Time domain and time series models for human activity in compensatory tracking experiments, Ph.D. Thesis

Abstract

Analytical understanding of voluntary human behaviour while performing as an element of a closed-loop manual control situation has been sought since the 1940s. However, a total appreciation of human behaviour has been elusive and has been limited by the bewildering complexity of the situation itself and the capabilities of contemporary analytical tools. This work is an effort at modeling the human pilot by the time-domain and time-series approaches employing contemporary identification procedures. In this thesis, time-domain modeling of the human pilot activity in a compensatory tracking task has been performed using experimentally derived input-output data. The only a priori knowledge assumed has been that the pilot model belongs to the class of systems describable by linear discrete difference equation models excited either deterministically or stochastically. The linear models considered are the various special cases of the general discrete difference equation proposed by Åström. These special structures are derived by invoking some special properties of the parameters of Åström’s model. The various cases are studied in detail, some particular forms of which have already been proposed in the context of human pilot modeling in the literature. They are the impulse response model due to Taylor and Wingrove, the recent discrete parametric models by Stankovic and Koufenberg, and the time-series models by Shinners. The thesis considers the various versions of the Åström model from the point of view of a linear representation for the pilot, a pilot-induced noise structure, and their superposition. Four graded models are considered in particular:

A Noise-Free (NF) model structure where the pilot-induced noise is lumped at the output and the noise structure is additive in nature. This description is similar to the definition of a quasi-linear pilot model. A Least Squares (LS) model structure, where the noise is considered internal to the pilot. This noise structure is implicit in a least squares estimation problem, and the definition is contrived from that. An Autoregressive (AR) model structure where it is proposed that the pilot is actuated by an innovative noise, which is synthesized by the pilot from the observation of actual input. An Autoregressive Moving Average (ARMA) model structure where the AR model embeds a moving average feature at the output.

The AR and ARMA models proposed by the author in this thesis are time-series models, but are different from the one proposed by Shinners. The latter model is derived from the pilot input-output data, whereas the current models are synthesized from innovative reconstructed inputs. The identification and estimation problems associated with the various pilot structure postulates, given the input-output data, are considered. The identification of the model order is based on hypothesis testing and on the final prediction error method due to Akaike. The estimation of the pilot model parameters is performed by either single or two-stage least squares procedures of the one-shot type. The pilot models so obtained in the time domain are transformed to frequency domain descriptions for ease of comparison and quickness of analysis. The details of experimental facility, the experimentation, the choice of loop disturbance spectra, the data processing procedure, and the sampling methods with emphasis on sampling interval are discussed. Two types of compensatory tracking loop disturbances—viz., band-limited white noise and sinusoidal disturbances—are used with controlled plants of type K, K/s, and K/s(s+a). The white noise excited parametric pilot models are shown to possess frequency domain descriptions very similar in features to the quasi-linear describing function models. New AR and ARMA models generated entirely from the pilot output data are shown to exhibit features similar to the input-output based models such as NF and LS models. This paves the way to a new hypothesis that the human pilot activity is not a simple input-output activity, but an innovative process wherein the pilot generates an output based on the responses of the loop to his commands whose effects he observes at the actual input. Another major effort of the thesis has been to fill a gap in the knowledge on the performance of human pilots when exposed to sinusoidal input disturbance situations in compensatory tracking, when the controlled element has complex dynamics. It is singular that almost all the published data on pilot performance for periodic disturbances has been for the pure gain plant. For the first time, such data has been generated for a plant with dynamics of the type K/s(s+a). It is shown that the pilot performs at a lower level of perception than the normally expected level of pre-recognition when the plant is complex. In conclusion, parametric time-domain models postulated in this thesis not only explain certain well-known features of pilot behaviour, but also provide new insights into the pilot-adopted strategies in terms of his innovative actions. Furthermore, these new models, by virtue of their time-domain descriptions, readily lend themselves for usage in time-domain manual control studies.