Robust Fault-Tolerant Tracking Control for Nonlinear Systems Using a Takagi-Sugeno Fuzzy Model Based on a State and Fault Fuzzy Observer

Abstract

This article presents a robust fault-tolerant tracking control (RFTTC) scheme based on the $H_{\infty }$ criterion to mitigate the effects of disturbances. The scheme integrates a state and fault fuzzy observer to enhance system performance by estimating faults while simultaneously reducing the number of states that need to be measured. The proposed controller is capable of controlling a nonlinear system to track a reference model when faults occur by estimating the faults and integrating this information with the fault-tolerant tracking control (FTTC) mechanism and the reference model control signal. The Takagi-Sugeno (T-S) fuzzy model is used to describe general nonlinearity within a certain sector, decomposing it into local linear subsystems. The fault-tolerant tracking control/fault estimation (FTTC/FE) scheme enhances performance using $H_{\infty }$ criteria, which is expressed not only in the FTTC mechanism but also indirectly through the controller of the reference model to achieve RFTTC, especially when the system faces uncertainties or external disturbances. By using an RFTTC mechanism based on a state and fault fuzzy observer, the information related to unknown states and faults is derived. Furthermore, by exploiting the separation principle, the design procedure can be considerably simplified. The controller design conditions are formulated using linear matrix inequalities (LMI) based on the Lyapunov theorem. Finally, to demonstrate the efficiency of the proposed method, numerical simulations for a Rotary Inverted Pendulum with actuator faults and external disturbances are implemented.