|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
International Journal of Control, Automation, and Systems, vol. 18, no. 9, pp.2206-2219, 2020
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.
Adaptive sliding mode FTC, adaptive sliding mode observer, Lipschitz nonlinear system, simultaneous actuator and sensor faults estimation, virtual sensor.