Delay and its time-derivative dependent Stability of teleoperation systems

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 force-force (FF) architecture. This scheme is modeled first by state-space equations testing that the system is Hurwitz stable for zero delay and verifying the Schur-Cohn stability of the matrix C, a necessary and sufficient stability condition for the neutral-type system. Then, by frequencial Laplace techniques, the 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. This let us apply delay-dependent stability conditions as a function of the upper bounds on the time-varying delay magnitude and variation, that are treated in the integral quadratic constraint (IQC) framework. Final discussions are provided regarding expected tracking capabilities and agreement of the theory and simulation results, which are satisfactory.