Abstract: An effective fractional order sliding mode control method is proposed for the nonlinear and uncertain robotic arm system by combining the advantages of the fractional calculus theory and the sliding mode control strategy. In the design of the controller, the fractional calculus is introduced into the sliding mode control by using the fractional order reaching law and the fractional order sliding mode control law respectively, and is proved by the Lyapunov theory to ensure the stability of the system. The proposed control method is applied to a two-joint robotic arm and is verified by the MATLAB simulation software. The results show that the proposed control strategy can effectively improve the tracking speed and tracking accuracy of the joints, and the controller is of good effectiveness and strong robustness.

Key words: robotic arm, fractional calculus, fractional order reaching law, sliding mode control, Lyapunov theory