Time-varying identification of human effective time delay in manual control

Abstract

The identification of time-varying human operator (HO) dynamics is critical for advancing adaptive support systems in manual control tasks. This study evaluates the performance of Adaptive Model Selection (AMS), a framework extending recursive ARX identification methods, for estimating time-varying HO parameters, particularly effective time delay (τ(t)). Two configurations of AMS were tested: AMS_q, employing the z-domain ARX representation, and AMS_δ, utilizing the delta-domain ARX representation.

A Monte Carlo simulation framework was used to simulate a compensatory manual control task under varying conditions, including remnant noise (P_n) and dynamic transitions in system parameters. Stability and convergence rates of delay estimates were analyzed for different window sizes (W_s). Results show that the correlation between W_s and convergence time was linear and remained unaffected by remnant noise, demonstrating that window size is the primary determinant of responsiveness. Larger Ws improved stability but introduced tracking delays, whereas smaller W_s allowed for faster adaptation to dynamic changes at the cost of increased sensitivity to noise.

The comparative analysis between the configurations revealed a strong dependence of delay estimation accuracy on the precision of the natural frequency estimate of the neuromuscular system (NMS). The natural frequency estimation directly influences HO dynamic response modeling, and inaccuracies in this parameter propagate through the recursive identification process, affecting the reliability of delay estimates.

These findings underscore the critical role of window size and natural frequency estimation in determining the accuracy and stability of effective time delay estimation through AMS. This study provides a foundation for refining AMS to better balance stability and responsiveness in estimating time-varying HO dynamics. Such advancements can facilitate more accurate modeling of time-varying HO behavior, deepen understanding of HO adaptation, and contribute to the advancement of adaptive support systems.