Time-varying sliding mode control based finite-time prescribed performance function for robotic manipulators

Sliding mode control (SMC) is valued for its robustness and capacity to handle uncertainties in robot-manipulator applications that require precise tracking. However, it is limited by chattering, and starting far from the sliding surface can lead to extended reaching phases, compromising the global control efficacy and robustness. While Time-Varying Sliding Mode Surfaces (TVSMS) have been proposed to eliminate the reaching phase, they often suffer from sensitivity to initial conditions and parameter selection, limiting precise finite-time error convergence. Ensuring robustness during the reaching and sliding phases while achieving finite-time convergence from any initial position is a challenging task. This study presents a novel approach by integrating a Finite-Time Prescribed Performance Function (FTPPF) into a TVSMS design. The proposed TVSMS, based on FTPPF, ensures error convergence within a predetermined time frame, eliminates the reaching phase, and reduces sensitivity to initial conditions. Furthermore, the designed TVSMS addresses the weakness of robustness during the reaching phase of the Power Rate Reaching Law (PRRL) employed in the control law design, thereby mitigating the chattering problem of the SMC. Three FTPPFs with minimal parameter tuning are introduced, offering flexible transient response shaping, robustness, and improved error convergence compared to traditional TVSMS. The proposed Time-Varying Sliding-Mode Controller (TVSMC) not only simplifies control implementation but also significantly enhances robustness and resilience to external disturbances, making it a promising solution for high-precision robotic applications. Finite-time stability analysis is validated using the Lyapunov theorem, and experimental validation on the MICO 4-DOF robot demonstrates superior performance across various case studies compared to conventional methods.