Applications of discrete network simulation in space vehicle checkout. Volume 2 - Computer programs Final report
Modified computer programs for time oriented discrete network simulation and analysis of man machine systems
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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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A general algorithm for solving the algebraic Riccati equation
The generalized eigenvalue problem provides a suitable framework for reliable solutions of many system theoretic, control, and estimation problems. A general algorithm for solving the matrix algebraic Riccati equation (ARE) which utilizes a pencil structure is described here. This algorithm avoids unnecessary inversion of cost or transition matrices, making it a numerically sound way to solve for the gains and/or ARE with singular quadratic costs, for cases satisfying detectability and stabilizability conditions. Examples are solution with discrete dead-beat control, noiseless measurements in Kalman filters and time-delays in discrete-time systems, which cause difficulties in the Hamiltonian standard eigenvalue problem formulation. The ARE algorithm implementatiton and numerical examples are shown.
Walker, R. A.↗
Estimability and regulability of linear systems
A linear state-space system will be said to be estimable if in estimating its state from its output the posterior error covariance matrix is strictly smaller than the prior covariance matrix. It will be said to be regulable if the quadratic cost of state feedback control is strictly smaller than the cost when no feedback is used. These properties, which are shown to be dual, are different from the well known observability and controllability properties of linear systems. Necessary and sufficient conditions for estimability and regulability are derived for time variant and time invariant systems, in discrete and continuous time.
Baram, Yoram↗
Estimability and regulability of linear systems
A linear state-space system will be said to be estimable if in estimating its state from its output the posterior error covariance matrix is strictly smaller than the prior covariance matrix. It will be said to be regulable if the quadratic cost of state feedback control is strictly smaller than the cost when no feedback is used. These properties, which are are shown to be dual, are different from the well known observability and controllability properties of linear systems. Necessary and sufficient conditions for estimability and regulability are derived for time variant and time invariant systems, in discrete and continuous time.
Baram, Yoram↗
Improved Autoassociative Neural Networks
Improved autoassociative neural networks, denoted nexi, have been proposed for use in controlling autonomous robots, including mobile exploratory robots of the biomorphic type. In comparison with conventional autoassociative neural networks, nexi would be more complex but more capable in that they could be trained to do more complex tasks. A nexus would use bit weights and simple arithmetic in a manner that would enable training and operation without a central processing unit, programs, weight registers, or large amounts of memory. Only a relatively small amount of memory (to hold the bit weights) and a simple logic application- specific integrated circuit would be needed. A description of autoassociative neural networks is prerequisite to a meaningful description of a nexus. An autoassociative network is a set of neurons that are completely connected in the sense that each neuron receives input from, and sends output to, all the other neurons. (In some instantiations, a neuron could also send output back to its own input terminal.) The state of a neuron is completely determined by the inner product of its inputs with weights associated with its input channel. Setting the weights sets the behavior of the network. The neurons of an autoassociative network are usually regarded as comprising a row or vector. Time is a quantized phenomenon for most autoassociative networks in the sense that time proceeds in discrete steps. At each time step, the row of neurons forms a pattern: some neurons are firing, some are not. Hence, the current state of an autoassociative network can be described with a single binary vector. As time goes by, the network changes the vector. Autoassociative networks move vectors over hyperspace landscapes of possibilities.
Hand, Charles↗
Program verification document for the ASTP flight program
The various segments of the Apollo Soyuz Test Project (ASTP) flight program were verified. This included checks on the following: general verification, reference systems and transformations, launch preparations, boost navigation and guidance, orbital navigation and guidance, time bases, discretes, and interrupts, launch vehicle attitude control, switch selector processing, digital command system, real time telemetry and data compression, and algorithms.
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Stability analysis of combined continuous and discrete systems
A discrete, time-invariant system is represented by an equivalent continuous, periodic system. A combined continuous plant and discrete controller may then be formulated as a single continuous, periodic coefficient system. The exact stability solution for the combined system is obtained, as a matrix eigenvalue problem. Periodic system theory also gives some information about the type of instabilities which may be encountered in the combined plant and controller.
Johnson, W.↗
Real-time Exponential Curve Fits Using Discrete Calculus
This paper presents an improved solution for curve fitting data to an exponential equation (Y = AeBt + C). This improvement is in four areas ? speed, stability, determinant processing time, and the removal of limits. The solution presented in this paper avoids iterative techniques and their stability errors by using three mathematical ideas ? discrete calculus, a special relationship (between exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation Y = AxB + C and the general geometric growth equation Y = AkBt + C.
Rowe, Geoffrey K.↗
An experimental modal testing/identification technique for personal computers
A PC-based system for mode shape identification is evaluated. A time-domain modal identification procedure is utilized to identify the mode shapes of a beam apparatus from discrete time-domain measurements. The apparatus includes a cantilevered aluminum beam, four accelerometers, four low-pass filters, and the computer. The method's algorithm is comprised of an identification algorithm: the Eigensystem Realization Algorithm (ERA) and an estimation algorithm called Minimum Model Error (MME). The identification ability of this algorithm is compared with ERA alone, a frequency-response-function technique, and an Euler-Bernoulli beam model. Detection of modal parameters and mode shapes by the PC-based time-domain system is shown to be accurate in an application with an aluminum beam, while mode shapes identified by the frequency-domain technique are not as accurate as predicted. The new method is shown to be significantly less sensitive to noise and poorly excited modes than other leading methods. The results support the use of time-domain identification systems for mode shape prediction.
Roemer, Michael J.↗
Real-Time Exponential Curve Fits Using Discrete Calculus
An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.
Rowe, Geoffrey↗
Comparison of continuous and discrete adaptive identification algorithms
Discretization of a popular continuous-time control algorithm is effected and an equivalent discrete-time identification law developed and compared to a published discrete identification algorithm developed from Lyapunov Theory. Results are compared as regards asymptotic stability as insured using Lyapunov theory. Some analysis and design guidelines are proposed as regards implementation and practical utility.
Colburn, B. K.↗
Switched steerable multiple beam antenna system
A steerable multibeam five element cross-feed cluster antenna system is described. The feed power is divided into five branches. Each branch includes a switching network comprised of a plurality of time delay elements each individually controlled by a respective electromagnetic latching switch. Frequency independent individual two-dimensional beam steering at intermediate (IF) scanning frequencies is thereby provided wherein discrete incremental time delays are introduced by the switching networks into each branch and the signals recombined thereafter to form each beam. The electromagnetic latched switching reduces power consumption and permits higher power switching and reciprocal coincident tranmsit and receive operation. Frequency independence due to incremental time delay switching permits coincident reciprocal operation and steering for transmit-receive signal paths carrying different transmit-receive frequencies. Diagonal quarter wave plates in the waveguides alter polarization from the circular to orthogonal linear to provide transmitter-receiver isolation.
Richard S Iwasaki↗
3-D Unsteady Flow Visualization in Computational Fluid Dynamics
Presently, there are very few visualization systems available for time-dependent flow fields. Although existing visualization systems for instantaneous flow fields may be used to view time-dependent flow fields at discrete points in time, the time variable is usually not considered in the visualization technique. A simple and effective approach for visualizing time-dependent flow fields using streaklines is presented. Some results from this approach are shown.
Lane, David A.↗
Algorithms for Maneuvering Spacecraft Around Small Bodies
A document describes mathematical derivations and applications of autonomous guidance algorithms for maneuvering spacecraft in the vicinities of small astronomical bodies like comets or asteroids. These algorithms compute fuel- or energy-optimal trajectories for typical maneuvers by solving the associated optimal-control problems with relevant control and state constraints. In the derivations, these problems are converted from their original continuous (infinite-dimensional) forms to finite-dimensional forms through (1) discretization of the time axis and (2) spectral discretization of control inputs via a finite number of Chebyshev basis functions. In these doubly discretized problems, the Chebyshev coefficients are the variables. These problems are, variously, either convex programming problems or programming problems that can be convexified. The resulting discrete problems are convex parameter-optimization problems; this is desirable because one can take advantage of very efficient and robust algorithms that have been developed previously and are well established for solving such problems. These algorithms are fast, do not require initial guesses, and always converge to global optima. Following the derivations, the algorithms are demonstrated by applying them to numerical examples of flyby, descent-to-hover, and ascent-from-hover maneuvers.
Acikmese, A. Bechet↗
Finite Volume Methods: Foundation and Analysis
Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.
Barth, Timothy↗
The Additive Manufacturing Moment Measure (AM3) Approach to Predictions of Solid Cooling Rate and Time Above Melt
Qualification of a laser powder bed fusion additive manufacturing (LPBF-AM) process requires knowledge of the multi-scale material physics during the process, per part. As the LPBF-AM build occurs, each moment is influenced by the process history. Knowledge of the build sequence can be used to generate a discretized time-space-condition point field that when coupled with a nearest neighbors’ calculation results in a generalized and fully parallel process model computation. This GPU accelerated approach was developed for part-scale analysis of build files along with in-situ process monitoring sensor data and is termed the “Additive Manufacturing Moment Measure” (AM3). The AM3 approach will be presented and then used to evaluate an AM Bench relevant geometry with synchronized in-situ process data, ex-situ nondestructive evaluation, and optical microscopy observations. These comparisons permit a better understanding of how the process actions can affect the LPBF-AM build quality and the signals generated during in-situ process monitoring.
Additive Manufacturing↗
Optimal open multistep discretization formulas for real-time simulation
The performance of digital real-time simulations is considered. A figure of merit is derived that quantifies a simulation's fidelity in terms of the time-domain discrepancy between its output and that of the plant it simulates, assuming that the plant is linearizable and asymptotically stable. This performance index is then used in deriving an easily automated procedure for calculating optimal values for free parameters in plant discretizations based on a generalized form of open linear multistep integration formulas. The theory is demonstrated in simulating the rigid-body dynamics of a fully articulated helicopter rotor blade system.
Moerder, Daniel D.↗
Nonlinear Control and Discrete Event Systems
As the operation of large systems becomes ever more dependent on extensive automation, the need for an effective solution to the problem of design and validation of the underlying software becomes more critical. Large systems possesses much detailed structure, typically hierarchical, and they are hybrid. Information processing at the top of the hierarchy is by means of formal logic and sentences; on the bottom it is by means of simple scalar differential equations and functions of time; and in the middle it is by an interacting mix of nonlinear multi-axis differential equations and automata, and functions of time and discrete events. The lecture will address the overall problem as it relates to flight vehicle management, describe the middle level, and offer a design approach that is based on Differential Geometry and Discrete Event Dynamic Systems Theory.
Meyer, George↗