A Fast Reaching Law in Sliding Mode Control with Application to an Inverted Pendulum Robot

Sliding mode control (SMC) is an effective and robust technique for managing uncertain nonlinear systems. The conventional SMC approach integrates a constant-rate reaching law with the boundary layer method to regulate the system. However, it does not address scenarios in which the initial state variables are significantly distant from the boundary layer. To expedite the process of reaching the sliding surface, this study introduces a fast reaching law in SMC, ensuring a fixed control time for reaching the sliding mode surface. The proposed fast reaching law is applied to an inverted pendulum robot, demonstrating its effectiveness in this typical system. In addition, we propose a qualitative evaluation method to compare various existing reaching law methods. The simulation results indicate that the proposed reaching law outperforms current approaches, substantiating its effectiveness.