Premium
Nonlinear observer design for two‐time‐scale systems
Author(s) -
Duan Zhaoyang,
Kravaris Costas
Publication year - 2020
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.16956
Subject(s) - observer (physics) , nonlinear system , control theory (sociology) , computer science , convergence (economics) , mathematics , state observer , separation principle , manifold (fluid mechanics) , engineering , artificial intelligence , physics , control (management) , quantum mechanics , economics , economic growth , mechanical engineering
A two‐time‐scale system involves both fast and slow dynamics. This article studies observer design for general nonlinear two‐time‐scale systems and presents two alternative nonlinear observer design approaches, one full‐order and one reduced‐order. The full‐order observer is designed by following a scheme to systematically select design parameters, so that the fast and slow observer dynamics are assigned to estimate the corresponding system modes. The reduced‐order observer is derived based on a lower dimensional model to reconstruct the slow states, along with the algebraic slow‐motion invariant manifold function to reconstruct the fast states. Through an error analysis, it is shown that the reduced‐order observer is capable of providing accurate estimation of the states for the detailed system with an exponentially decaying estimation error. In the last part of the article, the two proposed observers are designed for an anaerobic digestion process, as an illustrative example to evaluate their performance and convergence properties.