This paper proposes a robust supertwisting algorithm (STA) design for nonlinear systems where both matched and unmatched uncertainties are considered. The main contributions reside primarily to conceive a novel structure of STA, in order to ensure the desired performance of the uncertain nonlinear system. The modified algorithm is formed of double closed-loop feedback, in which two linear terms are added to the classical STA. In addition, an integral sliding mode switching surface is proposed to construct the attractiveness and reachability of sliding mode. Sufficient conditions are derived to guarantee the exact differentiation stability in finite time based on Lyapunov function theory. Finally, a comparative study for a variable-length pendulum system illustrates the robustness and the effectiveness of the proposed approach compared to other STA schemes.

The purpose of this study is to present a new robust sliding mode control design for nonlinear systems where both matched and unmatched uncertainties are considered. The proposed controller strategy is composed of two components: the integral sliding mode control and the optimal feedback control law. Moreover, an integral sliding mode surface in integral type is developed to construct the reachability of sliding mode using the Lyapunov functions method. The main advantages of the proposed approach are ensuring the robustness throughout the whole system response against the uncertainties, decrease the chattering effect and eliminate the reaching phase. Finally, the validity of the proposed design strategy is demonstrated through the simulation of a flexible joint robot.

This paper deals with the modeling and the control of a parallel robot with six degree of freedom (dof). The mathematical model of the 6-DOF parallel manipulator includes dynamics model which is on the Lagrange method. The model is built in generalized coordinate system. The kinematics model is based on the closed-form solutions. The latter has six electric actuators at six legs. The model-based controller is presented with feedback of platform positions. Two control laws of the actuators positions of the robot are proposed: PID control and Sliding Mode Control (SMC). Simulation results are given to show the comparison performance in term of robustness.

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