Robust H-infinity Takagi-Sugeno Fuzzy Controller Design for a Bilateral Tele-operation System via LMIs

This paper presents a new approach to a robust fuzzy controller design for the bilateral teleportation system with varying time delays using linear matrix inequalities. Communication channels are considered with different forwarding and returning time delays. The time delays of communication channels are assumed to be unknown and randomly time varying, but the upper bounds of the delay interval and the derivative of the delay are assumed to be known. In order to design the controllers, first, an impedance controller is designed for the master system to achieve desired impedance behavior for the master. Then, nonlinear Euler-Lagrange equation of motion of the slave system is linearized in the neighborhood of some operating points. In the sequel, an open-loop scheme is considered for the slave system. The linear model of the slave system has two imaginary/unstable poles. The slave system is stabilized by a PD-controller to be used in the open-loop scheme. To design the slave controller, the tele-operator block diagram is rearranged such that the tele-operator block diagram converts to a standard representation of a feedback control system which helps us to design a robust H-infinity controller for the slave system. The local linear models of the system are combined to form a Takagi-Sugeno fuzzy model of the whole tele-operation system. A Lyapunov-Krasovskii function is defined to analyze the closed-loop system’s stability and derive a sufficient delay-dependent stability criterion. An H-infinity performance index is defined and the design criteria for the slave controller are expressed as a set of LMIs, which can be tested readily using standard numerical software.