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NASA NTRS2007

Computational Workbench for Multibody Dynamics

PyCraft is a computer program that provides an interactive, workbenchlike computing environment for developing and testing algorithms for multibody dynamics. Examples of multibody dynamic systems amenable to analysis with the help of PyCraft include land vehicles, spacecraft, robots, and molecular models. PyCraft is based on the Spatial-Operator- Algebra (SOA) formulation for multibody dynamics. The SOA operators enable construction of simple and compact representations of complex multibody dynamical equations. Within the Py-Craft computational workbench, users can, essentially, use the high-level SOA operator notation to represent the variety of dynamical quantities and algorithms and to perform computations interactively. PyCraft provides a Python-language interface to underlying C++ code. Working with SOA concepts, a user can create and manipulate Python-level operator classes in order to implement and evaluate new dynamical quantities and algorithms. During use of PyCraft, virtually all SOA-based algorithms are available for computational experiments.

Edmonds, Karina↗

NASA NTRS1997

LQR Control of Thin Shell Dynamics: Formulation and Numerical Implementation

A PDE-based feedback control method for thin cylindrical shells with surface-mounted piezoceramic actuators is presented. Donnell-Mushtari equations modified to incorporate both passive and active piezoceramic patch contributions are used to model the system dynamics. The well-posedness of this model and the associated LQR problem with an unbounded input operator are established through analytic semigroup theory. The model is discretized using a Galerkin expansion with basis functions constructed from Fourier polynomials tensored with cubic splines, and convergence criteria for the associated approximate LQR problem are established. The effectiveness of the method for attenuating the coupled longitudinal, circumferential and transverse shell displacements is illustrated through a set of numerical examples.

delRosario, R. C. H.↗

NASA NTRS1989

Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series

Two dimensions of a dynamical system given by experimental time series are distinguished. Statistical dimension gives a theoretical upper bound for the minimal number of degrees of freedom required to describe the attractor up to the accuracy of the data, taking into account sampling and noise problems. The dynamical dimension is the intrinsic dimension of the attractor and does not depend on the quality of the data. Singular Spectrum Analysis (SSA) provides estimates of the statistical dimension. SSA also describes the main physical phenomena reflected by the data. It gives adaptive spectral filters associated with the dominant oscillations of the system and clarifies the noise characteristics of the data. SSA is applied to four paleoclimatic records. The principal climatic oscillations and the regime changes in their amplitude are detected. About 10 degrees of freedom are statistically significant in the data. Large noise and insufficient sample length do not allow reliable estimates of the dynamical dimension.

Vautard, R.↗

NASA NTRS1994

Dynamic Stability Instrumentation System (DSIS). Volume 1: Hardware description

This paper is a hardware description manual for the Dynamic Stability Instrumentation System that is used in specific NASA Langley wind tunnels. The instrumentation system performs either a synchronous demodulation or a fast Fourier transform on dynamic balance strain gage signals, and ultimately computes aerodynamic coefficients. The DSIS consists of a double rack of instruments, a remote motor-generator set, two special stings each with motor driven shafts, and specially designed balances. The major components in the instrumentation rack include a personal computer, digital signal processor microcomputers, computer-controlled signal conditioners, function generator, digital multimeter, and an optional fast Fourier transform analyzer.

Jordan, T. L.↗

NASA NTRS1982

Methods of sequential estimation for determining initial data in numerical weather prediction

Numerical weather prediction (NWP) is an initial-value problem for a system of nonlinear differential equations, in which initial values are known incompletely and inaccurately. Observational data available at the initial time must therefore be supplemented by data available prior to the initial time, a problem known as meteorological data assimilation. A further complication in NWP is that solutions of the governing equations evolve on two different time scales, a fast one and a slow one, whereas fast scale motions in the atmosphere are not reliably observed. This leads to the so called initialization problem: initial values must be constrained to result in a slowly evolving forecast. The theory of estimation of stochastic dynamic systems provides a natural approach to such problems. For linear stochastic dynamic models, the Kalman-Bucy (KB) sequential filter is the optimal data assimilation method, for linear models, the optimal combined data assimilation-initialization method is a modified version of the KB filter.

Cohn, S. E.↗

NASA NTRS1983

Classical linear-control analysis applied to business-cycle dynamics and stability

Linear control analysis is applied as an aid in understanding the fluctuations of business cycles in the past, and to examine monetary policies that might improve stabilization. The analysis shows how different policies change the frequency and damping of the economic system dynamics, and how they modify the amplitude of the fluctuations that are caused by random disturbances. Examples are used to show how policy feedbacks and policy lags can be incorporated, and how different monetary strategies for stabilization can be analytically compared. Representative numerical results are used to illustrate the main points.

Wingrove, R. C.↗

NASA NTRS1976

The uncertainty threshold principle - Fundamental limitations of optimal decision making under dynamic uncertainty

The fundamental limitations of the optimal control of dynamic systems with random parameters are analyzed by studying a scalar linear-quadratic optimal control example. It is demonstrated that optimum long-range decision making is possible only if the dynamic uncertainty (quantified by the means and covariances of the random parameters) is below a certain threshold. If this threshold is exceeded, there do not exist optimum decision rules. This phenomenon is called the 'uncertainty threshold principle'. The implications of this phenomenon to the field of modelling, identification, and adaptive control are discussed.

Athans, M.↗

NASA NTRS1990

Analysis of airframe/engine interactions - An integrated control perspective

Techniques for the analysis of the dynamic interactions between airframe/engine dynamical systems are presented. Critical coupling terms are developed that determine the significance of these interactions with regard to the closed loop stability and performance of the feedback systems. A conceptual model is first used to indicate the potential sources of the coupling, how the coupling manifests itself, and how the magnitudes of these critical coupling terms are used to quantify the effects of the airframe/engine interactions. A case study is also presented involving an unstable airframe with thrust vectoring for attitude control. It is shown for this system with classical, decentralized control laws that there is little airframe/engine interaction, and the stability and performance with those control laws is not affected. Implications of parameter uncertainty in the coupling dynamics is also discussed, and effects of these parameter variations are also demonstrated to be small for this vehicle configuration.

Schmidt, David K.↗

NASA NTRS1991

Adaptive control of space-based robot manipulators

A control method is presented that achieves globally stable trajectory tracking in the presence of uncertainties in the inertial parameters of the system. The 15-DOF system dynamics are divided into two components: a 9-DOF invertible portion and 6-DOF noninvertible portion. A controller is then designed to achieve trajectory tracking of the invertible portion of the system, which consists of the manipulator-joint positions and the orientation of the base. The motion of the noninvertible portion is bounded but otherwise unspecified. This portion of the system consists of the position of the robot's base and the position of the reaction wheels. A simulation is presented to demonstrate the effectiveness of the controller. A quadratic polynomial is used to generate the desired trajectory to illustrate the trajectory-tracking capability of the controller.

Walker, Michael W.↗

NASA NTRS1998

In-Space Transportation with Tethers

The annual report covers the research conducted on the following topics related to the use of spaceborne tethers for in-space transportation: ProSEDS tether modeling (current collection analyses, influence of a varying tether temperature); proSEDS mission analysis and system dynamics (tether thermal model, thermo-electro-dynamics integrated simulations); proSEDS-tether development and testing (tether requirements, deployment test plan, tether properties testing, deployment tests); and tethers for reboosting the space-based laser (mission analysis, tether system preliminary design, evaluation of attitude constraints).

Lorenzini, Enrico↗

NASA NTRS2006

Stochastic Representation of Chaos Using Terminal Attractors

A nonlinear version of the Liouville equation based on terminal attractors is part of a mathematical formalism for describing postinstability motions of dynamical systems characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism can be applied to both conservative systems (e.g., multibody systems in celestial mechanics) and dissipative systems (e.g., viscous fluids). The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Zak, Michail↗

NASA NTRS2021

Dynamic Radioisotope Power System (DRPS) Permanently Shadowed Region (PSR) Demonstrator Rover

This conceptual design study investigated trading several Dynamic Radioisotope Power Systems (DRPS) in development to supply power to a lunar science rover which operates for long periods (months) in permanently shadowed regions (PSR) over many years. The design was conducted by the Compass team and relied heavily on the planned VIPER rover design, which is limited to only a few hours of operations in PSRs and less than a month near the south pole. As such this conceptual design shows what a DRPS can do for a follow-on type VIPER rover. In addition to the long duration, go anywhere DRPS power system, the Compass team added a communications system that utilizes the Gateway spacecraft as a relay node for nearly 24/7 communications link to the DRPS rover in lunar craters not visible from the earth. The Compass design includes a notional conops, launch and delivery, subsystem designs of power, mobility, structures, science, command and data handling, communications, guidance and control, and thermal. The thermal design was especially important due the low temperatures in PSRs where the science environment needs to be shielded from the waste heat from the DRPS.

Dynamic Radioisotope Power Systems↗

NASA NTRS1971

On stochastic control and optimal measurement strategies

The control of stochastic dynamic systems is studied with particular emphasis on those which influence the quality or nature of the measurements which are made to effect control. Four main areas are discussed: (1) the meaning of stochastic optimality and the means by which dynamic programming may be applied to solve a combined control/measurement problem; (2) a technique by which it is possible to apply deterministic methods, specifically the minimum principle, to the study of stochastic problems; (3) the methods described are applied to linear systems with Gaussian disturbances to study the structure of the resulting control system; and (4) several applications are considered.

Kramer, L. C.↗

NASA NTRS2003

Balloon Borne Arc-Second Pointer Feasibility Study

For many years scientists have been utilizing stratospheric balloons as low-cost platforms on which to conduct space science experiments. A major hurdle in extending the range of experiments for which these vehicles are useful has been the imposition of the gondola dynamics on the accuracy with which an instrument can be kept pointed at a celestial target. A significant number of scientists have sought the ability to point their instruments with jitter in the arc-second range. This paper presents the design and analysis of a stratospheric balloon borne pointing system that is able to meet this requirement. The foundation for a high fidelity controller simulation is presented. The flexibility of the flight train is represented through generalized modal analysis. A multiple controller scheme is introduced for coarse and fine pointing. Coarse azimuth pointing is accomplished by an established pointing system, with extensive flight history, residing above the gondola structure. A pitch-yaw gimbal mount is used for fine pointing, providing orthogonal axes when nominally on target. Fine pointing actuation is from direct drive dc motors, eliminating backlash problems. An analysis of friction nonlinearities and a demonstration of the necessity in eliminating static fiction are provided. A unique bearing hub design is introduced that eliminates static fiction from the system dynamics. A control scheme involving linear accelerometers for enhanced disturbance rejection is also presented. Results from a linear analysis of the total system and the high fidelity simulation are given. This paper establishes that the proposed control strategy can be made robustly stable with significant design margins. Also demonstrated is the efficacy of the proposed system in rejecting disturbances larger than those considered realistic. Finally, we see that sub arc-second pointing stability can be achieved for a large instrument pointing at an inertial target.

Ward, Philip R.↗

NASA NTRS2006

Demonstration of a Balloon Borne Arc-Second Pointer Design

Many designs for utilizing stratospheric balloons as low-cost platforms on which to conduct space science experiments have been proposed throughout the years. A major hurdle in extending the range of experiments for which these vehicles are useful has been the imposition of the gondola dynamics on the accuracy with which an instrument can be kept pointed at a celestial target. A significant number of scientists have sought the ability to point their instruments with jitter in the arc-second range. This paper presents the design and analysis of a stratospheric balloon borne pointing system that is able to meet this requirement. The test results of a demonstration prototype of the design with similar ability are also presented. Discussion of a high fidelity controller simulation for design analysis is presented. The flexibility of the flight train is represented through generalized modal analysis. A multiple controller scheme is utilized for coarse and fine pointing. Coarse azimuth pointing is accomplished by an established pointing system, with extensive flight history, residing above the gondola structure. A pitch-yaw gimbal mount is used for fine pointing, providing orthogonal axes when nominally on target. Fine pointing actuation is from direct drive dc motors, eliminating backlash problems. An analysis of friction nonlinearities and a demonstration of the necessity in eliminating static friction are provided. A unique bearing hub design is introduced that eliminates static friction from the system dynamics. A control scheme involving linear accelerometers for enhanced disturbance rejection is also presented. Results from a linear analysis of the total system and the high fidelity simulation are given. Results from a generalized demonstration prototype are presented. Commercial off-the-shelf (COTS) hardware was used to demonstrate the efficacy and performance of the pointer design for a mock instrument. Sub-arcsecond pointing ability from a ground hang test setup is shown from the testing results. This paper establishes that the proposed control strategy can be made robustly stable with significant design margins. Also demonstrated is the efficacy of the proposed system in rejecting disturbances larger than those considered realistic. The system is implemented and demonstrates sub arc second pointing ability using COTS hardware. Finally, we see that sub arc-second pointing stability can be achieved for a large instrument pointing at an inertial target.

DeWeese, Keith D.↗

NASA NTRS1990

Ignition and combustion characteristics of metallized propellants

Shakedown and calibration of the experimental apparatus designed to study secondary atomization and ignition characteristics of aluminum slurry propellants was begun and nears completion. The burner was tested over an array of equivalence ratios and oxygen mass fractions to determine the permissible range of operating conditions. A burner flow control system was designed and fabricated which permits independent control of flame stoichiometry and oxidant O2 concentrations. The Sun slurry formulation was selected as the base for initial testing. Laser beam waists at the focal volume of the single particle sizing system were determined to be 396 microns for the Ar-ion and 81 microns for the He-Ne laser. Size calibrations using pinholes were completed and compared to Mie theory for light scattering from particles. A vibrating office droplet generator was used to test the single particle sizing system dynamically by producing a water droplet laden gas flow. The data acquisition and analysis programming was completed and testing is in progress. From initial results, the particle sizing, atomization and ignition detection systems appear to be performing as expected.

Turns, S. R.↗

NASA NTRS1996

Satellite Angular Rate Estimation From Vector Measurements

This paper presents an algorithm for estimating the angular rate vector of a satellite which is based on the time derivatives of vector measurements expressed in a reference and body coordinate. The computed derivatives are fed into a spacial Kalman filter which yields an estimate of the spacecraft angular velocity. The filter, named Extended Interlaced Kalman Filter (EIKF), is an extension of the Kalman filter which, although being linear, estimates the state of a nonlinear dynamic system. It consists of two or three parallel Kalman filters whose individual estimates are fed to one another and are considered as known inputs by the other parallel filter(s). The nonlinear dynamics stem from the nonlinear differential equation that describes the rotation of a three dimensional body. Initial results, using simulated data, and real Rossi X ray Timing Explorer (RXTE) data indicate that the algorithm is efficient and robust.

Azor, Ruth↗

NASA NTRS2000

Identification of Low Order Equivalent System Models From Flight Test Data

Identification of low order equivalent system dynamic models from flight test data was studied. Inputs were pilot control deflections, and outputs were aircraft responses, so the models characterized the total aircraft response including bare airframe and flight control system. Theoretical investigations were conducted and related to results found in the literature. Low order equivalent system modeling techniques using output error and equation error parameter estimation in the frequency domain were developed and validated on simulation data. It was found that some common difficulties encountered in identifying closed loop low order equivalent system models from flight test data could be overcome using the developed techniques. Implications for data requirements and experiment design were discussed. The developed methods were demonstrated using realistic simulation cases, then applied to closed loop flight test data from the NASA F-18 High Alpha Research Vehicle.

Morelli, Eugene A.↗