A New Exponential Reaching Law Approach to the Sliding Mode Control: A Multilevel Multifunction Converter Application

This article presents a new exponential reaching law (ERL) approach for the sliding mode control. Contrary to the existing reaching law methods, the proposed ERL does not employ a sign function and yields a faster reaching time. An expression of reaching time in terms of reaching law gains is derived analytically. The article will show that the reaching time to the sliding surface is very small provided that the gains are selected properly. The stability of the proposed reaching law will be proven. The proposed reaching law with sliding mode control is employed to control a 5-kW three-phase multilevel multifunction converter. It is shown that the system can operate as a rectifier, as a shunt active power filter (SAPF) or as a combination of both rectifier and SAPF simultaneously. Experimental results corresponding to each operation mode are presented to confirm the efficacy of the proposed reaching law under fast-changing nonlinear load currents.