A technique for identifying pilot describing functions from routine flight-test records
Problem of identifying input-output of pilot by measuring data from flight tests with pilot providing feedback control
Edwards, F. G.↗
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The influence of a prediction display on the quasi-linear describing function and remnant measured with an adaptive analog-pilot in a closed loop
The effect of a prediction display on the human transfer characteristics is explained with the aid of a quasi-linear model. The prediction display causes an increase of the gain factor and the lead factor, a diminishing of the lag factor and a decrease of the remnant. Altogether, these factors yield a smaller mean square value of the control deviation and a simultaneous decrease of the mean square value of the stick signal.
Dey, D.↗
In-flight measured human pilot describing function and remnant for pitch attitude control
Flight tests have been performed with a variable pitch-rate-command/attitude-hold flight control system in a Beechoraft Queen air-80 aircraft. Some results of in-flight measured runs for two pilots controlling typical easy and difficult dynamics are presented together with the initial results of the same tracking experiment performed on a ground-based flight simulator. Results are compared with results of other investigators using fixed-base flight simulators.
Mooij, H. A.↗
Application of describing functions for evaluation of space shuttle landing aid display concepts
Explore the source record for details and available documents.
Chase, W. D.↗
Digital controller design: Continuous and discrete describing function analysis of the IPS system
The digital IPS with wire cable and flex pivot nonlinearity is simulated on the digital computer to determine the effects of varying the sampling period T on the system stability, and to determine a range of optimal values of the parameters of the digital controller. The listing of the computer program is shown as well as the Dahl model for the flex pivot nonlinearity. For the wire cable nonlinearity, two ranges of values were used and the nominal values of the digital controller parameters are included.
Source record↗
Describing functional requirements for knowledge sharing communities
Human collaboration in distributed knowledge sharing groups depends on the functionality of information and communication technologies (ICT) to support performance. Since many of these dynamic environments are constrained by time limits, knowledge must be shared efficiently by adapting the level of information detail to the specific situation. This paper focuses on the process of knowledge and context sharing with and without mediation by ICT, as well as issues to be resolved when determining appropriate ICT channels. Both technology-rich and non-technology examples are discussed.
NASA Discipline Space Human Factors↗
Limit cycles resulting from quantization in digital control systems.
The existence of quantizer-induced limit cycles in digital control systems is a well-known phenomenon. This paper reports the results of an investigation into the discrete describing function technique which is applicable not only to the quantizer nonlinearity but also to any nonlinearity in an otherwise linear discrete system. First a general expression is developed for the discrete describing function that is applicable to any nonlinearity. The describing function is then obtained for the quantizer nonlinearity. Finally, the use of the discrete describing function is illustrated by an example of a digital control system.
Phillips, C. L.↗
Human operator dynamics for aural compensatory tracking
The human operator's ability to control using aural information only and using combined aural and visual displays was investigated for a simple tracking task. Tracking error was presented to the test subjects using one- and two-ear displays. For both displays the pitch of the tone represented the magnitude of the tracking error. The operator's aural control characteristics were modeled as a describing function plus a remnant. The effects on the measured describing function and remnant of different system dynamics, changes in the frequency content of the input and different displays were determined during the study. The describing function and remnant data indicate that humans can control as well with aural cues as with visual cues for the task considered. However, the reduction in operator time delays, expected because of the generally faster human response to aural stimuli, was not evident in the results. It was also determined that the operators could control equally well with either the one- or two-ear display.
Vinje, E. W.↗
Closed-loop, pilot/vehicle analysis of the approach and landing task
In the case of approach and landing, it is universally accepted that the pilot uses more than one vehicle response, or output, to close his control loops. Therefore, to model this task, a multi-loop analysis technique is required. The analysis problem has been in obtaining reasonable analytic estimates of the describing functions representing the pilot's loop compensation. Once these pilot describing functions are obtained, appropriate performance and workload metrics must then be developed for the landing task. The optimal control approach provides a powerful technique for obtaining the necessary describing functions, once the appropriate task objective is defined in terms of a quadratic objective function. An approach is presented through the use of a simple, reasonable objective function and model-based metrics to evaluate loop performance and pilot workload. The results of an analysis of the LAHOS (Landing and Approach of Higher Order Systems) study performed by R.E. Smith is also presented.
Anderson, M. R.↗
Measurement of driver/vehicle multiloop response properties with a single disturbance input
Multiloop response properties of controllers are, in general, very difficult to obtain because an independent forcing function is needed for each describing function to be measured, and interpolation procedures may be required to obtain intermediate describing functions at common frequencies. Two examples are provided for the measurement of driver/vehicle multiloop response properties using a single disturbance input. The validity of the procedure is based on current multiloop operator adjustment rules and is made plausible by comparison with experimental data.
Mcruer, D. T.↗
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.↗
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↗
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.↗
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.↗
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.↗
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.↗
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.↗
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.↗