Asymptotic Estimation of State, Fault and Perturbation for Nonlinear Systems and Its Fault-tolerant Control Application
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Asymptotic Estimation of State, Fault and Perturbation for Nonlinear Systems and Its Fault-tolerant Control Application Jianglin Lan* and Ron Patton Abstract: This paper addresses the challenge of robust simultaneous estimation of state and actuator faults for Lipschitz nonlinear systems with unknown perturbations acting on both the state dynamics and output measurements. The existing methods enhance the estimation robustness by suppressing the perturbations or decoupling them under satisfaction of the matching condition. This work considers a total elimination of the perturbation effects through perturbation reconstruction. An adaptive sliding mode unknown input observer (ASMUIO) is developed to realize simultaneous asymptotic estimation of the state, faults and perturbations. It leverages a descriptor system reformulation of the original system by regarding partial perturbations as virtual state and the rest part as virtual faults. The proposed ASMUIO has feasibility guarantee and is solved via a linear matrix inequality (LMI) setting. Based on the ASMUIO, an adaptive backstepping fault-tolerant control (FTC) is further designed to achieve good tracking performance. The design efficacy is illustrated through comparative simulations of the proposed method against representative methods in the literature. Keywords: Fault estimation, fault-tolerant control, linear matrix inequality, perturbation.
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INTRODUCTION
Fault diagnosis is fundamental for active fault-tolerant control (FTC) by providing information of fault occurrence, location and magnitude [1]. The traditional fault diagnosis scheme, fault detection and isolation (FDI), involves the procedure of detection, isolation and, in some cases, estimation, subject to robust optimal designs of residual and threshold. This work considers an alternative diagnosis scheme, observer-based fault estimation (FE), which directly reconstruct the fault signals. Existing studies have shown effectiveness of the FE scheme in obtaining fault estimates that can be used for fault compensation in the active FTC systems. Multiple FE methods have been developed using state observers, e.g., sliding mode observers (SMOs) [2–4], adaptive observer [5], extended state observer [6, 7], intermediate estimator [8], and augmented state unknown input observer [9, 10]. Using state observers for FE also generates state estimation that is important for control designs [11–13]. The FE designs are effective unless having good robustness to system perturbations, including external disturbance and/or system uncertainty affecting the state dynamics and/or output measurements [10, 14]. The FE robustness can be improved using three approaches: (i) At-
tenuation approach, which suppresses the perturbations by using H∞ optimization [6, 7, 10, 15] or adaptive design [5]. (ii) Decoupling approach, which removes the perturbation from the estimation error dynamics provided that the perturbation distribution matrix satisfies a certain rank condit
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