Fixed-Time Nonsingular Terminal Sliding Mode Control with Compound Sliding Surface

A nonsingular terminal sliding mode (NTSM) control scheme with fixed-time convergence is proposed for a class of second-order nonlinear systems subject to matched uncertainties and external disturbances. A compound sliding surface is firstly constructed to eliminate the singularity and the upper bound of convergence time is estimated. A fixed-time NTSM controller is then developed and a guaranteed upper bound of the closed-loop settling time independent of initial states is presented based on the phase plane analysis and Lyapunov stability theory. Finally, a lot of simulations for a single inverted pendulum system are conducted to validate the effectiveness of the proposed methodology.