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NASA NTRS1991

Continuous system modeling

A comprehensive and systematic introduction is presented for the concepts associated with 'modeling', involving the transition from a physical system down to an abstract description of that system in the form of a set of differential and/or difference equations, and basing its treatment of modeling on the mathematics of dynamical systems. Attention is given to the principles of passive electrical circuit modeling, planar mechanical systems modeling, hierarchical modular modeling of continuous systems, and bond-graph modeling. Also discussed are modeling in equilibrium thermodynamics, population dynamics, and system dynamics, inductive reasoning, artificial neural networks, and automated model synthesis.

Cellier, Francois E.↗

NASA NTRS1997

Flow and Crystallization in Two-Layer Liquid Systems with and without a Magnetic Field

Flow, heat and mass transfer in a two-layer liquid system is investigated when the layers are subjected to a static magnetic field. The physical system consists of two immiscible liquids in a layer configuration with a free surface and an interfacial layer simulating two crystal growth configurations, namely, floating zone and horizontal zone melting. Mass transfer effects due to crystallization of one of the layers is also considered. The resulting flows are categorized into three types depending on: (a) the dominance of the free surface effect top layer, (b) a balance between the thermocapillary effect on the free surface and the interface effect between the two layers, or (c) the dominance of interfacial effects, in determining the system thermo-fluid characteristics. The use of an additional liquid layer atop the crystallizing layer leads to a reduction of the radial dopant inhomogeneity in comparison to the one-layer case. The effect an externally imposed magnetic field on dopant distribution in this two-layer configuration is rather ambiguous and depends on its direction and intensity resulting in the necessity of optimizing the applied magnetic field for a specific situation. In case of electrically non-conducting melts, the calculations show that some measure of flow control can be achieved by using an electrically conducting encapsulant layer of the desired thickness.

Feonychev, Alexander I.↗

NASA NTRS2006

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Nguyen, Nhan↗

NASA NTRS1995

Sensitivity Analysis and Optimization of Enclosure Radiation with Applications to Crystal Growth

In engineering, simulation software is often used as a convenient means for carrying out experiments to evaluate physical systems. The benefit of using simulations as 'numerical' experiments is that the experimental conditions can be easily modified and repeated at much lower cost than the comparable physical experiment. The goal of these experiments is to 'improve' the process or result of the experiment. In most cases, the computational experiments employ the same trial and error approach as their physical counterparts. When using this approach for complex systems, the cause and effect relationship of the system may never be fully understood and efficient strategies for improvement never utilized. However, it is possible when running simulations to accurately and efficiently determine the sensitivity of the system results with respect to simulation to accurately and efficiently determine the sensitivity of the system results with respect to simulation parameters (e.g., initial conditions, boundary conditions, and material properties) by manipulating the underlying computations. This results in a better understanding of the system dynamics and gives us efficient means to improve processing conditions. We begin by discussing the steps involved in performing simulations. Then we consider how sensitivity information about simulation results can be obtained and ways this information may be used to improve the process or result of the experiment. Next, we discuss optimization and the efficient algorithms which use sensitivity information. We draw on all this information to propose a generalized approach for integrating simulation and optimization, with an emphasis on software programming issues. After discussing our approach to simulation and optimization we consider an application involving crystal growth. This application is interesting because it includes radiative heat transfer. We discuss the computation of radiative new factors and the impact this mode of heat transfer has on our approach. Finally, we will demonstrate the results of our optimization.

Tiller, Michael M.↗

NASA NTRS2010

SimCheck: An Expressive Type System for Simulink

MATLAB Simulink is a member of a class of visual languages that are used for modeling and simulating physical and cyber-physical systems. A Simulink model consists of blocks with input and output ports connected using links that carry signals. We extend the type system of Simulink with annotations and dimensions/units associated with ports and links. These types can capture invariants on signals as well as relations between signals. We define a type-checker that checks the wellformedness of Simulink blocks with respect to these type annotations. The type checker generates proof obligations that are solved by SRI's Yices solver for satisfiability modulo theories (SMT). This translation can be used to detect type errors, demonstrate counterexamples, generate test cases, or prove the absence of type errors. Our work is an initial step toward the symbolic analysis of MATLAB Simulink models.

Roy, Pritam↗

NASA NTRS1975

On the stabilization of bilinear systems via hyperstability

The problem of feedback stabilization for continuous and discrete bilinear systems is investigated. Attention is also given to the 'drift' term case to take into account physical systems in which preassigned values are imposed on some of the controls. A proposed set of controls for asymptotic stabilization is applicable to a fairly large class of bilinear systems. It is pointed out that the results presented can be used to design nonlinear adaptive controllers which in some cases are preferable to linear controllers.

Ionescu, T.↗

NASA NTRS1989

Integration of perception and reasoning in fast neural modules

Artificial neural systems promise to integrate symbolic and sub-symbolic processing to achieve real time control of physical systems. Two potential alternatives exist. In one, neural nets can be used to front-end expert systems. The expert systems, in turn, are developed with varying degrees of parallelism, including their implementation in neural nets. In the other, rule-based reasoning and sensor data can be integrated within a single hybrid neural system. The hybrid system reacts as a unit to provide decisions (problem solutions) based on the simultaneous evaluation of data and rules. Discussed here is a model hybrid system based on the fuzzy cognitive map (FCM). The operation of the model is illustrated with the control of a hypothetical satellite that intelligently alters its attitude in space in response to an intersecting micrometeorite shower.

Fritz, David G.↗

NASA NTRS1988

IUE observations of the dwarf nova BV Centauri

The IUE observations of the dwarf nova BV Cen in quiescence are summarized. The reprocessed spectra from January 1979 are analyzed to show that the maximum temperature of the white dwarf primary star, based on its brightness at 1375 A, ranges from 42,000 to about 125,000 K depending upon the adopted values of interstellar reddening, the mass of the white dwarf, and the distance to the system. Physical arguments based on the likely state of the quiescent accretion disk in the BV Cen system suggest that the effective temperature of the white dwarf is significantly lower than this maximum temperature. The disk is more likely to be optically thick than optically thin. The impact of these findings on models for dwarf nova outbursts is discussed, but no firm conclusions can be drawn. The ultraviolet emission-line spectrum from observations obtained in August 1985 is described in detail.

Williger, G.↗

NASA NTRS1979

Analytical aspects of Randomdec analysis

Relationships between Randomdec analysis and conventional methods of analysis such as Fourier and modal analysis are shown. The Randomdec signature is described in terms of the Fourier amplitude coefficients. Using this result, the effect of filtering the time history is shown. For a linear, two mode model, signatures are compared to the free response of the system subjected to different initial conditions to show the relationship of displacement and acceleration signatures to the physical system. Detection and location of flaws is also discussed.

Reed, R. E.↗

NASA NTRS2003

Discrete Abstractions of Hybrid Systems: Verification of Safety and Application to User-Interface Design

Human interaction with a complex control system involves the user, the automation’s discrete mode logic, and the underlying continuous dynamics of the physical system. The user-interface of such systems always displays a reduced set of information about the entire system. Designing interfaces such that all the pertinent information is available and assuring that this information is correct is important for any user-interface, but especially so for safety-critical systems such as automotive systems and autopilots. Here we describe a methodology for the analysis of hybrid control systems that incorporate user interaction, with the goal of assuring that the information provided to the user is correct. That is, the user-interface must contain all information necessary to safely complete a desired procedure or task. We begin with a hybrid system model which incorporates discrete mode logic as well as nonlinear continuous dynamics. Using a hybrid computational tool for reachability, we find the largest region of the state-space in which we can guarantee the state of the system can always remain – this is the safe region of operation. By implementing a controller for safety which arises from this computation, we mathematically guarantee that this safe region is invariant, meaning that the system will always remain within the safe region if the determined controller is used on the boundary of the safe region. Verification within a hybrid framework allows us to account for the continuous dynamics underlying the discrete representations displayed to the user. Using the computed invariant regions as discrete states, we can abstract a discrete event system from this hybrid system with safety restrictions. This abstraction can be used to determine what information must be provided on the display. Furthermore, in cases in which an interface already exists, the abstraction provides the necessary input into existing interface verification methods. We provide two examples: a car traveling through a yellow light at an intersection and an aircraft autopilot in an automatic landing/go-around maneuver. The examples demonstrate the applicability of this methodology to hybrid systems that have operational constraints we can pose in terms of safety. This methodology differs from existing work in hybrid system verification in that we directly account for the user’s interactions with the system.

Meeko Oishi↗

NASA NTRS2008

Advanced Diagnostic and Prognostic Testbed (ADAPT) Testability Analysis Report

As system designs become more complex, determining the best locations to add sensors and test points for the purpose of testing and monitoring these designs becomes more difficult. Not only must the designer take into consideration all real and potential faults of the system, he or she must also find efficient ways of detecting and isolating those faults. Because sensors and cabling take up valuable space and weight on a system, and given constraints on bandwidth and power, it is even more difficult to add sensors into these complex designs after the design has been completed. As a result, a number of software tools have been developed to assist the system designer in proper placement of these sensors during the system design phase of a project. One of the key functions provided by many of these software programs is a testability analysis of the system essentially an evaluation of how observable the system behavior is using available tests. During the design phase, testability metrics can help guide the designer in improving the inherent testability of the design. This may include adding, removing, or modifying tests; breaking up feedback loops, or changing the system to reduce fault propagation. Given a set of test requirements, the analysis can also help to verify that the system will meet those requirements. Of course, a testability analysis requires that a software model of the physical system is available. For the analysis to be most effective in guiding system design, this model should ideally be constructed in parallel with these efforts. The purpose of this paper is to present the final testability results of the Advanced Diagnostic and Prognostic Testbed (ADAPT) after the system model was completed. The tool chosen to build the model and to perform the testability analysis with is the Testability Engineering and Maintenance System Designer (TEAMS-Designer). The TEAMS toolset is intended to be a solution to span all phases of the system, from design and development through health management and maintenance. TEAMS-Designer is the model-building and testability analysis software in that suite.

Ossenfort, John↗

NASA NTRS1965

Rational approximation to the response of a dynamic system described by a nonlinear differential equation final report, 15 jan. 1964 - 14 jan. 1965

Linear fractional transformation for obtaining rational approximations to response of physical system defined by second order nonlinear differential equation with constant coefficients

LINEAR TRANSFORMATION↗

NASA NTRS1987

Near Identifiability of Dynamical Systems

Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.

Hadaegh, F. Y.↗

NASA NTRS1990

Integration of system identification and robust controller designs for flexible structures in space

A novel approach is developed using experimental data from the structural testing of a physical system to identify a reduced-order model and its error for a robust controller design. There are three steps involved in the approach. First, an approximately balanced model is identified using the eigensystem realization algorithm, which is an identification algorithm. Second, the model error is calculated and described in frequency domain in terms of the H(infinity) norm. Third, a pole-placement technique in combination with an H(infinity) control method is applied to design a controller for the system. A set of experimental data from an existing setup, namely the Mini-Mast system, is used to illustrate and verify the approach development in this paper.

Juang, Jer-Nan↗

NASA NTRS1994

The birthplace of compact groups of galaxies

We use complete redshift surveys to study the redshift neighborhoods of 38 Hickson compact groups (HCGs). Twenty-nine of these HCGs (76%) are embedded in rich looser systems which we call HCG associations. Analysis of the redshift neighborhood of HCGs outside the CfA survey suggests that most HCGs are embedded in more extended physical systems. Rich loose groups extracted from the CfA survey (Ramella et al. (1994)) have physical properties similar to those of the HCG associations. These rich loose groups often contain compact configurations. N-body experiments (Diaferio (1994)) suggest that compact configurations analogous to HCGs form continually during the collapse of rich loose groups. These observational and numerical results suggest that rich loose groups are the birthplace of HCGs.

Ramella, Massimo↗

NASA NTRS1989

Vapor condensation on liquid surface due to laminar jet-induced mixing: The effects of system parameters

The effects of system parameters on the interface condensation rate in a laminar jet induced mixing tank are numerically studied. The physical system consists of a partially filled cylindrical tank with a slightly subcooled jet discharged from the center of the tank bottom toward the liquid-vapor interface which is at a saturation temperature corresponding to the constant tank pressure. Liquid is also withdrawn from the outer part of the tank bottom to maintain the constant liquid level. The jet velocity is selected to be low enough such that the free surface is approximately flat. The effect of vapor superheat is assumed to be negligible. Therefore, the interface condensation rate can be determined from the resulting temperature field in the liquid region alone. The nondimensional form of the steady state conservation equations are solved by a finite difference method for various system parameters including liquid height to tank diameter ratio, tank to jet diameter ratio, liquid inflow to outflow area ratio, and a heat leak parameter which characterizes the uniform wall heat flux. Detailed analyses based on the numerical solutions are performed and simplified equations are suggested for the prediction of condensation rate.

Lin, Chin-Shun↗

NASA NTRS1990

Vapor condensation on liquid surface due to laminar jet-induced mixing - The effects of system parameters

Lin, Chin-Shun↗

NASA NTRS1992

Fault management for the Space Station Freedom control center

This paper describes model based reasoning fault isolation in complex systems using automated digraph analysis. It discusses the use of the digraph representation as the paradigm for modeling physical systems and a method for executing these failure models to provide real-time failure analysis. It also discusses the generality, ease of development and maintenance, complexity management, and susceptibility to verification and validation of digraph failure models. It specifically describes how a NASA-developed digraph evaluation tool and an automated process working with that tool can identify failures in a monitored system when supplied with one or more fault indications. This approach is well suited to commercial applications of real-time failure analysis in complex systems because it is both powerful and cost effective.

Clark, Colin↗