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NASA NTRS1979

A kinetic approach to compressible turbulence

A kinetic theory of strong turbulence is developed by decomposing fluctuation of distribution function into scaled components, or ranks, to represent three transport processes: macroscopic evolution, transport property and relaxation. Closure is obtained by formulating a relaxation process for the approach of eddy diffusivity to equilibrium. The kinetic equation is solved and three transport functions of turbulence in adiabatic gas are derived: two transfer functions describe turbulent mode transfer, and a coupling function describes the build-up of kinetic energy at the expense of internal energy. The energy balance in the inertial subrange of homogeneous and isotropic turbulence in an adiabatic gas yields a k to the -3rd law, in agreement with numerical computations from one dimensional model of compressible turbulence.

Tchen, C. M.↗

NASA NTRS2011

Characterizing Observed Limit Cycles in the Cassini Main Engine Guidance Control System

The Cassini spacecraft dynamics-related telemetry during long Main Engine (ME) burns has indicated the presence of stable limit cycles between 0.03-0.04 Hz frequencies. These stable limit cycles cause the spacecraft to possess non-zero oscillating rates for extended periods of time. This indicates that the linear ME guidance control system does not model the complete dynamics of the spacecraft. In this study, we propose that the observed limit cycles in the spacecraft dynamics telemetry appear from a stable interaction between the unmodeled nonlinear elements in the ME guidance control system. Many nonlinearities in the control system emerge from translating the linear engine gimbal actuator (EGA) motion into a spacecraft rotation. One such nonlinearity comes from the gear backlash in the EGA system, which is the focus of this paper. The limit cycle characteristics and behavior can be predicted by modeling this gear backlash nonlinear element via a describing function and studying the interaction of this describing function with the overall dynamics of the spacecraft. The linear ME guidance controller and gear backlash nonlinearity are modeled analytically. The frequency, magnitude, and nature of the limit cycle are obtained from the frequency response of the ME guidance controller and nonlinear element. In addition, the ME guidance controller along with the nonlinearity is simulated. The simulation response contains a limit cycle with similar characterstics as predicted analytically: 0.03-0.04 Hz frequency and stable, sustained oscillations. The analytical and simulated limit cycle responses are compared to the flight telemetry for long burns such as the Saturn Orbit Insertion and Main Engine Orbit Trim Maneuvers. The analytical and simulated limit cycle characteristics compare well with the actual observed limit cycles in the flight telemetry. Both have frequencies between 0.03-0.04 Hz and stable oscillations. This work shows that the stable limit cycles occur due to the interaction between the unmodeled nonlinear elements and linear ME guidance controller.

stable limit cycle↗

NASA NTRS1989

Pulse modulated control synthesis for a flexible spacecraft

The describing function method is employed for the nonlinear control analysis and design of a flexible spacecraft equipped with pulse modulated reaction jets. The method provides a means of characterizing the pulse modulator in terms of its gain and phase for structural mode limit cycle analysis. Although the describing function method is inherently inexact and is not widely used in practice, a new way of utilizing it for practical control design problems is presented. It is shown that the approximations inherent in the method can be accounted as a modeling uncertainty for the nonlinear control robustness analysis. The pulse modulated control system of the Intelsat 5 spacecraft is used as an example to illustrate the concept and methodology developed in the paper. The nonlinear stability margins predicted by the describing function analysis are verified from nonlinear simulations.

Anthony, Tobin C.↗

NASA NTRS1972

An auditory display in a dual-axis tracking task.

Results of a study in which subjects were presented concurrently with the primary task of controlling a second-order plant and the secondary task of controlling a first-order plant. The plant errors for the two tasks were shown on separate visual displays. An auditory display, whose output varied in frequency and volume with the error, was used to supplement the secondary task in half of the runs. To study the effects of the auditory display, two performance measures were obtained: (1) the integral of the squared error (ISE) and (2) the describing functions of the human operator. Statistical analysis of the ISE measures indicated that when the secondary task was supplemented with an auditory display, there was a significant improvement in performance on the secondary task. The performance on the primary task improved on the average, but not significantly. The variances of the ISE values decreased for both the tasks, indicating a more consistent behavior with the auditory display. The describing function analysis showed that supplementing the secondary task with the auditory display increased the low frequency gain of the human operator for this task. The describing functions for the primary task did not show any apparent changes.

Mirchandani, P. B.↗

DOE OSTI2021

Assessing density functionals for describing methane dissociative chemisorption on Pt(110)-(2×1) surface

In this work, we explore the suitability of several density functionals with the generalized gradient approximation (GGA) and beyond for describing the dissociative chemisorption of methane on the reconstructed Pt(110)-(2×1) surface. The bulk and surface structures of the metal, methane adsorption energy, and dissociation barrier are used to assess the functionals. A van der Waals corrected GGA functional (optPBE-vdW) and a metaGGA functional with van der Waals correction (MS PBEl-rVV10) are selected for ab initio molecular dynamics calculations of the sticking probability. Our results suggest that the use of these two functionals may lead to a better agreement with existing experimental results, thus serving as a good starting point for future development of reliable machine-learned potential energy surfaces for the dissociation of methane on the Pt(110)-(2×1) surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2010

Trade Spaces in Crewed Spacecraft Atmosphere Revitalization System Development

Developing the technological response to realizing an efficient atmosphere revitalization system for future crewed spacecraft and space habitats requires identifying and describing functional trade spaces. Mission concepts and requirements dictate the necessary functions; however, the combination and sequence of those functions possess significant flexibility. Us-ing a closed loop environmental control and life support (ECLS) system architecture as a starting basis, a functional unit operations approach is developed to identify trade spaces. Generalized technological responses to each trade space are discussed. Key performance parameters that apply to functional areas are described.

Perry, Jay L.↗

NASA NTRS1984

A frequency domain stability analysis of a phase plane control system

A describing function is used to model a phase plane controller which is part of the Space Shuttle on-orbit Reaction Control System autopilot. A frequency domain stability analysis of the closed-loop control system is applied to a study of potential flight control system interaction with the Orbiter and a class of payloads deployed from a tilt table. Phase-gain plot techniques are used to show that expansion of phase plane angular rate limits and stiffening of the tilt table pivot do not always enhance system stability. Instability region approximations are mapped as a function of rate limit, payload geometry, jet used, and natural frequency of the pivot. Comparison of the describing function analysis with simulation results shows excellent correlation.

Hattis, P. D.↗

NASA NTRS1965

Human Tracking Performance in Uncoupled and Coupled Two-Axis Systems

This report presents tile results of an experimental and analytical study of human performance in uncoupled and coupled control systems. Human pilot performance in single and two-axis systems was mathematically modeled by linear second-order describing functions. Model parameters were determined using model matching techniques. Analysis of the models showed that the amplitude ratio and phase lead of the describing function increased with training indicating an increase in open loop bandwidth. The phase margin also decreased with training. Increasing the plant lag time constant resulted in an increase in the model lead time constant and a decrease in the zero frequency gain. No significant difference was found to exist in the normalized tracking error per axis between the two-axis tasks and the single-axis tasks. However tile model lead time constant was significantly greater in two-axis tracking. Manual tracking of two-axis systems with cross-coupling was studied experimentally and analytically. Approximate methods for modeling two-axis performance were developed and checked using a precise spectral analysis approach. Coupled and uncoupled, symmetrical and asymmetrical two-axis performance was compared. The results show that modeling of cross-coupled systems is feasible and that trained subjects are capable of decoupling the axes of some systems. A methodology study compared the identification performance of continuous, iterative, and extrapolation model matching techniques. An iterative technique employing sensitivity equations for the generation of influence coefficients was found to be the best technique due to its excellent identification accuracy and ease of implementation. Convergence in iterative techniques can be improved substantially by equalizing the parameter adjustment rates and limiting the maximum correction per iteration.

Todosiev, E. P.↗

NASA NTRS1985

Control response measurements of the Skyship-500 airship

An examination is conducted of the Skyship 500's dynamic response to control inputs from elevators, rudders, and throttles at zero, 25, and 40 kts indicated airspeed. Input frequency sweeps were made with pitch and turn controls at 25 and 40 kts, ranging in frequency from about 0.03 to 1.5 Hz. FFT data analysis was then applied to compute describing functions for each run. Frequency responses are noted to be very smooth, and comparisons between repeat runs indicate excellent agreement. Summary plots of the faired describing functions from each run form the core of the data presented. These data constitute a comprehensive and reliable data base on which to predicate future dynamic simulation mathematical models of small airship dynamic response.

Jex, H. R.↗

NASA NTRS1981

Influence of combined visual and vestibular cues on human perception and control of horizontal rotation

Measurements are made of manual control performance in the closed-loop task of nulling perceived self-rotation velocity about an earth-vertical axis. Self-velocity estimation is modeled as a function of the simultaneous presentation of vestibular and peripheral visual field motion cues. Based on measured low-frequency operator behavior in three visual field environments, a parallel channel linear model is proposed which has separate visual and vestibular pathways summing in a complementary manner. A dual-input describing function analysis supports the complementary model; vestibular cues dominate sensation at higher frequencies. The describing function model is extended by the proposal of a nonlinear cue conflict model, in which cue weighting depends on the level of agreement between visual and vestibular cues.

Zacharias, G. L.↗

NASA NTRS1988

Steady-state evoked potentials possibilities for mental-state estimation

The use of the human steady-state evoked potential (SSEP) as a possible measure of mental-state estimation is explored. A method for evoking a visual response to a sum-of-ten sine waves is presented. This approach provides simultaneous multiple frequency measurements of the human EEG to the evoking stimulus in terms of describing functions (gain and phase) and remnant spectra. Ways in which these quantities vary with the addition of performance tasks (manual tracking, grammatical reasoning, and decision making) are presented. Models of the describing function measures can be formulated using systems engineering technology. Relationships between model parameters and performance scores during manual tracking are discussed. Problems of unresponsiveness and lack of repeatability of subject responses are addressed in terms of a need for loop closure of the SSEP. A technique to achieve loop closure using a lock-in amplifier approach is presented. Results of a study designed to test the effectiveness of using feedback to consciously connect humans to their evoked response are presented. Findings indicate that conscious control of EEG is possible. Implications of these results in terms of secondary tasks for mental-state estimation and brain actuated control are addressed.

Junker, Andrew M.↗

NASA NTRS1989

Overview of computational control research at UT Austin

An overview of current research activities at UT Austin is presented to discuss certain technical issues in the following areas: (1) Computer-Aided Nonlinear Control Design: In this project, the describing function method is employed for the nonlinear control analysis and design of a flexible spacecraft equipped with pulse modulated reaction jets. INCA program has been enhanced to allow the numerical calculation of describing functions as well as the nonlinear limit cycle analysis capability in the frequency domain; (2) Robust Linear Quadratic Gaussian (LQG) Compensator Synthesis: Robust control design techniques and software tools are developed for flexible space structures with parameter uncertainty. In particular, an interactive, robust multivariable control design capability is being developed for INCA program; and (3) LQR-Based Autonomous Control System for the Space Station: In this project, real time implementation of LQR-based autonomous control system is investigated for the space station with time-varying inertias and with significant multibody dynamic interactions.

Bong, Wie↗

NASA NTRS1987

Influence of visual and motion cues on manual lateral stabilization

The ability of humans to detect and control their own lateral acceleration was measured by means of a closed-loop nulling task. Wide-field moving visual cues enhanced the operator's performance in nulling self-motion, especially at lower frequencies. Even visual cues, fixed relative to the operator, resulted in performance improvement relative to self-motion nulling in the dark. Describing function (frequency response) data was obtained for random acceleration conditions consisting of the visual field fixed relative to the laboratory, fixed relative to the subject, moving at constant velocity relative to the subject, and in the dark. The describing function data was corrected for the dynamics of operator manual control strategy. The resulting frequency responses were used to develop a linear model of self-motion detection which required a lead term of 1.5 rad/s to be added to the existing model in order to match the higher sensitivity at higher frequencies.

Huang, J.-K.↗

DOE OSTI2022

Simple new methods for deducing lifetimes in recoil distance Doppler-shift measurements

In this work, new approaches for lifetime determination using data from recoil distance Doppler-shift experiments are presented based on the fundamental properties of the functions describing the time evolution of the population of excited nuclear states. To some extent, one of them represents a contraction of the well-known Differential decay-curve method (DDCM) by using the most reliable data point [the maximum of the $n_i(t)$ function describing the population of level $\textit{i}$ in time] and a purely numerical procedure avoiding any fitting of decay curves. The combination with the standard DDCM analysis is promising for improving the reliability and the precision of the results for the lifetimes obtained. The novel part of the approach consists of using a chain of equations at the consecutive maxima of the ni(t) functions, which allow us to precisely determine the ratio of the lifetimes of two consecutive levels and, in the case where one of these lifetimes is known, to determine the unknown one. In addition, a simple integral derivation of the lifetime is presented involving the peak areas measured at different distances, and an application of the first moments (expectation values and centroids in time) of the $n_i(t)$ functions for determining lifetimes is also demonstrated to be useful.

47 OTHER INSTRUMENTATION↗

NASA NTRS1976

Stability analysis of the discrete-data Large-Space-Telescope system

This paper considers the application of the discrete describing function to the stability analysis of the Large-Space Telescope (LST) system. An analytical model of the CMG gimbal friction is derived, which is then used to arrive at a closed-form analytical expression for the discrete describing function of the nonlinearity. The analysis is used for the study of the fine-pointing stability of the LST vehicle. Simulation results corroborate the conclusions from the analytical analysis.

Kuo, B. C.↗

DOE OSTI2021

A probability density function model describing height estimation uncertainty due to image pixel intensity noise in digital fringe projection measurements

Digital fringe projection is a surface-profiling technique used for highly accurate non-contact measurements. As with any measurement technique, a variety of sources degrade to the measurement accuracy of the method. Here, this paper presents an analytically-derived probability density function that explicitly models the surface height measurement error due to inevitable phase measurement error, and it includes the specific case of pixel noise inducing the phase measurement error that ultimately leads to the height estimation error. The accuracy of the model was validated through Monte-Carlo simulations of resultant height distributions subject to arbitrarily correlated pixel intensity noise and experimental digital fringe projection measurements where the pixel-by-pixel height uncertainty estimations were compared to the predictions of the derived model.

42 ENGINEERING↗

NASA NTRS1977

Manual control of yaw motion with combined visual and vestibular cues

Measurements are made of manual control performance in the closed-loop task of nulling perceived self-rotation velocity about an earth-vertical axis. Self-velocity estimation was modelled as a function of the simultaneous presentation of vestibular and peripheral visual field motion cues. Based on measured low-frequency operator behavior in three visual field environments, a parallel channel linear model is proposed which has separate visual and vestibular pathways summing in a complementary manner. A correction to the frequency responses is provided by a separate measurement of manual control performance in an analogous visual pursuit nulling task. The resulting dual-input describing function for motion perception dependence on combined cue presentation supports the complementary model, in which vestibular cues dominate sensation at frequencies above 0.05 Hz. The describing function model is extended by the proposal of a non-linear cue conflict model, in which cue weighting depends on the level of agreement between visual and vestibular cues.

Zacharias, G. L.↗

NASA NTRS1988

A computer-aided approach to nonlinear control systhesis

The major objective of this project is to develop a computer-aided approach to nonlinear stability analysis and nonlinear control system design. This goal is to be obtained by refining the describing function method as a synthesis tool for nonlinear control design. The interim report outlines the approach by this study to meet these goals including an introduction to the INteractive Controls Analysis (INCA) program which was instrumental in meeting these study objectives. A single-input describing function (SIDF) design methodology was developed in this study; coupled with the software constructed in this study, the results of this project provide a comprehensive tool for design and integration of nonlinear control systems.

Wie, Bong↗