Practical relative degree in SMC systems: Frequency domain approach

A variety of output regulation problems can be addressed via sliding mode control when system´s relative degree is known. The difficulties in the implementation of sliding mode controllers emerge when the relative degree is unknown. On the other hand, practical systems controlled by sliding mode algorithms always work under tolerance limits, which are frequently known. This behavior is called real sliding motion. In this work, the concept of practical relative degree in single-input-single-output systems controlled by sliding mode controllers is revisited from the view point of frequency analysis. Practical relative degree is understood as the smallest order of the sliding mode controller that satisfies the tolerance limits. Also, the notion of practical relative degree is analyzed in terms of the definitions of performance margins. The usefulness of the proposed concept is the way to design sliding mode controllers for systems that can be considered a black-box. The practical relative degree is studied and illustrated via examples and simulations.