Robust State/Fault Estimation and Fault-Tolerant Control in Discrete-Time T–S Fuzzy Systems: An Embedded Smoothing Signal Model Approach
提出一种嵌入故障平滑信号模型的T-S模糊系统方法，用于离散非线性系统的鲁棒状态/故障估计和容错控制，通过传统模糊观测器和LMI优化实现，仿真验证了有效性。
This study investigates a simple design method of the robust state/fault estimation and fault-tolerant control (FTC) of discrete-time Takagi–Sugeno (T–S) fuzzy systems. To avoid the corruption of the fault signal on state estimation, a novel smoothing signal model of fault signal is embedded in the T-S fuzzy model for the robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> state/fault estimation of the discrete-time nonlinear system with external disturbance by the traditional fuzzy observer. When the component and sensor faults are generated from different fault sources, two smoothing signal models for component and sensor faults are both embedded in the T-S fuzzy system for robust state/fault estimation. Since the nonsingular smoothing signal model and T-S fuzzy model are augmented together for signal reconstruction, the traditional fuzzy Luenberger-type observer can be employed to robustly estimate state/fault signal simultaneously from the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> estimation perspective. By utilizing the estimated state and fault signal, a traditional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> observer-based controller is also introduced for the FTC with powerful disturbance attenuation capability of the effect caused by the smoothing model error and external disturbance. Moreover, the robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> observer-based FTC design is transformed into a linear matrix inequality (LMI) -constrained optimization problem by the proposed two-step design procedure. With the help of LMI TOOLBOX in MATLAB, we can easily design the fuzzy Luenberger-type observer for efficient robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> state/fault estimation and solve the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> observer-based FTC design problem of discrete nonlinear systems. Two simulation examples are given to validate the performance of state/fault estimation and FTC of the proposed methods.