## 6 Conclusions  
In this paper, an FTC scheme for the sensor fault in the transition process of VCE based on AEMM is proposed. The scheme adopts closed-loop control of speed and open-loop control of other control variables for transition control. To diagnose the sensor faults and study the control of acceleration process, a modeling study is first carried out. The fuel flow and the nozzle area are selected as the two scheduling variables to establish the EMM of VCE with multiple inputs and multiple outputs. Then the AEMM is obtained by introducing health parameters and Kalman filter. After that, the AEMM is combined with the Kalman filter bank to design a fault diagnosis scheme for the single sensor fault and double sensor faults. The simulation results of bias and drift fault cases show that the proposed scheme can accurately diagnose the fault sensors except when two fault sensors are grouped in the same group. But in either case, the scheme can accurately estimate the state and reconstruct the signal. Then, the target shooting method is used to optimize the engine acceleration control plan, and based on this, the fault simulation of the low spool speed sensor is carried out. Finally, a HIL simulation platform is built to verify the FTC method considering the actuation characteristics and other limitations of the actuator in the actual process. The results show that the fault sensor can be diagnosed and signal reconstruction can be carried out within 0.2 s by using the proposed scheme.  
The method proposed in this paper can complete the FTC of sensor fault in a very short time, and is not too complicated, and has strong engineering feasibility and application value. At the same time, this method is also suitable for general turbofan engine fault-tolerant control. But there are still many areas that need to be further studied. For example, when two faulty sensors appear in the same group, only accurate signal reconstruction can be carried out, but the location of the faulty sensor cannot be diagnosed. And in addition to the acceleration process of the VCE, the FTC of the mode switching process should be paid more attention to. In this paper, only the fault-tolerant design of the sensor is carried out, and there may also be actuator fault, component fault and other forms. Therefore, the FTC problem of VCE needs more and more in-depth research.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Before the Acceleration** & **After the Acceleration** \\  & **Process** & **Process** \\ \hline Low spool speed (\%) & 67.87 & 99.9 \\ High spool speed (\%) & 84.37 & 98.5 \\ Stall margin of CDFS (\%) & 7.62 & 10.13 \\ Inlet temperature of HPT (K) & 1435.25 & 1823.69 \\ Fuel flow (kg/s) & 0.33 & 0.80 \\ High spool speed (\%) & 84.37 & 98.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters before and after the acceleration process.  
Figure 28: Changing curve of control quantity in HIL test.  
**Author Contributions:** Conceptualization, L.L. and Y.Y.; methodology, L.L. and Y.Y.; soft-ware, X.Z.; validation, L.L., Y.Y. and X.Z.; formal analysis, T.Z.; investigation, S.W.; resources, T.Z.; data curation, L.L.; writing--original draft preparation, L.L.; writing--review and editing, S.W.; visualization, X.Z. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the confidentiality of the data generated during the research process in this paper.  
The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.