# Fault-Tolerant Control for Carrier-Based Aircraft Based on Adaptive Fuzzy Sliding-Mode Method
## 3 Landing Environment
### Autonomous Carrier Landing System (ACLS) Control Framework  
The CBA is susceptible to external disturbances, such as the carrier air wake and sea wind and waves during landing, and to unfavourable conditions, such as actuator faults, leading to reduced or even unstable control performance. To avoid unfavourable conditions, ensure landing safety and improve the landing success rate, an ACLS must be developed for the CBA to track the reference path accurately and quickly, thereby providing support for the CBA to reach the ideal touchdown point. ACLS is targeted at correcting the initial position, controlling the perturbations from the carrier air wake, tracking the glide path and effectively solving the fault-induced degradation problems of the control system. As shown in Figure 2, its control framework comprises a glide-path generation subsystem, a guidance subsystem, a flight controller subsystem and an aircraft-fault subsystem. The function of the glide-path generation subsystem is to collect the longitudinal and lateral errors between the CBA and the expected glide path. The ideal touchdown point on the carrier deck is a 6 DOF spatial motion point because of the impact of complex sea conditions, while the expected glide path. The ideal touchdown point on the carrier deck is a 6 DOF spatial motion point because of the impact of complex sea conditions, while the expected glide path is directly affected by the ideal touchdown point. Therefore, there is a need to build a relative positional relationship between the CBA and the ideal touchdown point. The centre-of-gravity position of the CBA is defined as \((x_{a},y_{a},z_{a})\), while the ideal touchdown point is defined as \((x_{c},y_{c},z_{c})\). Therefore, the relative positional relationship between the CBA and the aircraft carrier is described as  
Figure 1: Relationship between centre of gravity of aircraft carrier and ideal touchdown point. \[ \begin{bmatrix}x_{r}\\ y_{r}\\ z_{r}\end{bmatrix} =L_{cg} \begin{bmatrix}x_{a}-x_{p}\\ y_{a}-y_{p}\\ z_{a}-z_{p}\end{bmatrix}  \tag{14}\]  
where \(L_{cg}\) is the transfer matrix from the Earth-surface inertial reference frame to the motion reference frame of the aircraft carrier. Figure 3 shows the positional relationship between the CBA and the ideal touchdown point, where \(\gamma_{p}\) is the expected glide-path angle and \(\sigma_{p}\) is the angle between the expected glide path and the aircraft carrier. Therefore, the path-tracking error is obtained as  
\[ \begin{bmatrix}H_{e}\\ Y_{e}\end{bmatrix} = \begin{bmatrix}z_{r}-x_{r}\tan\sigma_{p}\\ y_{r}\end{bmatrix}  \tag{15}\]  
\[\tan\sigma_{p}=\frac{\sin\gamma_{p}}{\cos\gamma_{p}-V_{a}/V_{c}} \tag{16}\]  
The function of the guidance subsystem is to transform position errors into angular commands to control the angular variations. The guidance subs  
Figure 3: Diagram of CBA landing. Figure 2: ACLS Control Framework. into a longitudinal channel and a lateral channel. The longitudinal channel selects the path controller containing a \(\sigma-\beta\) filter to transform flight altitude tracking commands into a pitch angle control command \(\theta_{d}\), while the lateral channel uses PID control to transform lateral deviations into the expected side-slip angle \(\beta_{d}\) and roll angle \(\phi_{d}\). The two input terms in the aircraft-fault subsystem are actuator fault and unknown disturbance, the occurrence times of which are indefinite. If unknown faults is added, the CBA cannot steadily track the glide path, leading to significant influences on landing safety and success rate. Therefore, there is necessary to develop an effective fault-tolerant flight system to address the fault-induced uncertainties. The flight controller subsystem comprises an approach power compensator system (APCS), a longitudinal flight controller subsystem and a lateral flight controller subsystem.