Implicit and explicit discrete-time realizations of the robust exact filtering differentiator. Issue 8 (May 2022)

• Record Type: Journal Article
• Authors: Carvajal-Rubio, J.E.; Defoort, M.; Sánchez-Torres, J.D.; Djemai, M.; Loukianov, A.G.
• Is Part Of: Journal of the Franklin Institute. Volume 359:Issue 8(2022)
• Page Start: 3951
• Page End: 3978
• Publication Date: 2022-05
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2022.03.007
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: This paper presents explicit and implicit discrete-time realizations for the robust exact filtering differentiator, aiming to facilitate an adequate posterior implementation structure in digital devices. This paper firstly presents an analysis of an explicit discrete-time realization of the filtering differentiator based on linear systems' exact discretization with a zero-order holder. For this case, however, high-order terms in the filter dynamics may cause instability of the estimation error for signals with unbounded derivatives. Hence, two other new discrete-time realizations of the filtering differentiator are derived by removing some high-order terms in the filter dynamics. The first one is an explicit discrete-time realization, while the second one is implicit. After a finite time, both preserve the accuracy of the continuous-time robust exact filtering differentiator in the presence of measurement noise. For each proposed discrete-time scheme, a stability analysis based on homogeneity is provided. Finally, the simulation results include comparisons between the proposed implicit and explicit discrete-time realizations with other existing schemes. These numerical studies highlight that the implicit scheme supersedes the explicit one, consistent with the implicit and explicit realizations of other continuous-time algorithms.