Higher order sliding: differentiation and black-box control

Sliding modes describe motions on discontinuity sets of dynamic systems and are provided by a persistent system switching with theoretically infinite frequency. The standard sliding modes are applicable to control output variables with relative degree 1. Having preserved or generalized the main properties of standard sliding mode, higher order sliding modes (HOSM) may be applied with any relative degree and, when properly used, totally remove the chattering effect. That allows full real-time control of the output variables, when only the relative degree of the dynamic system is known, and the system is actually considered as a “black box”. The HOSM controllers being based on the use of real-time higher-order output derivatives, robust exact differentiation becomes the key problem of the HOSM theory. Fortunately, the HOSM technique may also be applied to solve the differentiation problem. Differentiation usage in HOSM control is demonstrated by computer simulation of model and real-life examples