Discrete-time sliding mode control with inverse hyperbolic sine reaching law

Discrete-time sliding mode control (DTSMC) is a popular control strategy used in applications like drones, aerospace, and automotive due to its robustness against parameter uncertainties and external disturbances. One of the crucial components of DTSMC is the reaching law, which governs the motion of the system towards the sliding surface. In this paper, a novel reaching law based on the inverse hyperbolic sine function is proposed. Initially, we examine the unperturbed (nominal) system case, followed by a subsequent scenario involving unidentified disturbances i.e. for the perturbed system. It is observed that the proposed reaching law not only decreases the control effort but also results in a smoother control input characterized by reduced chattering within a low quasi-sliding band. The simulation results show that the proposed reaching law outperforms the existing reaching law (seminal work of Gao et al.) in terms of both lower control effort and quasi-sliding mode band. Additionally, the proposed reaching law is compared with a similar class of reaching law i.e. with the hyperbolic tangent reaching law and the inverse tangent reaching law. The comparison results demonstrate superior performance in terms of robustness, further demonstrating the effectiveness of the proposed reaching law.