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At least 1,351 records · Page 75
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

The solution of non-linear hyperbolic equation systems by the finite element method

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

Loehner, R.↗
NASA NTRS1984

Multidisciplinary systems optimization by linear decomposition

In a typical design process major decisions are made sequentially. An illustrated example is given for an aircraft design in which the aerodynamic shape is usually decided first, then the airframe is sized for strength and so forth. An analogous sequence could be laid out for any other major industrial product, for instance, a ship. The loops in the discipline boxes symbolize iterative design improvements carried out within the confines of a single engineering discipline, or subsystem. The loops spanning several boxes depict multidisciplinary design improvement iterations. Omitted for graphical simplicity is parallelism of the disciplinary subtasks. The parallelism is important in order to develop a broad workfront necessary to shorten the design time. If all the intradisciplinary and interdisciplinary iterations were carried out to convergence, the process could yield a numerically optimal design. However, it usually stops short of that because of time and money limitations. This is especially true for the interdisciplinary iterations.

Sobieski, J.↗
NASA NTRS1987

Non-linearity in measurement systems: Evaluation method and application to microwave radiometers

A simple method for determination and correction of nonlinaearity in measurement systems is presented. The technique is applicable to a wide range of measuring systems. The basic concept, an analysis, and a sample application are given. Nonlinearity of the Goldstone DSS 13 low noise HEMT 2.3 GHz (S-band) radiometer system results in noise temperature measurement errors. These errors are successfully correct with this method.

Stelzried, C. T.↗
NASA NTRS1988

Robust eigenvalue/eigenvector selection in linear state feedback systems

Design procedures are developed to select both eigenvalues and eigenvectors to improve system robustness. A robustness metric based on the determinant of the normalized eigenvector matrix defined. It is shown that this metric significantly speeds up the convergence of robust eigenvector solutions close to the optimal. A procedure to blend multiple inputs to improve achievable system robustness in the lower dimensional pseudo control space has also been derived.

Srinathkumar, S.↗
NASA NTRS1993

Control of nonlinear systems represented in quasilinear form

Methods to synthesize controllers for nonlinear systems are developed by exploiting the fact that under mild differentiability conditions, systems of the form: x-dot = f(x) + G(x)u can be represented in quasilinear form, viz: x-dot = A(x)x + B(x)u. Two classes of control methods are investigated. The first is zero-look-ahead control, where the control input depends only on the current values of A(x) and B(x). For this case the control input is computed by continuously solving a matrix Riccati equation as the system progresses along a trajectory. The second is controllers with look-ahead, where the control input depends on the future behavior of A(x) and B(x). These controllers use the similarity between quasilinear systems and linear time varying systems to find approximate solutions to optimal control type problems. The methods that are developed are not guaranteed to be globally stable. However in simulation studies they were found to be useful alternatives for synthesizing control laws for a general class of nonlinear systems.

Coetsee, Josef A.↗
NASA NTRS2000

A Simple Approach for Calibrating Imaging Systems with a Solid-State Sensor

Solid-state array imaging has become an indispensable tool for various modem scientific instrumentation and industrial applications. Often in experiments, use of an imaging system with linear response is very desirable. The linearity of commercial products, however, has yet to be accurately determined in order to assess their nonlinearity effects. Linearity is affected both by sensors and electronics. It is also very desirables to employ low-cost products if we can provide the performance comparable of expensive ones through calibration. Here, we present a very simple approach for approximately checking linearity of imaging systems and also a simple calibration method for precisely measuring intensity ratio or relative intensity variation. These methods can be readily implemented with existing equipment. The calibration method works well with an intermediate-grade analog sensor interfaced by a frame grabber. In our initial attempt for calibration, the nonlinearity of the camera can be reduced from about five percent to much less than one percent in standard deviation.

Leslie, Fred W.↗
NASA NTRS1982

Model reference adaptive control for linear time varying and nonlinear systems

Model reference adaptive control is applied to linear time varying systems and to nonlinear systems amenable to virtual linearization. Asymptotic stability is guaranteed even if the perfect model following conditions do not hold, provided that some sufficient conditions are satisfied. Simulations show the scheme to be capable of effectively controlling certain nonlinear systems.

Abida, L.↗
NASA NTRS2004

Stochastic Stability of Sampled Data Systems with a Jump Linear Controller

In this paper an equivalence between the stochastic stability of a sampled-data system and its associated discrete-time representation is established. The sampled-data system consists of a deterministic, linear, time-invariant, continuous-time plant and a stochastic, linear, time-invariant, discrete-time, jump linear controller. The jump linear controller models computer systems and communication networks that are subject to stochastic upsets or disruptions. This sampled-data model has been used in the analysis and design of fault-tolerant systems and computer-control systems with random communication delays without taking into account the inter-sample response. This paper shows that the known equivalence between the stability of a deterministic sampled-data system and the associated discrete-time representation holds even in a stochastic framework.

Gonzalez, Oscar R.↗
NASA NTRS1972

A graphical test for checking the stability of a linear time-invariant feedback system.

A continuous-time scalar linear time-invariant feedback system is considered for the purpose of checking Willems' (1969, 1970) graphical test for a scalar linear time-invariant feedback system with constant feedback. Heavy reliance is placed on the theory of almost periodic functions. Following definition of the problem and layout of notation, attention is given to solution of the problem, considering only the almost periodic part of the open-loop transfer function.

Callier, F. M.↗
NASA NTRS2006

Parameter and Structure Inference for Nonlinear Dynamical Systems

A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.

Morris, Robin D.↗
NASA NTRS1980

System identification of large space structures

The paper deals with the problem of system identifiability for a linear dynamical system. Two theorems are given relating the sufficient condition of system identifiability for certain linear structures to the total number of inputs and outputs. The principle of least squares, that seeks the minimization of a cost function is employed to carry out the system identification process. To illustrate the concept of the paper, a structural model of a beam with point masses is examined. Parameter identification methods are studied and a random search technique is introduced.

Juang, J. N.↗
NASA NTRS1991

Neighboring extremal guidance for systems with a piecewise linear control

The neighboring extremal feedback control law is developed for systems with a piecewise linear control for the case where the optimal control is obtained by nonlinear programming techniques. To develop the control perturbation for a given deviation from the nominal path, the second variation is minimized subject to the constraint that the final conditions be satisfied. This process leads to a feedback relationship between the control perturbation and the measured deviation from the nominal state. A simple example, the lunar launch problem, is used to demonstrate the validity of the guidance law. For model errors on the order of 5 percent, the results indicate that 5 percent errors occur in the final conditions.

Hull, David G.↗
NASA NTRS1992

Formally biorthogonal polynomials and a look-ahead Levinson algorithm for general Toeplitz systems

Systems of linear equations with Toeplitz coefficient matrices arise in many important applications. The classical Levinson algorithm computes solutions of Toeplitz systems with only O(n(sub 2)) arithmetic operations, as compared to O(n(sub 3)) operations that are needed for solving general linear systems. However, the Levinson algorithm in its original form requires that all leading principal submatrices are nonsingular. An extension of the Levinson algorithm to general Toeplitz systems is presented. The algorithm uses look-ahead to skip over exactly singular, as well as ill-conditioned leading submatrices, and, at the same time, it still fully exploits the Toeplitz structure. In our derivation of this algorithm, we make use of the intimate connection of Toeplitz matrices with formally biorthogonal polynomials.

Freund, Roland W.↗