying out the second order expansion in wave amplitude when the acoustic pressure oscillations are finite in amplitude. Offset in the burning rate shows a negative sign in the whole frequency region considered, and it verifies the experimental results of Price. Finally, the velocity coupling in the two-dimensional model is discussed.

Chung, T. J.↗
NASA NTRS1988

Convergence acceleration for vector sequences and applications to computational fluid dynamics

Some recent developments in acceleration of convergence methods for vector sequences are reviewed. The methods considered are the minimal polynomial extrapolation, the reduced rank extrapolation, and the modified minimal polynomial extrapolation. The vector sequences to be accelerated are those that are obtained from the iterative solution of linear or nonlinear systems of equations. The convergence and stability properties of these methods as well as different ways of numerical implementation are discussed in detail. Based on the convergence and stability results, strategies that are useful in practical applications are suggested. Two applications to computational fluid mechanics involving the three dimensional Euler equations for ducted and external flows are considered. The numerical results demonstrate the usefulness of the methods in accelerating the convergence of the time marching techniques in the solution of steady state problems.

Sidi, Avram↗
NASA NTRS1988

Vacillations in a coupled ocean-atmosphere model

Results are presented from a 35-year integration of a coupled ocean-atmosphere model. Both ocean and atmosphere are two-level, nonlinear primitive equation models. The global atmospheric model is forced by a steady, zonally symmetric Newtonian heating. The ocean model is solved in a rectangular tropical basin. Heat fluxes between ocean and atmosphere are linear in air-sea temperature differences, and the interfacial stress is proportional to lower-level atmospheric winds. The coupled models produce ENSO-like variability on time scales of 3 to 5 years. Since there is no external time-dependent forcing, these are self-sustained vacillations of the nonlinear system. It is argued that the energetics of the vacillations is that of unstable coupled modes and that the time scale is crucially dependent on the effects of ocean waves propagating in a closed basin.

Schopf, Paul S.↗
NASA NTRS1989

A class of high resolution explicit and implicit shock-capturing methods

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

Yee, H. C.↗
NASA NTRS1989

Parallel linear equation solvers for finite element computations

The overall objective of this research is to develop efficient methods for the solution of linear and nonlinear systems of equations on parallel and supercomputers, and to apply these methods to the solution of problems in structural analysis. Attention has been given so far only to linear equations. The methods considered for the solution of the stiffness equation Kx=f have been Choleski factorization and the conjugate gradient iteration with SSOR and Incomplete Choleski preconditioning. More detail on these methods will be given on subsequent slides. These methods have been used to solve for the static displacements for the mast and panel focus problems in conjunction with the CSM testbed system based on NICE/SPAR.

Ortega, James M.↗
NASA NTRS1989

Adaptive control: Stability, convergence, and robustness

The deterministic theory of adaptive control (AC) is presented in an introduction for graduate students and practicing engineers. Chapters are devoted to basic AC approaches, notation and fundamental theorems, the identification problem, model-reference AC, parameter convergence using averaging techniques, and AC robustness. Consideration is given to the use of prior information, the global stability of indirect AC schemes, multivariable AC, linearizing AC for a class of nonlinear systems, AC of linearizable minimum-phase systems, and MIMO systems decouplable by static state feedback.

Sastry, Shankar↗
NASA NTRS1990

A control problem for Burgers' equation with bounded input/output

A stabilization problem for Burgers' equation is considered. Using linearization, various controllers are constructed which minimize certain weighted energy functionals. These controllers produce the desired degree of stability for the closed-loop nonlinear system. A numerical scheme for computing the feedback gain functional is developed and several numerical experiments are performed to show the theoretical results.

Burns, John A.↗
NASA NTRS1990

Efficient Implementation of Minimal Polynomial and Reduced Rank Extrapolation Methods

The minimal polynomial extrapolation (MPE) and reduced rank extrapolation (RRE) are two effective techniques that have been used in accelerating the convergence of vector sequences, such as those that are obtained from iterative solution of linear and nonlinear systems of equation. Their definitions involve some linear least squares problems, and this causes difficulties in their numerical implementation. Timewise efficient and numerically stable implementations for MPE and RRE are developed. A computer program written in FORTRAN 77 is also appended and applied to some model problems.

Sidi, Avram↗
NASA NTRS1989

An improved adaptive control for repetitive motion of robots

An adaptive control algorithm is proposed for a class of nonlinear systems, such as robotic manipulators, which is capable of improving its performance in repetitive motions. When the task is repeated, the error between the desired trajectory and that of the system is guaranteed to decrease. The design is based on the combination of a direct adaptive control and a learning process. This method does not require any knowledge of the dynamic parameters of the system.

Pourboghrat, F.↗
NASA NTRS1989

Parallel iterative methods for sparse linear and nonlinear equations

As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.

Saad, Youcef↗
NASA NTRS1990

Convergence acceleration for vector sequences and applications to computational fluid dynamics

Some recent developments in acceleration of convergence methods for vector sequences are reviewed. The methods considered are the minimal polynomial extrapolation, the reduced rank extrapolation, and the modified minimal polynomial extrapolation. The vector sequences to be accelerated are those that are obtained from the iterative solution of linear or nonlinear systems of equations. The convergence and stability properties of these methods as well as different ways of numerical implementation are discussed in detail. Based on the convergence and stability results, strategies that are useful in practical applications are suggested. Two applications to computational fluid mechanics involving the three dimensional Euler equations for ducted and external flows are considered. The numerical results demonstrate the usefulness of the methods in accelerating the convergence of the time marching techniques in the solution of steady state problems.

Sidi, Avram↗
NASA NTRS1990

Studies in astronomical time series analysis. IV - Modeling chaotic and random processes with linear filters

While chaos arises only in nonlinear systems, standard linear time series models are nevertheless useful for analyzing data from chaotic processes. This paper introduces such a model, the chaotic moving average. This time-domain model is based on the theorem that any chaotic process can be represented as the convolution of a linear filter with an uncorrelated process called the chaotic innovation. A technique, minimum phase-volume deconvolution, is introduced to estimate the filter and innovation. The algorithm measures the quality of a model using the volume covered by the phase-portrait of the innovation process. Experiments on synthetic data demonstrate that the algorithm accurately recovers the parameters of simple chaotic processes. Though tailored for chaos, the algorithm can detect both chaos and randomness, distinguish them from each other, and separate them if both are present. It can also recover nonminimum-delay pulse shapes in non-Gaussian processes, both random and chaotic.

Scargle, Jeffrey D.↗
NASA NTRS1991

Transfer Functions Via Laplace- And Fourier-Borel Transforms

Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.

Can, Sumer↗