Adaptive Controller Design Based On Predicted Time-delay for Teleoperation Systems Using Lambert W function

This study develops an approach of controller design, on the basis of Lambert W function structure for Internet-based bilateral teleoperation systems. Actually, time-delay terms in bilateral teleoperation systems lead to an infinite number of characteristic equation roots making difficulty in analysis of systems by classical methods. As delay differential equations (DDEs) have infinite eigenspectrums, all closed-loop eigenvalues are not feasible to locate in desired positions by using classical control methods. Therefore, this study suggests a new feedback controller for assignment of eigenvalues, in compliance with Lambert W function. In this regard, an adaptive controller is accurately employed in order to provide the controller with updated predicted time-delay and robust the system against the time-delay. This novel control approach causes the rightmost eigenvalues to locate exactly in desired positions in the stable left hand of the imaginary axis. The simulation results show strong and robust closed-loop performance and better tracking in constant and time-varying delay.