Second Order Sliding Mode Control for Robot Arms with Time Base Generators for Finite-Time Tracking

A novel chattering-free dynamic sliding mode controller for a class of uncertain mechanical systems is proposed in order to account globally for a time-varying sliding regime for all time and for any initial condition. The new sliding surface, parametrized by a time base generator, plays the role of moving, and rotating continuously the nominal sliding surface, while shifting is done through a known, state-independent, vanishing vector to eliminate the reaching phase for any initial condition, a weaker assumption in comparison to some moving sliding surface designs. In this way, the closed-loop system yields finite-time convergence of tracking errors, whose convergence time can be fixed independently of initial conditions, in contrast to terminal sliding mode wherein convergence time depends on initial conditions. To implement the controller, the upper bound of the derivative of the sliding surface is required, a weaker assumption in contrast to some dynamic sliding mode controllers. The performance of the closed-loop system is visualized through simulation.