A Robust LMI-Based Stabilizing Control Method for Bilateral Teleoperation Systems

Abstract

This paper introduces a novel structure to design a robust PID controller based on a Linear Matrix Inequality (LMI) approach. The objectives of the controller establishment are to achieve complete transparency and robust stability despite the large time-delay of communication channels and uncertainty in various parts of a teleoperation system. In this structure two local controllers must be implemented by applying an LMI-based H∞ theory. One of these controllers is responsible for tracking the master position in the remote site which is called slave controller. The slave controller is a novel robust PID controller which is implemented by employing an LMI-based H∞ framework. Furthermore, the other one controller called master controller is in charge of force tracking as well as guaranteeing stability of the closed-loop system and it requires to be established by applying an LMI-based multiobjective H2/H∞ method. Finding optimal values for the parameters of the controllers can be ensured by applying the convex optimization method in both sites. As it can be seen from the simulation results, the proposed control method is highly effective in providing a stable transparent teleoperation system under uncertain, but bounded, time-delay in communication channel and task environment. Since the simulation results illustrates time responses of the system for nominal values of the parameters, μ-analysis has been used to investigate stability of the overall system in spite of changes in the parameters of the master and/or slave manipulators in modified range.