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Describing functions to analyze feedback control systems containing nonlinearities of dead zone and backlash
Describing function for analysis of feedback control systems with time-invariant nonlinear elements, simplifying derivation by taking derivative of output of nonlinear element with respect to input
Describing functions for stability analysis of integral pulse frequency modulated unity feedback closed loop system
Measurement of pilot describing functions in single controller multiloop tasks
Pilot describing functions measurement and error reduction in flight test data with example from Gemini 10
The automobile-driver describing function for lateral position control was estimated for three subjects from frequency response analysis of straight road test results. The measurement procedure employed an instrumented full size sedan with known steering response characteristics, and equipped with a lateral lane position measuring device based on video detection of white stripe lane markings. Forcing functions were inserted through a servo driven double steering wheel coupling the driver to the steering system proper. Random appearing, Gaussian, and transient time functions were used. The quasi-linear models fitted to the random appearing input frequency response characterized the driver as compensating for lateral position error in a proportional, derivative, and integral manner. Similar parameters were fitted to the Gabor transformed frequency response of the driver to transient functions. A fourth term corresponding to response to lateral acceleration was determined by matching the time response histories of the model to the experimental results. The time histories show evidence of pulse-like nonlinear behavior during extended response to step transients which appear as high frequency remnant power.
Describing-function analysis of launch vehicle stability with nonlinear thrust vectoring
Modified fast Fourier transform for hybrid computer program data processing of human operator describing functions
Evaluation of pilot describing function method applied to manual control analysis of large flexible booster in Saturn 5 launch vehicle simulator
Error reduction in identifying pilot describing function from flight test data by shifting input signal by pilot delay time in simulated computer model
Three types of manual control maneuvers conducted during the Gemini-10 mission have been analyzed in order to measure and document the describing function of the pilot, the vehicle and the pilot-vehicle combination during an actual space mission. Measurements made from the data records of the reentry maneuver (a single axis control task) indicate that the pilot's control behavior changes during critical portions of the reentry. Measurements made of the deorbit maneuver and of a terminal phase initiation maneuver (three axis tasks) show that the pilot assigns priorities to the separate axes and controls them differently. His control technique is also influenced by the magnitude of the thrust disturbance present during the maneuvers. The results for all three types of maneuvers show that the pilot adapts to the nonlinear spacecraft control system in such a way that the combined pilot-vehicle dynamics take the form of the linear crossover model.
An analytical study was made of an automatic reaction-control system for the upper stages of a missile to determine limit cycle characteristics, corresponding duty cycles, and the effects of the various system parameters on these quantities. A nonlinear servo analysis (describing function) technique was used to obtain a mathematical representation of the nonlinear components of the system. The results obtained by this analysis are compared with the results obtained from an analog simulation including the jet reaction-control hardware. The good agreement between the results of the two studies tends to indicate the feasibility of using such an analysis technique in the early design phase of a reaction-control system, since by so doing, the parameters for good system performance can be determined quite readily.
As part of a program to develop a comprehensive theory of manual control displays, six display formats were used by three instrument-rated pilots to regulate against random disturbances with a controlled element under both foveal and 10 deg parafoveal viewing conditions. The six display formats were: CRT line, CRT thermometer bar, 14-bar quantized on a CRT, a rotary dial and pointer, and two variations of a moving scale tape-drive. All were scaled to equivalent movement and apparent brightness. Measures included overall performance, describing functions, error remnant power spectra, critical instability scores, and subjective display ratings. The results show that the main effect of display format is on the loop closure properties. Less desirable displays induce lower bandwidth closures with consequent effects on the closed-loop remnant and performance.
Predicted results of a simulation of the pilot's approach control strategy in the presence of pilot remnant are presented. The aircraft dynamics and the turbulence environment are representative of a trainer-type aircraft. The non-intrusive pilot identification program (NIPIP) was used to identify the pilot's control strategy required by this highly-coupled, multiloop control task. The results are presented in terms of frequency responses of the individual elements of the pilot's control strategy and indicate that NIPIP can identify the pilot's describing functions even in the presence of significant amounts of pilot remnant.
The dynamic equations and the mathematical model of the continuous-data IPS control system are developed. The IPS model considered included one flexible body mode and was hardmounted to the Orbiter/Pallet. The model contains equations describing a torque feed-forward loop (using accelerometers as inputs) which will aid in reducing the pointing errors caused by Orbiter disturbances.
Nonlinear control system, discussing method to obtain estimate of region of stable initial conditions
Crossover models and optimal control theory for obtaining pilot performance data
Feasibility and reliability analysis in use of pilots to guide and control launch vehicles of Saturn 5 class