VARIABLE-STRUCTURE CONTROL OF ROBOT MANIPULATORS WITH NONLINEAR SLIDING MANIFOLDS

Performance characteristics of a sliding mode controller depend essent ially on a selected sliding manifold. Customarily, the variable-struct ure controllers operate with linear sliding surfaces. However, using n onlinear or time-varying manifolds may provide definite advantages; in particular, they may provide faster convergence. In this paper, a con trol algorithm is presented which guarantees the occurrence of the sli ding mode on nonlinear or time-varying manifolds. The bounds needed fo r calculating the switching gains are determined in terms of parameter variations rather than bounds on the system matrices. The parameter b ounds are usually evident and can be easily established or estimated, while matrix bounds can rarely be justified in practical problems. In this paper, we also present an adaptive version of the controller, whi ch provides an automatic estimation of the parameter bounds. The robus tness of the controller with respect to a class of state-dependent unc ertainties is analysed by the Lyapunov method. Application of the deve loped theory is illustrated by an example of robotic manipulator contr ol with a nonlinear sliding manifold.