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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

A note on the solution of the variational equations of a class of dynamical systems

Some properties are derived for the solutions of the variational equations of a class of dynamical systems. It is shown that under rather general conditions, the matrix of the linearized Lagrangian equations of motion have an important property for which the word 'skew-symplectic' has been introduced. It is also shown that the fundamental matrix of solutions is 'symplectic', the word symplectic being used here in a more general sense than in the classical literature. Two consequences of the symplectic property are that the fundamental matrix is easily invertible and that the eigenvalues appear in reciprocal pairs. The effect of coordinate transformations is also analyzed; in particular, the change from Lagrangian to canonical systems.

Broucke, R.↗
NASA NTRS1983

Riccati group invariants of linear hamiltonian systems

The action of the Riccati group on the Riccati differential equation is associated with the action of a subgroup of the symplectic group on a set of hamiltonian matrices. Within this framework various sets of canonical forms are developed for the matrix coefficients of the Riccati differential equation. The canonical forms presented are valid for arbitrary Kronecker indices, and it is shown that the Kronecker indices are invariants for this group action. These canonical forms are useful for studying problems arising in the areas of optimal decentralized control and the spectral theory of optimal control problems.

Garzia, M. R.↗
NASA NTRS1987

Control-System Design Program

Control-theory design package, Optimal Regulator Algorithms for Control of Linear Systems (ORACLS), developed to aid in design of controllers and optimal filters for systems modeled by linear, time-invariant differential and difference equations. Optimal linear quadratic regulator theory, Linear-Quadratic-Gaussian (LQG) problem, most widely accepted method of determining optimal control policy. Provides for solution to time-in-variant continuous or discrete LQG problems. Attractive to control-system designer providing rigorous tool for dealing with multi-input and multi-output dynamic systems in continuous and discrete form. CDO version written in FORTRAN IV. VAX version written in FORTRAN 77.

Frisch, Harold P.↗
NASA NTRS1978

Estimation and filter stability of stochastic delay systems

Linear and nonlinear filtering for stochastic delay systems are studied. A representation theorem for conditional moment functionals is obtained, which, in turn, is used to derive stochastic differential equations describing the optimal linear or nonlinear filter. A complete characterization of the optimal filter is given for linear systems with Gaussian noise. Stability of the optimal filter is studied in the case where there are no delays in the observations. Using the duality between linear filtering and control, asymptotic stability of the optimal filter is proved. Finally, the cascade of the optimal filter and the deterministic optimal quadratic control system is shown to be asymptotically stable as well.

Kwong, R. H.↗
NASA NTRS1973

Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations (identification of lifting rotor system parameters from transient response data), Phase 7-B

System identification methods have been applied to rotorcraft to estimate stability derivatives from transient flight control response data. While these applications assumed a linear constant coefficient representation of the rotorcraft, the computer experiments used transient responses in flap-bending and torsion of a rotor blade at high advance ratio which is a rapidly time varying periodic system. It was found that a simple system identification method applying a linear sequential estimator also called least square estimator or equation of motion estimator, is suitable for this periodic system and can be used directly if only the acceleration data are noise polluted. In the case of noise being present also in the state variable data the direct application of the estimator gave poor results.

Hohenemser, K. H.↗
NASA NTRS1992

Computational modeling of femtosecond optical solitons from Maxwell's equations

An algorithm is developed that permits the direct time integration of full-vector nonlinear Maxwell's equations. This capability permits the modeling of both linear and nonlinear instantaneous and dispersive effects in the electric polarization in material media. The modeling of the optical carrier is retained. The fundamental innovation is to notice that it is possible to treat the linear and nonlinear convolution integrals, which describe the dispersion, as new dependent variables. A coupled system of nonlinear second-order ordinary differential equations can then be derived for the linear and nonlinear convolution integrals, by differentiating them in the time domain. These equations, together with Maxwell's equations, are solved to determine the electromagnetic fields in nonlinear dispersive media. Results are presented of calculations in one dimension of the propagation and collision of femtosecond electromagnetic solitons that retain the optical carrier, taking into account as the Kerr and Raman interactions.

Goorjian, Peter M.↗
NASA NTRS1991

Modeling of linear isentropic flow systems

A modeling approach for linear isentropic flow systems based on the quasi-one-dimensional Euler equations of non-viscous, compressible flow are presented. Such systems are representative of certain high speed propulsion systems. Accurate models useful in control system studies are developed. A supersonic inlet is considered, and the resulting set of partial differential equations with boundary conditions is solved for a linear transfer matrix using Laplace transforms.

Sarantopoulos, Athan D.↗
NASA NTRS1991

Modeling of linear isentropic flow systems

A modeling approach for linear isentropic flow systems based on the quasi-one-dimensional Euler equations of non-viscous, compressible flow are presented. Such systems are representative of certain high speed propulsion systems. Accurate models useful in control system studies are developed. A supersonic inlet is considered, and the resulting set of partial differential equations with boundary conditions is solved for a linear transfer matrix using Laplace transforms.

Sarantopoulos, Athan D.↗
NASA NTRSDate not supplied

Co-Optimization of Navigation System Requirements and Trajectory Design Using a Sweeping Gradient Method and Linear Covariance Analysis

We describe the application of a sweeping gradient method for ordinary differential equations with events (SGM) and linear covariance analysis (LinCov) to the co-optimization of navigation system requirement generation and robust trajectory design. SGM is a method for computing the gradient of trajectory analyses defined by performance indices over initial value problems with events with respect to static parameters. LinCov is an analytic technique for predicting stochastic behavior of dynamical systems. By combining SGM and LinCov, it is possible use efficient, off-the-shelf, gradient-based optimizers to solve a combined robust optimal trajectory and navigation system design problem. In this paper, we formulate the required models to apply the combined SGM and LinCov techniques to a Near-Rectilinear Halo Orbit rendezvous approach scenario and show results for several intermediate problems.

Benjamin W L Margolis↗
NASA NTRS1976

Conservation properties of numerical integration methods for systems of ordinary differential equations

If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

Rosenbaum, J. S.↗
NASA NTRS1975

Development of a digital adaptive optimal linear regulator flight controller

Digital adaptive controllers have been proposed as a means for retaining uniform handling qualities over the flight envelope of a high-performance aircraft. Towards such an implementation, an explicit adaptive controller, which makes direct use of online parameter identification, has been developed and applied to the linearized lateral equations of motion for a typical fighter aircraft. The system is composed of an online weighted least-squares parameter identifier, a Kalman state filter, and a model following control law designed using optimal linear regulator theory. Simulation experiments with realistic measurement noise indicate that the proposed adaptive system has the potential for onboard implementation.

Berry, P.↗
NASA NTRS1999

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

Muravyov, Alexander A.↗
NASA NTRS1986

Analysis of the transient behavior of rubbing components

Finite element equations are developed for studying deformations and temperatures resulting from frictional heating in sliding system. The formulation is done for linear steady state motion in two dimensions. The equations include the effect of the velocity on the moving components. This gives spurious oscillations in their solutions by Galerkin finite element methods. A method called streamline upwind scheme is used to try to deal with this deficiency. The finite element program is then used to investigate the friction of heating in gas path seal.

Quezdou, M. B.↗
NASA NTRS1976

Lagrangian density for collisional plasma

For the purpose of deriving appropriate Lagrangians for plasma equations that include effects of energy loss, the paper examines the inverse problem of the calculus of variations for systems of first- and second-order quasi-linear partial differential equations. This results in convenient forms of the sufficient conditions under which the given differential equations are Euler-Lagrange equations of a Lagrangian. These conditions are then applied to determine the necessary transformation that converts equations, apparently not already in it, into Euler-Lagrange form. The appropriate Lagrangian for a warm collisional plasma is obtained, and the Lagrangian is derived for a resistive transmission line.

Peng, Y.-K. M.↗
NASA NTRS1983

Cubic spline approximation techniques for parameter estimation in distributed systems

Approximation schemes employing cubic splines in the context of a linear semigroup framework are developed for both parabolic and hyperbolic second-order partial differential equation parameter estimation problems. Convergence results are established for problems with linear and nonlinear systems, and a summary of numerical experiments with the techniques proposed is given.

Banks, H. T.↗
NASA NTRS1990

Improved solution for system identification equations by Epsilon-Decomposition

Matrix eigenvalue theory is used to examine the source of ill-conditioning in linear algebraic equations. This approach highlights the crucial role played by the zero and near-zero eigenvalues and corresponding eigenvectors of poorly conditioned systems. Insight gained from this approach is used to significantly improve a recently developed solution procedure called Epsilon-Decomposition (E-D). E-D is an efficient alternative to Singular Value Decomposition (SVD) for ill-conditioned systems arising in parameter estimation and system identification studies. The efficiency of the improved E-D over SVD resides in the need to only obtain the zero and near-zero eigenvalues of the coefficient matrix as opposed to all of its eigenvalues and vectors (as required by SVD). Thus, the efficiency of E-D is significant for large matrices with small rank deficiency.

Ojalvo, Irving U.↗
NASA NTRS1988

Linear quadratic regulators with eigenvalue placement in a specified region

A linear optimal quadratic regulator is developed for optimally placing the closed-loop poles of multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at + or - pi/2k (k = 2 or 3) from the negative real axis with a sector angle of pi/2 or less, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane. The design method is mainly based on the solution of a linear matrix Liapunov equation, and the resultant closed-loop system with its eigenvalues in the desired region is optimal with respect to a quadratic performance index.

Shieh, Leang S.↗