Fractional Order Sliding Mode Control for Planar Flexible-Joint Robot 2-DOF Considering Parametric Uncertainty and External Disturbance

—This paper presents modelling and control for planar flexible-joint 2-DOF, an underactuated system. Thus designing to obtain stability of actuated joints and underactuated is a challenge for a control system. In the conventional sliding mode control method, the sliding surface is normally expressed based on the integer-order differentiation of the state variables. In the study, fractional order sliding mode control (FOSMC) algorithm is given, and then the sliding surface is designed by the fractional-order calculus,i.e, using fractional-order differentiation of the state variables. Thus, the fractional dimension accelerating the change rate of angle deviation is contained in the control output, which means that the control output of the FOSMC is sensitive to the change rate of angle deviation and provides a prompt control output for the system. From which, FOSMC based on Lyapunov theory and fractional calculus is proposed for the robot to achieve the global stability of two joints. The effectiveness and feasibility of the proposed method are demonstrated by MATLAB/SIMULINK simulation that the robot model considers parametric uncertainty and external disturbance.