Accommodative Convergence - An Adaptive Nonlinear Control System

Abstract

Accommodative convergence of the eyes relates to reflex convergence when the lens accommodates for distance. The system has been studied in both frequency and time domains by providing sinusoidal and pulse stimuli of target distance from the eye and measuring the degree of convergence as output. Both predictable single sinusoidal and nonpredictable multiple sinusoidal data are obtained and related to subject experience in tracking. The results for single sinusoidal input at varying input amplitudes show the system to behave as if it contained a nomemory nonlinearity. Open loop single sinusoidal data was measured directly and compared with open loop Bode plots theoretically derived from the closed loop data. Instability oscillations are demonstrated and their frequency is predicted by the open loop data. A mathematical model to describe the data is derived. The adaptive nature of the system is discussed and evidence is given for a prediction operator as an input adaptive feature. The instability oscillations are shown to occur in those situations in which one might predict small signals to be produced by an initial error sensing element in the system. It is suggested that one type of adaptive function is to vary the gain of the controller or error correcting portion of the system and hence the total open loop gain. When situations then arise that markedly increase open loop gain, instability oscillations result. Finally, the system is shown to behave as if it were not a sampled data system, but rather operates on data flow continuously.