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Investigation of Sampled Data Models of the Human Operator in a Control System

Report Number: ASD TDR 62-36
Author: Bekey, George A.
Corporate Author: California Univ Los Angeles
Laboratory: Flight Control Laboratory
Date of Publication: 1962-02
Pages: 358
Contract: AF 33(616)-7139
Project: 8225
Task: 822501
AD Number: AD0273347

The mathenmatical models most commonly used to represent the human operator in a closed-loop tracking system are linear differential equations whose parameters depend on the characteristics of both the input signal and the controlled process. This report presents an analytical and experimental study of a new class of human operator models which are based on discrete rather than continuous operations. While intermittent processes in human tracking have been hypothesized in the past, this research is the first systematic study of the implications of intermittency by means of the theory of sampled-data control systems. The resulting models are shown to be consistent with the large body of experimental evidence concerning tracking. For the inputs considered in this study, the outputs from the sampled-data models have certain characteristics which approximate experimental data more closely over a wider range of frequencies than those obtained from the quasi-linear continuous models.

Both analytical and experimental techniques are employed in the study. Systematic procedues for construction of the proposed sampled-data model are presented, beginning with the measurement of power spectra and cross-spectra of the system. The frequency characteristics of the sampled-data models with stationary random inputs are analyzed by means of z-transform techniques. Closed-form expressions are derived for computation of the power spectral density of the model output and error signals and the resultant values are compared both with data in the literature and with the experimental phase of the work. In addition to usind conventional zero-order and first-order "hold circuits" for reconstruction of sampled data, a "modified first-order hold circuit" is developed andd analyzed.

A prelminary analysis of transient response and stability of sampled data systems with variable sampling rates is presented, as an introduction to the study of adaptive sampled-data models.

An experimentalo program was designed to measure the power spectral density of the tracking error under a variety of conditions. Measurements were made using both analog and digital computer techniques. The results of the experimental program were used to compare with predicted values obtained by analysis. A second phase of the experimental program showed that use of intermittent displays yields results which are also consistent with the models proposed. The experimental work involved fairly extensive use of analog computer equipment and some novel techniques for simulation of sampled-data systems were explored.

The implications of the new sampled-data models for the design of man-machine systems are discussed and a number of suggestions for extensions of this work are presented.

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