A Novel Model-Free Continuous Sliding Mode Controller with a PI Sliding Surface for Industrial Robots: Achieving Near-Zero Tracking Errors and GUUB Stability

Document Type : Original Article

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Mechanical Design and Production Engineering Department, Zagazig University, Zagazig 44519, Egypt.

Abstract

This study presents a novel continuous sliding mode control (SMC) law for robotic arms, emphasizing computational efficiency, structural simplicity, and stability. The proposed controller, which does not require the robot's dynamic model in its structure, ensures Global Uniform Ultimate Bounded (GUUB) stability, focusing on minimizing joint tracking errors. To enhance tracking performance, the control law incorporates a nonlinear function that increases control effort only within the boundary layer, effectively reducing the ultimate bounds of tracking errors. Stability is demonstrated using Lyapunov theory, confirming the asymptotic convergence of tracking errors to near zero. Further improvement is achieved by replacing the original sliding surface with a proportional-integral (PI) sliding surface. This PI-based sliding mode controller maintains GUUB stability while delivering superior tracking accuracy, as evidenced by near-zero ultimate bounds of tracking errors. Simulation results with a two degrees of freedom manipulator validate the controllers' effectiveness in handling disturbances, with the enhanced PI-based controller showing superior performance, nearly eliminating tracking errors.

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The Egyptian International Journal of Engineering Sciences and Technology
Volume 51, Issue 2
September 2025
Pages 53-63

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