Time-varying sliding-mode control for finite-time convergence

This paper proposes a time-varying sliding-mode control scheme, in which a piecewise defined function of time that contains trigonometric functions is incorporated into the switching function not only to eliminate the reaching phase, but also to guarantee finite-time convergence of the tracking error. Without using fractional-power functions of certain state variable, the proposed control is both free from singularity around the equilibrium and also convenient for practical implementation. Moreover, the proposed scheme has the terminal time as an explicit parameter, which makes the controller design simple to meet the terminal-time requirement. Experiments were conducted on a two-link direct-drive manipulator to demonstrate the effectiveness of the proposed scheme.