# Blended Filter-Based Detection for Thruster Valve Failure and Control Recovery Evaluation for RLV
## 3 Thruster Control Recovery Evaluation Based on Proposed Fault Detection  
An RLV is a highly maneuverable vehicle that can implement missions of on-orbit, de-orbit, and reentry in the atmosphere. For different missions, the attitude control response needs to achieve different performances according to guidance commands, but when the working thrusters fail, the attitude control response performance will be affected. As an important actuator for an RLV, the thruster is usually designed with redundancy to ensure a safe flight. Based on the redundancy of the thruster, stopping the thruster failure and quickly selecting the fault-free thruster to recover the attitude control response performance are very helpful to improve the fault-tolerant ability of the RLV. This section describes the nonlinear model-based numerical prediction method that was used to evaluate whether the remaining fault-free thrusters can track the attitude control response performance under the failure of the thruster valve. The attitude control response includes the following parts:  
\[\text{Overshoot}\ \leq\alpha_{*}\%\] \[\text{Rise time}\ \leq t_{r}\] \[\text{Settling time}\ \leq t_{s}\] \[\text{Steady-state error}\ \leq e_{*}.\]  
In the RLV's longitudinal attitude loop, it has a plurality of thrusters for pitch control; the force generated by a single thruster is \(F\), the maximum thrust generated by the thrusters is \(F_{max}\), and the fault boundary of the thruster is \(F_{hold}\), as shown in Figure 5.  
For RLV longitudinal attitude control, the thrusters provide directional impulses in the \(\pm y\)-axis. Considering the RLV's longitudinal attitude nonlinear model from Equation (1), M represents the operating pitch moment of thrusters,  
\[M=\sum_{i=1}^{m}F_{i}L_{d}U_{i}, \tag{16}\]  
where \(F_{i}\) corresponds to the output of the \(i^{th}\) thruster, see Equation (2), \(U_{i}\) is the switch command of the \(i^{th}\) thruster valve for two states 0 and 1. The command to turn off the thruster valve is 0, and that to turn on the thruster valve is 1. \(L_{d}\) is the distance from the acting force to the center of gravity of the RLV. Figure 5: Thruster positions diagrams. In this study, when the fault was detected, the working thrusters were isolated and the other thrusters were employed to track the attitude control response performance. It is important to note that multiple thruster control allocation schemes may satisfy the attitude control response performance; however, minimum consumption of energy is the foremost objective for control allocation strategy:  
\[ \begin{array}{l}J=\min\{\text{S}_{1},\text{S}_{2},\cdots\text{S}_{n}\},\\ \text{S}_{j}=\sum\limits_{i=1}^{k}|v_{i}|,j=1,2\cdots n\end{array} , \tag{17}\]  
where \(\text{S}_{j}\) represents each thruster control allocation scheme of energy consumption in a selected time frame, \(v_{i}\) is the number of working thrusters at each control period and \(J\) is the priority objective for the control allocation strategy. An allocation scheme for thruster control that can satisfy the attitude control response of performance was determined in three steps. The first step was to calculate the gain \(K_{p}\) according to the required rise time after the attitude angle control command was given. The specific algorithm is as follows:  
```
Input:\(\alpha_{cmd}\) Output:\(\dot{q}\), \(q\), \(\alpha\) Control variable:\(M\)
1 Initialization Equation (1) state and parameters.