Implicit and explicit discrete-time realizations of the robust exact filtering differentiator |
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| Institution: | 1. Department of Automatic Control, CINVESTAV, Jalisco, Mexico;2. LAMIH UMR CNRS 8201, Université Polytechnique Hauts-de-France, Valenciennes, France;3. Department of Mathematics and Physics, ITESO, Jalisco, México;1. College of Electrical Power and Engineering, Taiyuan University of Technology, 79 Yingze West Street, Taiyuan, China;2. Agricultural Bank of China Changzhi Branch, Changzhi, Shanxi, China;3. Department of Chemical Engineering, Chung-Yuan Christian University, Taoyuan, Taiwan, R.O.C.;4. School of Electrical and Electronic Engineering, University of Adelaide, Adealide SA, 5005, Australia;1. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, Liaoning, 110819, China;2. School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore;3. College of Sciences, Northeastern University, Shenyang, Liaoning, 110819, China;1. AnHui Province Key Laboratory of Special Heavy Load Robot and School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan 243032, China;2. School of Automation and Electrical Engineering, Linyi University, Linyi 276005, China;3. School of Information Science and Engineering, Chengdu University, Chengdu, 610106, PR China;1. Faculty of Information Engineering, Guangdong University of Technology, Guangzhou, 510006, China |
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| 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. |
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