In this paper, a time-varying nonsingular terminal sliding mode (T-NTSM) controller is proposed and modified for the rigid robot manipulators with parametric uncertainties and external disturbances. First, in order to eliminate the reaching phase, a novel T-NTSM manifold is proposed by incorporating a piecewise defined function of time into a nonsingular terminal sliding mode manifold. Then a T-NTSM controller is derived from such a sliding surface, by which the robustness is ensured during the entire response of the system, and the convergence time can be chosen in advance. An especially effective method is provided for parameter selection to meet the convergence time requirement. Subsequently, a modified T-NTSM controller is proposed to enhance performance by introducing a time-varying gain in the proposed T-NTSM manifold. The modified controller ensures faster convergence rate and smaller control input amplitude. Finally, the proposed controllers are applied in the control of a two-link manipulator. All of the simulation results demonstrate the effectiveness of the proposed control methods.

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The attitude control for reentry vehicle is responsible for the robust operation to avoid the major deterioration from parametric uncertainties and external disturbances. Targeting these practical issues, both the cases with and without a priori knowledge of upper bound on the lumped uncertainty (i.e. the joint effect caused by external disturbance and inertia matrix uncertainty) are addressed, and correspondingly two continuous time-varying sliding mode based attitude controller design strategies are proposed to achieve the robust tracking of the attitude commands while alleviating the control chattering. Firstly, to deal with the case where the upper bound on the second derivative of the lumped uncertainty is known in advance, a nonlinear disturbance observer based continuous time-varying sliding mode control algorithm is developed so that the asymptotic stability of the closed system is guaranteed. Furthermore, in order to address the more practical case that the upper bound on the lumped uncertainty is unavailable, a continuous adaptive time-varying sliding mode control algorithm is derived with the related switching gains adjusted on-line, by which the trajectories of the closed-loop system are guaranteed to be uniformly ultimately bounded. Finally, the proposed strategies are applied to the attitude control of X-33 RLV in the reentry phase to illustrate the effectiveness of the theoretical results.

Purpose -The purpose of this paper is to design a global robust and continuous control scheme for the attitude tracking control problem of the reentry vehicle with parameter uncertainties and disturbances. Design/methodology/approach -First, feedback linearization is applied to the model of reentry vehicle, resulting in three independent uncertain subsystems. Then a new second-order time-varying sliding function is proposed, based on which a continuous second-order time-varying sliding mode control (SOTVSMC) law is proposed for each subsystem. The global robustness and convergence performance of the closed-loop reentry vehicle control system under the proposed control law are proved. Findings -Simulation is made for a reentry vehicle through the assumption that there is external disturbance to aerodynamic moment and the aerodynamic parameters as well as the atmospheric density are perturbed. The results verify the validity and robustness of the proposed strategy. Originality/value -The SOTVSMC attitude controller based on feedback linearization is proposed for the reentry vehicle. The advantages of the proposed SOTVSMC are twofold. First, the global second order sliding mode is established, which implies that the closed-loop system is global robust against matched parameter uncertainties and disturbances in reentry. Second, the chattering problem is significantly alleviated.