Title: Design of novel observers for robust fault detection in discrete-time Lipschitz non-linear systems with Euler-approximate models

Authors: Qingxian Jia; Yingchun Zhang; Wen Chen; Yunhai Geng

Addresses: Research Center of Satellite Technology, Harbin Institute of Technology, Harbin, 150001, China ' Research Center of Satellite Technology, Harbin Institute of Technology, Harbin, 150001, China ' Division of Engineering Technology, Wayne State University, Detroit, MI 48202, USA ' Research Center of Satellite Technology, Harbin Institute of Technology, Harbin, 150001, China

Abstract: This paper addresses the problem of observer-based robust fault detection in a class of Lipschitz non-linear systems. A Euler-approximate model for continuous-time Lipschitz non-linear systems is first established; then, a discrete time non-linear observer is designed such that the dynamic output-estimation error, which is assigned as a residual signal, asymptotically converges to zero if no actuator faults and external disturbances exist in the system. The new observer has similarity to a non-linear unknown input observer (UIO). Compared with the existing UIOs, the design of the presented observer requires fewer gain matrices and equation constraints; less computation load is therefore needed. On the other hand, the new observer is designed based on the Euler-approximate model. To ensure its implementation on the exact model, sufficient conditions for semiglobal practical convergence of the proposed observer are explicitly provided. With external disturbances, a nonlinear H_∞ observer is constructed to achieve robust actuator fault detection. Observer design problem can be systematically solved using linear matrix inequality (LMI)-based optimisation technique. Lastly, a single-link flexible robot is employed to illustrate the effectiveness of the proposed observer-based FD scheme.

Keywords: actuator fault detection; nonlinear unknown-input observers; observer design; linear matrix inequality; LMI; Lipschitz nonlinear systems; Euler approximate models; discrete-time systems; flexible robots; robot actuators.

DOI: 10.1504/IJAAC.2014.064160

International Journal of Automation and Control, 2014 Vol.8 No.3, pp.191 - 210

Received: 10 Mar 2014
Accepted: 29 Mar 2014
Published online: 28 Aug 2014 *

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