Robust H-infinity Takagi-Sugeno Fuzzy Controller Design for a Bilateral Tele-operation System via LMIs
AbstractThis 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.
 J.-P. Richard, “Time-delay systems: an overview of some recent advances and open problems”, Automatica 39(10):1667 – 1694 (2003).
 C. Lin, Q. G. Wang, T. H. Lee and Y. He,LMI “Approach to analysis and control of Takagi-Sugeno Fuzzy Systems with Time Delay”. Springer, 2007.
 R. J. Anderson and M. W. Spong, “Bilateral control of teleoperators with time delay”, IEEE Trans. Autom. Control 34(5):494-501 (1989).
 Elhajj, J. Tan, N. Xi, W.K. Fung, Y.H. Liu, T. Kaga and T. Fukuda, “Multi-site internet-based cooperative control of robotic operations”, in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems; Japan, 826–831 (2000).
 Munir S, Book W. “Internet-based teleoperation using wave variables with prediction”. IEEE/ASME Transactions on Mechatronics; 7(2):124-133 (2002).
 Ueda J, Yoshikawa T. “Force reflecting bilateral teleoperation with time delay by signal filtering”. IEEE Transactions on Robotics and Automation; 20(3):256-268 (2004).
 P. Arcara and C. Melchiorri, “Control schemes for teleoperation with time delay: A comparative study”, Robot. Autom. Syst. 38(1): 49-64 (2002).
 P. F. Hokayem and M. W. Spong, “Bilateral teleoperation. an historical survey”, Automatica, 42(12):2035-2057 (2006).
 F. Cuesta, A. Ollero, B.C. Arrue, R. Braunsting, “Intelligent control of nonholonomic mobile robots with fuzzy perception”. Fuzzy Sets and Systems 134:47–64 (2003).
 R. Lozano, N. Chopra and M. W. Spong, “Convergence Analysis of Bilateral Teleoperation with Constant Human Input”. in Proc. 2007 American Cont. Conf., Marriott Marquis Hotel at Times Square, New York City, USA, July 11-13 (2007).
 J.H. Park and H.C. Cho, “Sliding-mode controller for bilateral teleoperation systems with force reflection on the internet”. in Proc. IEEE/RSJ Int. Conf. Intelligent Robotics and Systems; Japan, 1187-1192 (2000).
 B. Widrow, E. Walach, Adaptive Inverse Control. Prentice-Hall: Upper Saddle River, NJ, (1996).
 J. Lam, H. Gao and C. wang, “Stability analysis for continuous systems with two additive time-varying delay components”, Syst. Cont. Lett. (2006), doi: 10.1016/j.sysconle.2006.07.005
 M. Boukhnifer and A. Ferreira, “wave-basedbpassive control for transparent micro-teleoperation system”, Robot. Autom. Syst. 54:601-615 (2006).
 E.A. Murakami, T. Yamada, T. kido and , K. Ito, “Performance evaluation of bilateral micro-teleoprated systems based on man-machine dynamic characteristics”, in: Proceeding of the International Conference on SICE, Osaka, Japan, 5-7 August, 2941-2946 (2002).
 PENBMI, a computer program for solving optimization problems : http://www.penopt.com.