Discrete higher order sliding mode: concept to validation

A formal definition and design methodology for discrete-time higher-order sliding mode (DHOSM) based on finite difference method is proposed. A generalised reaching law is proposed to achieve r-order sliding mode in discrete time, and its behaviour and stability are analysed. The proposed reaching law is used to design a higher-order sliding mode control for an uncertain LTI system. The concept is experimentally validated on a real-time rectilinear plant and is compared with the existing algorithms on the basis of sensitivity function and alternatives tex-math notation=LaTeX$(p,q_{r})$tex-math(p,qr)alternatives>-continuity. The results and comparison show that the proposed sliding algorithm has superior disturbance rejection capability as well as better continuity. This work is the first attempt to formally define and design DHOSM as opposed to discretisation of continuous time higher-order sliding mode.