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At least 649 records · Page 36

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NASA NTRS2007

Development of a Linear Stirling System Model with Varying Heat Inputs

The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC's nonlinear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.

Regan, Timothy F.↗

DOE OSTI2023

MFiX: Fractional-Step Method Implementation

A comprehensive, multiphase computational fluid dynamics (CFD) simulation solves several coupled transport equations including continuity, momentum, species, and energy. Chemical reactions further couple these equations through heats of reaction and rates of formation of products and rates of destruction of reactants. A fractional-step method separates changes attributed to chemical reactions from transport phenomena like convection and diffusion. When the governing equations are split into the transport and reacting components, efficient and independent methodologies can be exploited to solve the different systems. Specifically, discretization of field variable transport equations results in large, sparse matrices which are loosely coupled. These systems are solved in succession using iterative techniques that take advantage of the matrix structure. In contrast, chemical reactions tightly couple field variables locally within the domain (e.g., within a single computational cell) resulting in low dimensional but dense, nonlinear systems that are better solved using direct integration techniques.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1977

The application of charge-coupled device processors in automatic-control systems

The application of charge-coupled device (CCD) processors to automatic-control systems is suggested. CCD processors are a new form of semiconductor component with the unique ability to process sampled signals on an analog basis. Specific implementations of controllers are suggested for linear time-invariant, time-varying, and nonlinear systems. Typical processing time should be only a few microseconds. This form of technology may become competitive with microprocessors and minicomputers in addition to supplementing them.

Mcvey, E. S.↗

NASA NTRS1976

Vulnerability of dynamic systems

Directed graphs are associated with dynamic systems in order to determine in any given system if each state can be reached by at least one input (input reachability), or can each state reach at least one output (output reachability). Then, the structural perturbations of a dynamic system are identified as lines or points removals from the corresponding digraph, and a system is considered vulnerable at those lines or points of the digraph whose removal destroys its input or output reachability. A suitable framework is formulated for resolving the problems of reachability and vulnerability which applies to both linear and nonlinear systems alike.

Siljak, D. D.↗

NASA NTRS2003

Processing at the Speed of Light

Spatial Light Modulators (SLMs) are critical elements in optical processing systems used for imaging, displaying, data storage, communications, and other applications. By taking advantage of the natural properties of light beams, the devices process information at speeds unattainable by human operators and most machines, with high-resolution results.Boulder Nonlinear Systems, Inc., is one of the world s foremost SLM manufacturers. Applications of this technology are briefly described.

Source record↗

NASA NTRS1982

Theory of design using nonlinear transformations

This paper is presenting an overview of the theory of transformations from nonlinear systems to linear systems. Topics covered include (1) necessary and sufficient conditions for transformations to exist, (2) a method of constructing transformations (3) robustness in design (based on transformations theory) and Liapunov functions, (4) estimation theory, and (5) the relationship between transformation theory and 'nonlinear zeros'. Application of these results to automatic flight control is presented in another paper at this session.

Su, R.↗

DOE OSTI2020

Matrix-free subcell residual distribution for Bernstein finite elements: Monolithic limiting

This paper is focused on the aspects of limiting in residual distribution (RD) schemes for high-order finite element approximations to advection problems. Both continuous and discontinuous Galerkin methods are considered in this work. Discrete maximum principles are enforced using algebraic manipulations of element contributions to the global nonlinear system. The required modifications can be carried out without calculating the element matrices and assembling their global counterparts. The components of element vectors associated with the standard Galerkin discretization are manipulated directly using localized subcell weights to achieve optimal accuracy. Low-order nonlinear RD schemes of this kind were originally developed to calculate local extremum diminishing predictors for flux-corrected transport (FCT) algorithms. In the present paper, we incorporate limiters directly into the residual distribution procedure, which makes it applicable to stationary problems and leads to well-posed nonlinear discrete problems. To circumvent the second-order accuracy barrier, the correction factors of monolithic limiting approaches and FCT schemes are adjusted using smoothness sensors based on second derivatives. Finally, the convergence behavior of presented methods is illustrated by numerical studies for two-dimensional test problems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1971

A multifilter phase-lock loop.

The phase model for the generalized multifilter phase-lock loop (M PLL) is considered and state equations for this model are derived. A linear analysis is presented to aid in the preliminary design of an M PLL and to indicate the noise improvement over a conventional phase-lock loop (PLL). Performance characteristics are examined for an M PLL with low-pass and bandpass characteristics used in a specific FM communication system. Both single and double sinusoidal FM are used and a region of proper operation of the M PLL is determined in terms of modulation index and modulati ng frequency. These results are obtained from both analog and digital computer simulation of the nonlinear system.

Carden, F.↗

NASA NTRS2005

A Fundamental Mathematical Model of a Microbial Predenitrification System

Space flight beyond Low Earth Orbit requires sophisticated systems to support all aspects of the mission (life support, real-time communications, etc.). A common concern that cuts across all these systems is the selection of information technology (IT) methodology, software and hardware architectures to provide robust monitoring, diagnosis, and control support. Another dimension of the problem space is that different systems must be integrated seamlessly so that communication speed and data handling appear as a continuum (un-interrupted). One such team investigating this problem is the Advanced Integration Matrix (AIM) team whose role is to define the critical requirements expected of software and hardware to support an integrated approach to the command and control of Advanced Life Support (ALS) for future long-duration human space missions, including permanent human presence on the Moon and Mars. A goal of the AIM team is to set the foundation for testing criteria that will assist in specifying tasks, control schemes and test scenarios to validate and verify systems capabilities. This project is to contribute to the goals of the AIM team by assisting with controls planning for ALS. Control for ALS is an enormous problem it involves air revitalization, water recovery, food production, solids processing and crew. In more general terms, these systems can be characterized as involving both continuous and discrete processes, dynamic interactions among the sub-systems, nonlinear behavior due to the complex operations, and a large number of multivariable interactions due to the dimension of the state space. It is imperative that a baseline approach from which to measure performance is established especially when the expectation for the control system is complete autonomous control.

Hoo, Karlene A.↗

DOE OSTI2022

Utilizing CellBox to Describe Varied Dynamical Systems

CellBox is a hybrid modeling framework that integrates machine-learning approaches with explicit mathematical modeling to determine the behavior of dynamical systems, intended for determining the complex interactions of molecule and phenotype within a cellular environment using perturbation/response-based data. The original work utilized analysis of a melanoma cell line, SK-Mel-133, which we sought to expand to and evaluate effectiveness in describing other nonlinear systems both within and outside of biology. We evaluated with two models. One model is based upon the free-fall of an object under a velocity-dependent drag force; this produced inherent perturbation/response data. The other model is based upon a form of mass-action molecular kinetics; for this, we ran the simulation to steady state in each species for each perturbation and select the steady state as input for CellBox. We determined that CellBox, outside of its original use case, can still strongly predict even non-biological dynamical systems in the small-perturbation regime, with r = 0.99977 to 0.85123, p < 0.05 for freefall. However, CellBox cannot accurately predict behavior within large-perturbation regimes, p >> 0.05 for freefall. In addition, we performed a naïve comparison of CellBox network structure to known network structure in the mass-action model to assess accuracy.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

Dynamics of a spinning space station with a counterweight connected by multiple cables.

A unique and relatively simple approach is presented for obtaining the linearized equations of motion. A conservative system consisting of two rigid bodies connected by any number of massless cables with linear axial stiffness is assumed. The cable forces and torques are expanded in a Taylor series about the equilibrium values of the system coordinates which results in a cable stiffness matrix. The method of obtaining the equilibrium values of the coordinates is discussed and results are presented. The range of validity of the linear model is determined by comparing results with a digital simulation of the nonlinear system.

Nixon, D. D.↗

NASA NTRS1972

Perturbed nonlinear differential equations

The existence of a solution defined for all t and possessing a type of boundedness property is established for the perturbed nonlinear system y = f(t,y) + F(t,y). The unperturbed system x = f(t,x) has a dichotomy in which some solutions exist and are well behaved as t increases to infinity, and some solution exists and are well behaved as t decreases to minus infinity. A similar study is made for a perturbed nonlinear differential equation defined on a half line, R+, and the existence of a family of solutions with special boundedness properties is established. The ideas are applied to integral manifolds.

Proctor, T. G.↗

NASA NTRS1980

Hyperstability in variable structure systems

A variable structure control law is a discontinuous feedback law whose coefficients switch on hypersurfaces defined in the state space. Feedback systems with variable structure control laws are often referred to as variable structure systems (VSS). The main feature of VSS is the sliding motion which can occur at the intersection of the switching surfaces. Demonstrating existence and reaching in the case of vector control in n-dimensional space is in general a problem in stability of nonlinear systems. The present investigation is concerned with the projection of motion on an m-dimensional subspace, taking into account aspects of the hyperstability concept in VSS design. The considered concepts are illustrated with the aid of an example.

Calise, A. J.↗

NASA NTRS1973

Vibrational sensitivity of a measuring instrument and methods of increasing the accuracy of its determinations

The properties and peculiarities of two groups of measuring systems reacting to vibrations are discussed. Specifically, results of the action of a three dimensional, cophasal, monoharmonic vibration on the linear system of a measuring instrument was analyzed. Data are also given on the connection between vibration sensitivity and vibration resistance for instruments, methods for estimating vibration resistance, and formulas for expressing test results of vibration resistance. Experimental data are also given for decreasing errors in nonlinear systems during vibrations.

Mironov, Y. S.↗

NASA NTRS1988

Statistical analysis of SSME system data

A statistical methodology to enhance the Space Shuttle Main Engine (SSME) performance prediction accuracy is proposed. This methodology was to be used in conjunction with existing SSME performance prediction computer codes to improve parameter prediction accuracy and to quantify that accuracy. However, after a review of related literature, researchers concluded that the proposed problem required a coverage of areas such as linear and nonlinear system theory, measurement theory, statistics, and stochastic estimation. Since state space theory is the foundation for a more complete study of each of the before mentioned areas, these researchers chose to refocus emphasis to cover the more specialized topic of state vector estimation procedures. State vector estimation was also selected because of current and future concerns by NASA for SSME performance evaluation; i.e., there is a current interest in an improved evaluation procedure for actual SSME post flight performance as well as for post static test performance of a single SSME. A current investigation of analytical methods may be used to improve test stand failure detection. This paper considers the issue of post flight/test state variable reconstruction through the application of observations made on the output of the Space Shuttle propulsion system. Rogers used the Kalman filtering procedure to reconstruct the state variables of the Space Shuttle propulsion system. An objective of this paper is to give the general setup of the Kalman filter and its connection to linear regression. A second objective is to examine the reconstruction methodology for application to the reconstruction of the state vector of a single Space Shuttle Main Engine (SSME) by using static test firing data.

Temple, Enoch C.↗

NASA NTRS1986

Modeling of multi-rotor torsional vibrations in rotating machinery using substructuring

The application of FEM modeling techniques to the analysis of torsional vibrations in complex rotating systems is described and demonstrated, summarizing results reported by Soares (1985). A substructuring approach is used for determination of torsional natural frequencies and resonant-mode shapes, steady-state frequency-sweep analysis, identification of dynamically unstable speed ranges, and characterization of transient linear and nonlinear systems. Results for several sample problems are presented in diagrams, graphs, and tables. STORV, a computer code based on this approach, is in use as a preliminary design tool for drive-train torsional analysis in the High Altitude Wind Tunnel at NASA Lewis.

Soares, Fola R.↗

NASA NTRS1992

Controlled motion in an elastic world. Research project: Manipulation strategies for massive space payloads

The flexibility of the drives and structures of controlled motion systems are presented as an obstacle to be overcome in the design of high performance motion systems, particularly manipulator arms. The task and the measure of performance to be applied determine the technology appropriate to overcome this obstacle. Included in the technologies proposed are control algorithms (feedback and feed forward), passive damping enhancement, operational strategies, and structural design. Modeling of the distributed, nonlinear system is difficult, and alternative approaches are discussed. The author presents personal perspectives on the history, status, and future directions in this area.

Book, Wayne J.↗

NASA NTRS1993

Controlled motion in an elastic world

Book, Wayne J.↗