# In-the-Loop Simulation Experiment of Aero-Engine Fault-Tolerant Control Technology
## 1 Introduction  
The aeroengine is known as the heart of the aircraft and plays an important role in the aviation industry [1]. The engine control system works in the harsh environment of high temperature and strong vibration, and the controller, sensor, and actuator are prone to failure [2]. Although relevant factors have been considered in the process of processing and manufacturing, various faults may still occur, among which sensor faults account for more than four fifths of the total faults [3]. The safety of engine has always been the primary topic of research [4]. The improvement of safety requires fault diagnosis and fault-tolerant control, because when a fault occurs, the fault diagnosis can isolate it by finding the location of the fault. The fault-tolerant control system adopts appropriate means according to the type of fault, such as channel switching or adjusting the control law, so as to make the engine work normally or safely and minimize the impact of the fault. The International Federation of automation control (IFAC) gives the definition of fault diagnosis [5]: fault detection for judging whether there is a fault, fault isolation for judging the type and location of the fault, and fault identification for judging the characteristics of the fault. Fault diagnosis mainly includes four categories: based on signal processing,mathematical model, artificial intelligence, and hybrid algorithm. Among them, based on signal processing, wavelet analysis is mainly used to process vibration signals, so as to locate the characteristics, and then determine the engine wear condition [6]; based on artificial intelligence, automatic recognition of intelligent features is realized by learning monitoring data [7]; based on hybrid algorithm, the advantages of different algorithms are used to improve the diagnosis accuracy [8]. Among the four methods, the mathematical model method [9] is preferred, which can better show the dynamic characteristics and make the results more observable and reliable. Therefore, this paper mainly carries out fault diagnosis and fault-tolerant control based on mathematical model. The United States of America, Britain, and other developed countries have made great achievements in fault diagnosis. [PERSON] et al. [10] first used Kalman filter banks designed for different situations for fault detection and isolation. When the propulsion system fails, only a Kalman filter with correct assumptions can maintain the nominal estimation performance. The simulation results show that the diagnosis accuracy of the model reaches a high level [11]. [PERSON] and [PERSON] [12] verified the feasibility of applying a recursive maximum likelihood estimation algorithm to a Kalman filter based on Boeing 747. [PERSON] et al. [13] applied an extended Kalman filter to an airborne adaptive model for fault diagnosis. [PERSON] et al. [14] proposed the idea of using analytical redundancy to replace fault sensor parameters for the first time in view of system reliability and verified its feasibility. China has also achieved fruitful results in fault diagnosis. [PERSON], [PERSON] et al. [15] significantly improved the accuracy of analytical redundancy by using an engine component tracking filter (CTF). [PERSON] et al. [16] estimated four performance offset parameters (EDPS) by using the Kalman algorithm to modify the airborne model and enhance the convergence and tracking of the filter. [PERSON] et al. [17] used linear and nonlinear Kalman filters for linear and nonlinear models, respectively. Through comparison, it is verified that the diagnosis effect of a nonlinear Kalman filter is better. The extended Kalman filter algorithm of probability density function truncation and gain projection proposed by [PERSON] [18] improves the accuracy of health parameters. [PERSON] et al. [19] used a particle filter to estimate the health parameters of the gas path, resulting in important density function, avoiding the degradation of most particles and improving the filtering accuracy. [PERSON] et al.