Design of a Finite-Time Sliding Mode Controller Algorithm for a Two-Axis Robotic Arm

This paper presents the design of a finite-time sliding mode control (FT-SMC) algorithm for a two-axis robotic arm, grounded in the principles of sliding mode control (SMC). SMC is a robust nonlinear control strategy known for its rapid response and has been extensively applied in robotic arm control. However, traditional SMC suffers from a convergence speed that is highly dependent on the initial system state; specifically, larger deviations from the sliding surface result in prolonged convergence times. To overcome this limitation, the FT-SMC approach introduces a novel sliding surface and a corresponding control law, enabling the system to reach the sliding surface within a predefined time frame and maintain motion along it thereafter. This study outlines a comprehensive methodology for designing a robotic arm controller based on FT-SMC. The dynamic model of the robotic arm is first derived using the Newton-Euler method, leading to the formulation of state-space equations that account for system uncertainties and external disturbances. A second-order differentiator based on SMC is then developed, with its parameters optimized for performance. A non-singular terminal sliding surface and an associated control law are subsequently constructed, and the Lyapunov stability theory is employed to ensure finite-time convergence to the sliding surface. Finally, the proposed FT-SMC algorithm is validated through comparative Simulink/SolidWorks simulation experiments against Second-Order Sliding Mode Control (SOSMC) and Proportional-Derivative (PD) control algorithms. The results demonstrate the algorithm’s superior effectiveness, achieving enhanced tracking accuracy and stability.