# Blended Filter-Based Detection for Thruster Valve Failure and Control Recovery Evaluation for RLV
## 4 Results
### Thruster Fault Detection  
Considering the three fault types A, B, and C, the state estimation and fault-free status comparison were made among the three fault types using the blended Kalman filter, as shown in Figures 7-9. Figure 7 depicts the state estimation of the type A fault and the fault-free state using the blended Kalman filter. The thruster valve was closed in the previous time period, with an initial pitch rate of 0\({}^{\circ}\)/s, and, after a command to turn on the valve was given, the fault-free thruster generated a thrust to create an incremental pitch rate, as shown in Figure 7b. Figure 7a displays the type A fault state, that is, it was turned off in the previous moment, with a pitch rate of 0\({}^{\circ}\)/s; no response output occurred after a thrust command was given at the latter point as the valve was stuck. As shown in the above figures, the state estimation of the blended Kalman filter was consistent with the actual data trend in the fault and fault-free conditions, and the deviation was in the range of \(\pm\)0.1\({}^{\circ}\)/s. Figure 8: Type B fault vs. fault-free state estimation: (**a**) type B fault state estimation; (**b**) type B fault-free state estimation. Figure 7: Type A fault vs. fault-free state estimation: (**a**) type A fault state estimation; (**b**) type A fault-free state estimation. Figure 8 depicts the estimations of the type B fault and the fault-free state. On the premise that the RLV had a pitch rate at the initial moment of \(2^{\circ}\)/s, the thruster valve in the previous time period was turned on, and, after a command to turn off the valve was given, the thruster should close under the fault-free state and the pitch rate should have been maintained at around \(2^{\circ}\)/s. Figure 8 displays the type B fault state, that is, after a command to turn off the valve was given, the valve was stuck and did not close. Under the condition of the above-mentioned type B fault and the fault-free state, the state estimation of the blended Kalman filter agreed with the trend of the feedback data, with a deviation within the range of \(\pm 0.1^{\circ}\)/s. Figure 9 displays the estimation of the type C fault and the fault-free state. As shown above, when the vehicle had an initial pitch rate of \(2^{\circ}\)/s, the thruster valve at the previous time was turned on, and, after a command to turn the valve off was given, the thruster did not completely close, indicating a type C fault. Here, it was assumed that the ratio of the valves' incomplete closing distance to the nozzle width was \(\tau=0.2\) after the performance had been attenuated under the limit conditions. As the type C fault is a small thrust-related leakage problem, the pitch rate increment will be slowly generated, as shown in Figure 9. The pitch rate should fluctuate around the initial pitch rate of \(2^{\circ}\)/s under the fault-free state, as shown in Figure 9. The state estimation method adopted in this paper, as mentioned above, remained consistent with the trend of the observed data, with a deviation within the range of \(\pm 0.1^{\circ}\)/s. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Fault Type**} & \multirow{2}{*}{\(D[r_{\text{k-group}}]\)} & \multirow{2}{*}{\(mean[r_{\text{k-group}}]\)} & \multicolumn{2}{c}{**Fault-Free**} \\ \cline{3-5}  & & & \(D[r_{\text{k-group}}]\) & \(mean[r_{\text{k-group}}]\) \\ \hline A & 0.067100 & \(-\)0.542500 & 0.000062 & \(-\)0.000512 \\ B & 0.127900 & \(-\)0.514600 & 0.000064 & \(-\)0.000223 \\ C & 0.010700 & \(-\)0.124600 & 0.000026 & \(-\)0.000087 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Thruster fault detection. Figure 10: Type A, B, and C fault residuals vs. fault-free residuals: (**a**) type A fault residuals vs. fault-free residuals; (**b**) type B fault residuals vs. fault-free residuals; (**c**) type C fault residuals vs. fault-free residuals. extended Kalman filter (EKF) based solution is employed.