An Observer-Based Fixed Time Sliding Mode Controller for a Class of Second-Order Nonlinear Systems and Its Application to Robot Manipulators

An observer-based fixed-time sliding mode controller for a class of second-order nonlinear systems under matched uncertainties and disturbances is proposed and applied to robot manipulators in this paper. To begin with, a fixed-time disturbance observer (FxDO) based on a uniform robust exact differentiator (URED) proactively addresses external disturbances and uncertain terms. As a result of the designed observer, uncertain terms can be precisely approximated within a fixed time and contribute to reducing the chattering and improving the tracking performance of traditional sliding mode controllers. Secondly, on the basis of phase plane analysis and Lyapunov theory, we construct a modified fixed-time non-singular terminal sliding surface as well as a guaranteed closed-loop convergence time independent of initial states. Consequently, an observer-based fixed-time sliding mode controller was developed based on the combination of a designed fixed-time disturbance observer and a fixed-time sliding mode method. Finally, the proposed controller is applied to a 3-DOF FARA robot manipulator to demonstrate its effectiveness.