Non unique equivalent control in sliding mode with linear surfaces

This paper presents a new formulation for “Equivalent Control” used in sliding mode control. Although in literature there exist a unique equivalent control for a given system and linear sliding surface, it is shown that the equivalent control can be non unique. Further this flexibility in equivalent control is used to obtain the sliding mode control for specific needs such as actuator saturation, faster reaching without increasing chattering, confining the sliding mode in a specified sector and simple second order sliding mode control design.