Time-Delay Estimation in Nonlinear Systems: A Comparative Investigation of Control-Oriented Methods

Abstract

Time delay phenomena in nonlinear systems pose significant challenges in control engineering, particularly in industrial applications where system stability and performance are critical. This study presents a comprehensive comparative investigation of control-oriented time-delay estimation methods applied to nonlinear systems. The research methodology encompasses simulation-based analysis incorporating active disturbance rejection control (ADRC), proportional-integral-derivative (PID) controllers, and predictive extended state observer techniques. Three primary estimation methods were evaluated: sparse optimization algorithms, observer-based estimation techniques, and machine learning-based predictive approaches. The investigation utilized MATLAB/Simulink environment with nonlinear test systems featuring time-varying delays ranging from 0.1 to 2.5 seconds. Performance metrics included rise time, settling time, overshoot criteria, and integral of time-weighted absolute error (ITAE). Results demonstrate that TDE-ADRC methods achieve 25-40% improvement in transient response compared to conventional approaches. The sparse optimization algorithm showed superior accuracy in delay estimation with mean absolute error of 0.03 seconds. Machine learning-based methods exhibited robust performance under uncertainties, achieving stability margins of 15-20 dB. The study concludes that integrated TDE-ADRC approaches provide optimal balance between estimation accuracy and computational efficiency for industrial nonlinear systems. These findings contribute significantly to advancing control-oriented time delay estimation methodologies in complex engineering applications.