Stability of Teleoperation Systems for Time-Varying Delays by Neutral LMI Techniques

This paper investigates the delay-dependent stability of a teleoperation system based on the transparent Generalized Four-Channel control (G-4C) scheme under time-varying communication delays. To address stability we choose here a primitive result providing a Linear Matrix Inequalities (LMIs) approach based on Lyapunov-Krasovskii functionals. Firstly, the scheme is modeled as the neutral-type differential-delayed equation; that is, the delay affects not only the state but also the state derivative. Secondly, we apply a less conservative stability criteria based on LMIs that are delay dependent and delay's time-derivative dependent. The reason is that, for better performance in the case of small delays, we must accept the possibility that stability is lost for large delays. The approach is applied to an example, and its advantages are discussed. As a result, we propose to modify the values of standard controllers in G-4C defining the μ-4C scheme, which introduces a tuning factor μ to increase in practical conditions the stable region fixing the desired bounds on time-varying delay, with the particularity of maintaining the tracking properties provided by this transparent control scheme. The simulation results justify the proposed control architecture and confirm robust stability and performance

Four-Channel Teleoperation with Time-Varying Delays and Disturbance Observers

This paper addresses the robust stability of teleoperated systems under the four-channel architecture, affected by time-varying communication delays and using disturbance observers. It is based on our previous work which provides a framework for robust stability against delays with bounded variation and a bounded time-derivative, using structured singular values (SSV). The main new feature here is the inclusion of disturbance observers (DOBs). The DOB concept is well-documented and relevant to many applications, since only position (but not force) measurements are usually available. In this paper, we adapt two DOBs (master and slave) to our generic framework, by representing them as stable, fast filters affected by the uncertainty in the plant modelling. Our main result is an SSV test to verify robust stability. The simulation results confirm the usefulness of this approach