Design of the second‐order robust exact differentiator: A describing function approach

Abstract

AbstractThe paper proposes a design methodology for the second‐order robust exact differentiator in the presence of small time‐delays characterizing the time of signal processing. With this aim, the describing function is used to provide several sets of the gains ensuring high accuracy in the reconstruction of the first‐order derivative of smooth signals, that is, minimizing the main harmonic of chattering. The proposal fulfills the Loeb's criterion: if self‐excited oscillations appear in the trajectories of the delayed differentiator, they are orbital and asymptotically stable. Besides the global finite‐time stability of the error is proved for the non‐delayed differentiator under such gains settings by using a homogeneous Lyapunov function. Numerical examples are provided to illustrate the results.