Variable structure control of robot manipulators with nonlinear sliding manifolds

Abstract

Performance characteristics of a sliding mode controller depend essentially on a selected sliding manifold. Customarily, the variable-structure controllers operate with linear sliding surfaces. However, using nonlinear or time-varying manifolds may provide definite advantages; in particular, they may provide faster convergence. In this paper, a control algorithm is presented which guarantees the occurrence of the sliding mode on nonlinear or time-varying manifolds. The bounds needed for calculating the switching gains are determined in terms of parameter variations rather than bounds on the system matrices. The parameter bounds 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, which provides an automatic estimation of the parameter bounds. The robustness of the controller with respect to a class of state-dependent uncertainties is analysed by the Lyapunov method. Application of the developed theory is illustrated by an example of robotic manipulator control with a nonlinear sliding manifold.