Relative Degree Identification for Sliding Mode Controllers Design

In this paper, a novel approach to identify the relative degree of nonlinear uncertain single-input single-output systems is presented. The proposed approach can be profitably used to design sliding mode controllers even for systems with unknown relative degree. Assuming to measure only the output of the system and to apply a prescribed triangular input signal, we prove that a set of inequalities holds only for the r-th time derivative of the output, where r is the relative degree. A practical algorithm for the relative degree identification is also proposed. This makes use of the theoretical key-findings and relies on the use of successive higher order sliding mode differentiators. A numerical test case is discussed to show the effectiveness of the proposed scheme.