A global asymptotic stable variable structure algorithm using sliding mode observer

A global asymptotic stable variable structure control algorithm is proposed using the sliding mode observer with only joint-position measurement. Due to the uncertainty of the system´s parameters and states, interactions between the observer and controller occur. With respect to these interactions, a theorem is presented showing that the state estimation errors are limited with upper boundary limits. A second theorem shows that the sliding error tends to zero in the sense of global asymptotic stability. Total tracking errors are equivalent to the estimation errors. The nonlinear sliding area is suggested as a substitute for the classical sliding surface in order to improve convergence and control accuracy. Simulation and experimental results obtained on the JTR-1 manipulator illustrate the effectiveness and robustness of the algorithm