Robust Fault Tolerant Control Design for Nonlinear Systems not Satisfying Matching and Minimum Phase Conditions
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Robust Fault Tolerant Control Design for Nonlinear Systems not Satisfying Matching and Minimum Phase Conditions Riadh Hmidi*, Ali Ben Brahim, Fayçal Ben Hmida, and Anis Sellami Abstract: This paper proposes an adaptive sliding mode fault tolerant control design for lipschitz nonlinear system subject to simultaneous actuator and sensor faults. First, in order to estimate the system states, actuator and sensor faults, only one observer with an adaptive nonlinear gain is required where the minimum phase condition is relaxed to delectability and the matching condition is weakened to become a condition related to the system dimensions. Furthermore, our approach is applicable where there are faults greater than outputs. Next, a virtual sensor technique is developed to replace a failed, missing or corrupted sensor to provide a signal having the same effect of the nominal sensor. Then, this study provides an adaptive sliding mode fault tolerant control to achieve an optimal interaction between observer, virtual sensor and controller models. Thus, using the LMI technique with multiobjective optimization performance, sufficient conditions are derived to ensure the closed-loop Lipschitz nonlinear system stability and guarantee that the Lipschitz set of the adaptive sliding mode observer is a subset of the adaptive sliding mode control Lipschitz set. Two illustrative examples the first is the robotic manipulator model and the second is the longitudinal dynamics of the following vehicle system were performed to verify the effectiveness of the proposed approach. Keywords: Adaptive sliding mode FTC, adaptive sliding mode observer, Lipschitz nonlinear system, simultaneous actuator and sensor faults estimation, virtual sensor.
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INTRODUCTION
Fault tolerant control (FTC) which can be used to ensure the stability of the closed-loop system, has received considerable attention in recent years. FTC has been proposed to increase the system robustness with acceptable performance, especially in the presence of faults and uncertainties. As a result, Fault tolerant control for nonlinear system models such as Lipschitz nonlinear system has been the subject of much research [1–3]. In the literature, two main approaches have been proposed to design the FTC. The first is the passive FTC that has been proposed to design a robust control against disturbances and uncertainties without any fault information (location, magnitude, etc.). One basic limitation is that the closed-loop system cannot be stabilized even fault occurrence. Further, if there are additional disturbances or uncertainties other than faults, the passive FTC will be more vulnerable. Nevertheless, by using the fault estimation information, the active FTC, it occupies a key place in modern control applications [4–6]. Therefore, fault detection and isolation (FDI) is necessary for the active FTC design,
which increases performance and reliability requirements. Generating an alarm when a fault occurs and finding its loc
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