Stability of teleoperation systems for time-varying delays by Lyapunov-Krasovskii and frequencial techniques

This work presents a stability analysis for an architecture for teleoperating a laboratory crane using haptic devices. The teleoperation scheme chosen is the 2-channel position error (PE) architecture. This scheme is modeled first by state-space equations testing that the system is Hurwitz stable for zero delay and calculating the maximum constant value of the delay h_max > 0 for which the nominal system (constant delay) is asymptotically stable. Then, by frequencial Laplace techniques, the delay system to be analyzed is transformed in such a way that it becomes a feedback interconnection of a linear time-invariant plant and a time-delay operator. In this way, we obtain the upper bound on the time-varying delay for each nominal value in the interval 0 < h ¿ h_max. Final discussions are provided regarding expected tracking capabilities and agreement of the theory and simulation results, which are satisfactory.