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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Elastic Model Transitions: a Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)

A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes both quadratically constrained least squares (LSQI) and Direct Shape Mapping (DSM) algorithms to determine physical displacements. This approach is applicable to the simulation of the elastic behavior of launch vehicles and other structures that utilize multiple LTI finite element model (FEM) derived mode sets that are propagated throughout time. The time invariant nature of the elastic data for discrete segments of the launch vehicle trajectory presents a problem of how to properly transition between models while preserving motion across the transition. In addition, energy may vary between flex models when using a truncated mode set. The LSQI-DSM algorithm can accommodate significant changes in energy between FEM models and carries elastic motion across FEM model transitions. Compared with previous approaches, the LSQI-DSM algorithm shows improvements ranging from a significant reduction to a complete removal of transients across FEM model transitions as well as maintaining elastic motion from the prior state.

Jurenko, Robert J.↗
DOE OSTI2025

Fast and Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices with Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

In this work, we present an efficient and scalable algorithm for performing matrix-vector multiplications (matvecs) for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint, and (2) efficient fast Fourier transform–based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80% of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Design of non-interacting multivariable discrete time systems

The theory of decoupling a multivariable system with the help of state variable feedback is applied to discrete time systems. The system differential equations in the continuous time domain are converted to a discrete time representation. A discrete time controller is designed to control the overall input to the system such that a specified desired decoupled output response is obtained. The decoupled system behaves as a set of single-input, single-output systems and state variable techniques can be easily applied to control each output individually. Control is achieved by periodically sampling the inputs and all the states and feeding them back through a controller. For linear time invariant systems the control is time invariant. The basic theory of decoupling involves feeding back all the states twice, first to decouple the system and then to achieve a desired response. The states of the system are computed with the help of a state estimator which calculates all the present states of the system so that on-line control can be applied to real time systems. The theory is applied to a model of a nuclear rocket engine.

Agrawal, B. L.↗
NASA NTRS1999

Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm

A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and by appropriate choice of coordinates and simplified measurement modeling is formulated as a linear time-invariant system. Results for improvements to the GSFC algorithm and a multiple satellite formation will be addressed. The goal of this investigation is to progressively relax the assumptions that result in linear time-invariance, ultimately to the point of linearization of the non-linear dynamics about the current state estimate as in the extended Kalman filter. An assessment will then be made about the feasibility of the decentralized approach to the realistic formation flying application of the EO-1/Landsat 7 formation flying experiment.

Folta, David C.↗
NASA NTRS1991

Robustness analysis of multirate and periodically time varying systems

A new method for analyzing the stability and robustness of multirate and periodically time varying systems is presented. It is shown that a multirate or periodically time varying system can be transformed into an equivalent time invariant system. For a SISO system, traditional gain and phase margins can be found by direct application of the Nyquist criterion to this equivalent time invariant system. For a MIMO system, structured and unstructured singular values can be used to determine the system's robustness. The limitations and implications of utilizing this equivalent time invariant system for calculating gain and phase margins, and for estimating robustness via singular value analysis are discussed.

Berg, Martin C.↗
NASA NTRS2006

On Space-Time Inversion Invariance and its Relation to Non-Dissipatedness of a CESE Core Scheme

The core motivating ideas of the space-time CESE method are clearly presented and critically analyzed. It is explained why these ideas result in all the simplifying and enabling features of the CESE method. A thorough discussion of the a scheme, a two-level non-dissipative CESE solver of a simple advection equation with two independent mesh variables and two equations per mesh point is also presented. It is shown that the scheme possesses some rather intriguing properties such as: (i) its two independent mesh variables separately satisfy two decoupled three-level leapfrog schemes and (ii) it shares with the leapfrog scheme the same amplification factors, even though the a scheme and the leapfrog scheme have completely different origins and structures. It is also explained why the leapfrog scheme is not as robust as the a scheme. The amplification factors/matrices of several non-dissipative schemes are carefully studied and the key properties that contribute to their non-dissipatedness are clearly spelled out. Finally we define and establish space-time inversion (STI) invariance for several non-dissipative schemes and show that their non-dissipatedness is a result of their STI invariance.

Chang, Sin-Chung↗
NASA NTRS1991

A game theoretic approach to a finite-time disturbance attenuation problem

A disturbance attenuation problem over a finite-time interval is considered by a game theoretic approach where the control, restricted to a function of the measurement history, plays against adversaries composed of the process and measurement disturbances, and the initial state. A zero-sum game, formulated as a quadratic cost criterion subject to linear time-varying dynamics and measurements, is solved by a calculus of variation technique. By first maximizing the quadratic cost criterion with respect to the process disturbance and initial state, a full information game between the control and the measurement residual subject to the estimator dynamics results. The resulting solution produces an n-dimensional compensator which expresses the controller as a linear combination of the measurement history. A disturbance attenuation problem is solved based on the results of the game problem. For time-invariant systems it is shown that under certain conditions the time-varying controller becomes time-invariant on the infinite-time interval. The resulting controller satisfies an H(infinity) norm bound.

Rhee, Ihnseok↗
NASA NTRS1994

Growth-phase thinning of the near-Earth current sheet during the CDAW 6 substorm

The thinning of the near-Earth current sheet during the growth phase of the Coordinated Data Analysis Workshop (CDAW) 6 magnetospheric substorm is studied. The expansion onset of the substorm occurred at 1054 UT, March 22, 1979. During the growth phase, two spacecraft, International Sun Earth Explorer (ISEE) 1 and ISEE 2, were within the current sheet approximately 13 R(sub E) from the Earth and obtained simultaneous high-resolution magnetic data at two points in the current sheet. Plasma data were also provided by the ISEE spacecraft and solar wind data by IMP 8. To facilitate the analysis, the GSM magnetic field data are transformed to a 'neutral sheet coordinate system' in which the new x axis is parallel to the average magnetic field above and below the neutral sheet and the new y axis lies in the GSM equatorial plane. A model based on the assumption that the current sheet is a time-invariant structure fails to predict neutral sheet crossing times. Consequently, the Harris sheet model, which allows one to remove the restriction of time invariancy, is used instead. It is found that during the growth phase, a model parameter corresponding to the thickness of the current sheet decreased exponentially from about 5 R(sub E) to 1 R(sub E) with a time constant of about 14 min. In addition, the ISEE 1 and ISEE 2 neutral sheet crossings after expansion onset indicate that the neutral sheet was moving upward at 7 km/s relative to the spacecraft. Since both crossings occurred in approximately 80 s, the current sheet thickness is estimated to be about 500 km. These results demonstrate that the near-Earth current sheet undergoes dramatic thinning during the substorm growth phase and expansion onset.

Sanny, Jeff↗
NASA NTRS1995

A Game Theoretic Fault Detection Filter

The fault detection process is modelled as a disturbance attenuation problem. The solution to this problem is found via differential game theory, leading to an H(sub infinity) filter which bounds the transmission of all exogenous signals save the fault to be detected. For a general class of linear systems which includes some time-varying systems, it is shown that this transmission bound can be taken to zero by simultaneously bringing the sensor noise weighting to zero. Thus, in the limit, a complete transmission block can he achieved, making the game filter into a fault detection filter. When we specialize this result to time-invariant system, it is found that the detection filter attained in the limit is identical to the well known Beard-Jones Fault Detection Filter. That is, all fault inputs other than the one to be detected (the "nuisance faults") are restricted to an invariant subspace which is unobservable to a projection on the output. For time-invariant systems, it is also shown that in the limit, the order of the state-space and the game filter can be reduced by factoring out the invariant subspace. The result is a lower dimensional filter which can observe only the fault to be detected. A reduced-order filter can also he generated for time-varying systems, though the computational overhead may be intensive. An example given at the end of the paper demonstrates the effectiveness of the filter as a tool for fault detection and identification.

Chung, Walter H.↗
NASA NTRS1989

Failure detection and identification

Using the geometric concept of an unobservability subspace, a solution is given to the problem of detecting and identifying control system component failures in linear, time-invariant systems. Conditions are developed for the existence of a causal, linear, time-invariant processor that can detect and uniquely identify a component failure, first for the case where components can fail simultaneously, and then for the case where they fail only one at a time. Explicit design algorithms are provided when these conditions are satisfied. In addition to time-domain solvability conditions, frequency-domain interpretations of the results are given, and connections are drawn with results already available in the literature.

Massoumnia, Mohammad-Ali↗
NASA NTRS1973

Controllability of discrete bilinear systems with bounded control.

Controllability of time-invariant discrete-time bilinear systems is discussed. Bilinear systems are classified into two categories: homogeneous and inhomogeneous. Sufficient conditions which ensure the global controllability of discrete-time bilinear systems are obtained by localized analysis in control variables.

Tarn, T. J.↗
NASA NTRS1973

Controllability of discrete bilinear systems with bounded control.

The subject of this paper is the controllability of time-invariant discrete-time bilinear systems. Bilinear systems are classified into two categories; homogeneous and inhomogeneous. Sufficient conditions which ensure the global controllability of discrete-time bilinear systems are obtained by localized analysis in control variables.

Tarn, T. J.↗
NASA NTRS1975

Modern control concepts in hydrology

Two approaches to an identification problem in hydrology are presented, based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time-invariant or time-dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and confirm the results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.

Duong, N.↗
NASA NTRS1987

Performance evaluation of fault tolerant systems represented by Markov models

A method to evaluate the performance of fault tolerant systems whose configuration can be represented by time-invariant, discrete-time, discrete-state Markov models is introduced. Each state is assumed to be associated with a constant qualitative measure of the system's performance. The method first computes the moments of the performance probability mass function (PMF) and then finds an approximating function that has the same moments. The form of this function is a maximum entropy solution of the moment matching problem. A simple algorithm for calculating the necessary moments is derived and a method for finding the approximate performance PMF is suggested. After some modification, the method is applied to an example, the Inertial Upper Stage navigation system.

Missana, Jean-Olivier A. A.↗
NASA NTRS1988

Stabilization and robustness of non-linear unity-feedback system - Factorization approach

The paper is a self-contained discussion of a right factorization approach in the stability analysis of the nonlinear continuous-time or discrete-time, time-invariant or time-varying, well-posed unity-feedback system S1(P, C). It is shown that a well-posed stable feedback system S1(P, C) implies that P and C have right factorizations. In the case where C is stable, P has a normalized right-coprime factorization. The factorization approach is used in stabilization and simultaneous stabilization results.

Desoer, C. A.↗
NASA NTRS1987

Nonlinear plants, factorizations and stable feedback systems

For nonlinear plants represented by causal maps defined over extended spaces, right factorization and normalized right-coprime factorization concepts are discussed in terms of well-posed stable feedback systems. This setup covers continuous-time, discrete-time, time-invariant or time-varying input-output maps. The nonlinear maps are factored in terms of causal bounded-input bounded-output stable maps. In factored form, all instabilities of the original map are represented by the inverse of a causal stable `denominator' map. The existence of maps with right factorizations and normalized right-coprime factorizations is shown using a well-posed stable unity-feedback system. In the case where one of the subsystems has a normalized right-coprime factorization, the stability of the feedback system is equivalent to the stability of the pseudostate map.

Desoer, Charles A.↗
NASA NTRS1991

Hybrid state-space self-tuning control using dual-rate sampling

This paper presents a hybrid state-space self-tuning control scheme using dual-rate sampling for suboptimal digital adaptive control of linear time-invariant continuous-time multivariable stochastic systems with unknown parameters. An equivalent fast-rate discrete-time state-space innovation model (with estimated states) of the continuous-time system is constructed by using the estimated system parameters and Kalman gain. To utilize the existing optimal regional-pole assignment method developed in the continuous-time domain, the constructed fast-rate discrete-time model is converted into an equivalent continuous-time model for the development of a state-feedback optimal control law with pole placement in a specific region. The developed analog optimal control law is then converted into an equivalent pseudo-slow-rate digital control law via the proposed digital redesign technique, which can be realized via slow-rate digital electronics. The proposed method enables the development of a digitally implementable advanced control algorithm for digital adaptive control of continuous-time multivariable stochastic systems which may be unstable and/or have nonminimum phase.

Shieh, Leang S.↗
NASA NTRS1995

PLATSIM: An efficient linear simulation and analysis package for large-order flexible systems

PLATSIM is a software package designed to provide efficient time and frequency domain analysis of large-order generic space platforms implemented with any linear time-invariant control system. Time domain analysis provides simulations of the overall spacecraft response levels due to either onboard or external disturbances. The time domain results can then be processed by the jitter analysis module to assess the spacecraft's pointing performance in a computationally efficient manner. The resulting jitter analysis algorithms have produced an increase in speed of several orders of magnitude over the brute force approach of sweeping minima and maxima. Frequency domain analysis produces frequency response functions for uncontrolled and controlled platform configurations. The latter represents an enabling technology for large-order flexible systems. PLATSIM uses a sparse matrix formulation for the spacecraft dynamics model which makes both the time and frequency domain operations quite efficient, particularly when a large number of modes are required to capture the true dynamics of the spacecraft. The package is written in MATLAB script language. A graphical user interface (GUI) is included in the PLATSIM software package. This GUI uses MATLAB's Handle graphics to provide a convenient way for setting simulation and analysis parameters.

Maghami, Periman↗