# Blended Filter-Based Detection for Thruster Valve Failure and Control Recovery Evaluation for RLV
## 4 Results
### Thruster Control Recovery Evaluation  
This section describes the reference response curve employed to determine whether the remaining fault-free thruster can track the attitude control response performance under the failure of the thruster valve, as shown in Figure 12.  
The thruster configuration refers to the space shuttle's data [9]. The RLV includes 38 main thrusters and 6 moving thrusters. The thruster evaluation was studied with reference only to the main thrusters. In accordance with the RLV redundancy configuration, the RLV longitudinal attitude control was configured as \(\{-10,\ldots,-2,-1,0,1,2,\ldots,10\}\), where \"\(-\)\" indicates the \(+y\)-axis impulse generated. Figure 12 shows an AoA reference response curve and the thruster operation input in the fault-free state. In the rise time period, in order to shorten the rise time and the settling time, more thrusters were needed to generate the expected thrust. To conduct a simplified analysis of the number of operating thrusters and their operation time, as shown in Figure 12b, 1 s was taken as the unit time, assuming that a thruster was operating at full load for one second, i.e., two states including 1 s continuously turned on or 1 s continuously turned off. Figure 13 displays the AoA step response output and thruster operation input under type A, B, and C faults and fault-free conditions. During the rise time period, as shown in Figure 13b, the thruster shows a type A fault in the period of 2-5 s and stopped operating. During this period, the blended Kalman filter was used to diagnose and isolate the faulty thruster and, based on the reference response curve, the remaining fault-free thruster was employed to evaluate the control recovery performance using Algorithm 1 and Algorithm 2. The red part in Figure 13b represents the number of thrusters and the working time for the type A fault. During adjustment of the working thruster, the AoA response was as shown in Figure 13a, and to improve the settling time after fault tolerance, both the given pitch rate and the overshoot were increased, while the pitch angle was adjusted by the controller to reach the steady-state requirement. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Fault Type**} & \multirow{2}{*}{**Fault Number**} & **Miss Ratio P\({}_{\text{M}}\) (\%)** & **Fault Detection Rates P\({}_{\text{D}}\) (\%)** \\  & & **EKF Solution/** & **EKF Solution/** \\  & & **Blending Filter Solution** & **Blending Filter Solution** \\ \hline A & 1000 & 27.40/8.40 & 72.60/91.60 \\ B & 1000 & 18.00/6.30 & 82.00/93.70 \\ C & 1000 & 32.10/12.20 & 67.90/87.80 \\ B\&C & 1000 & 10.60/3.80 & 89.40/96.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fault detection rates test. Figure 12: Angle of attack (AoA) reference response curve and the number of working thrusters in the fault-free state: (**a**) An AoA reference response curve in the fault-free state; (**b**) the number of working thrusters in the fault-free state. In the stage of the attitude angle feedback control, as shown in Figure 13d, the thruster showed a type B fault in the period of 35-39 s, the thruster was turned on at the previous time and did not close at the latter time when the command to turn off was given. The steady-state error then increased, and the controller isolated and switched over the thruster, as shown in Figure 13d. To rapidly reduce the steady-state error, the number of active thrusters was increased, and after the  
Figure 13: Response output and the number of working thrusters for the type A, B, and C faults and the fault-free state: (**a**) AoA response output for the type A fault and the fault-free state; (**b**) the number of working thrusters in the type A fault and fault-free state; (**c**) AoA response output for the type B fault and the fault-free state; (**d**) the number of working thrusters in the type B fault and fault-free state; (**e**) AoA response output for the type C fault and the fault-free state; (**f**) the number of working thrusters in the type C fault and fault-free state.