# Blended Filter-Based Detection for Thruster Valve Failure and Control Recovery Evaluation for RLV
## 1 Introduction
In the literature [16], a velocity-free nonlinear proportional-integral control allocation scheme was provided for the fault-tolerant attitude control of flexible spacecraft under thruster redundancy. A uniform actuator fault model was established, but the system states before and after the fault were not considered; moreover, the noise signals that approximate the control input were also not regarded, leading to an output error from the model. The literature [17] proposed a sliding mode observer with an equivalent output injection to reconstruct external disturbances and actuator faults and developed a sliding mode-based attitude controller using an exponential reaching law. The exponential reaching law relies on the state of the system and the corresponding formation of the estimated parameters, although in the theoretical design process, the authors described the partial failure of the thruster using the thruster fault modeling. However, it could not detect faults under low thrust conditions due to the thruster leakage in the simulation verification process. The simulation results also showed that the fault detection time frame of the designed sliding observer was more than 6 s. In literature [18], an observer-based fault-tolerant controller was constructed such that the states of the resulting closed-loop systems were uniformly and ultimately bounded in the presence of model parameter uncertainty, external disturbances, time-varying input delay, actuator faults, and actuator saturation. However, the controller gain matrix and observer gain matrix were required to be designed for satisfying the results of the uniformly and ultimately bounded system. This method helped in dealing with several problems at the expense of optimal control performance in different situations, and the fixed gain of the observer did not consider the requirements of specific fault detection such as false alarm rates, fault detection rates, and fault detection time. Literature [19] showed that any motion-based fault detection and isolation is reliant on the accuracy of the measurement data used, thus, great care has been taken here to obtain highly accurate angular and translational acceleration estimates from the gyros and accelerometers. The motion-based method presented in this work was used and extended in this research. Unlike previous studies, in this study, the failure of thruster valves, including valve wear and leakage failure in addition to valve jams and difficulty in closure, was investigated. We proposeda detection solution for the failures based on motion state estimation with particular consideration of the noise that affects the RLV operation in initial reentry, on-orbit, and de-orbit phase, which is caused by electromagnetic radiation in near-Earth space [20]. In this paper, a physical filter was used in combination with a Kalman filter to suppress the input interference of the approximate control of the thruster valve, enhance the consistency of physical input and algorithm model input, improve the accuracy of motion state estimation, and thereby improve the fault detection rate. The paper aims at developing an online thruster fault detection method that can handle thruster valve failure and does not increase more hardware complexity or cost. Firstly, the failure of thruster valves under different working conditions was analyzed, and the thruster model caused by valve failure was established. Then, on the basis of the thruster model, a motion-based blending filter fault detection method is proposed. The blending filter was used to estimate the thruster state and suppress the noise signals that approximate the control signal. The fault detection was conducted by comparing the variance-based function of the observed output in a certain time window with the threshold.