Fixed-time Sliding Mode Control for a class of Second-order Perturbed systems with applications to Quadrotor and Robot Manipulator

Fixed-time convergence has recently gained much attention in the research community. Interest in Fixed-time control is because such techniques offer uniform boundedness on the settling time. In this paper, we propose a novel Fixed-time Sliding Mode Control (FxtSMC) scheme for a class of nonlinear second-order systems under matched disturbances. The design provides a fast convergence due to the purposeful addition of specific non-linear terms in the switching manifold. The control law proposed is continuous and free from singularity. Lyapunov method augmented with homogeneous system theory is employed to prove closed-loop stability and establish fixed-time convergence of states. Simulations illustrate the theoretical claims and highlight the efficacy control allocation. Further, the applicability of the proposed FxtSMC in robotic systems is tested for trajectory tracking application of quadrotor and 2-DOF robot manipulator. Results show that the design indeed offers a robust, chatter-free, high-precision fixed-time tracking performance.