## 5 Simulation  
In this section, the effectiveness of the proposed FTIGC for the flight vehicle with a strapdown seeker is verified by numerical simulations. The full aerodynamic forces and moments in the simulation are given by [33]  
\[\left\{ \begin{array}{l}X=qS\Big{(}c_{x0}+c_{x}^{\alpha}|\alpha|+c_{x}^{ \beta}|\beta|+c_{x}^{\alpha\beta}|\alpha\beta|+c_{x}^{\delta_{x}}|\delta_{x}|+c _{x}^{\delta_{y}}|\delta_{y}|+c_{x}^{\delta_{z}}|\delta_{z}|\Big{)}\\ Y=qS\Big{(}c_{y}^{\alpha}\alpha+c_{y}^{\beta}\beta+c_{y}^{\delta_{y}}\delta_{z }\Big{)}\\ Z=qS\Big{(}c_{x}^{\alpha}\alpha+c_{\beta}^{\beta}\beta+c_{z}^{\delta_{y}}\delta_{ y}\Big{)}\\ M_{x}=qSL\Big{(}m_{x}^{\alpha}\alpha+m_{z}^{\beta}\beta+m_{x}^{\delta_{x}} \delta_{x}\Big{)}\\ M_{y}=qSL\Big{(}m_{y}^{\beta}\beta+m_{y}^{\delta_{y}}\delta_{y}\Big{)}\\ M_{z}=qSL\Big{(}m_{z}^{\alpha}\alpha+m_{z}^{\delta_{z}}\delta_{z}\Big{)} \end{array} \right.\]where \(c_{x0}\) is the zero-lift drag coefficient. \(c_{x}^{\alpha}\), \(c_{x}^{\beta}\), \(c_{x}^{\delta}\), \(c_{x}^{\delta}\), \(c_{x}^{\delta}\), and \(c_{x}^{\delta_{z}}\) are the partial derivatives of the drag force coefficient with respect to \(\alpha\), \(\beta\), \(\delta_{x}\), \(\delta_{y}\), and \(\delta_{z}\). \(c_{x}^{\alpha\beta}\) is the second partial derivative of the drag force coefficient with respect to \(\alpha\) and \(\beta\). \(c_{y}^{\alpha}\), \(c_{y}^{\beta}\), and \(c_{y}^{\delta_{z}}\) are the partial derivatives of the lift force coefficient with respect to \(\alpha\), \(\beta\), and \(\delta_{z}\). \(c_{x}^{\alpha}\), \(c_{z}^{\delta}\), and \(c_{z}^{\delta}\) are the partial derivatives of the side force coefficient with respect to \(\alpha\), \(\beta\), and \(\delta_{y}\). Similarly, \(m_{x}^{\alpha}\), \(m_{x}^{\beta}\), and \(m_{x}^{\delta_{x}}\) are the partial derivatives of the rolling moment coefficient with respect to \(\alpha\), \(\beta\), and \(\delta_{x}\); \(m_{y}^{\beta}\) and \(m_{y}^{\delta_{y}}\) are the partial derivatives of the yawing moment coefficient with respect to \(\beta\) and \(\delta_{y}\); and \(m_{z}^{\alpha}\) and \(m_{z}^{\delta_{z}}\) are the partial derivatives of the pitching moment coefficient with respect to \(\alpha\) and \(\delta_{z}\). Considering the physical limitations, each fin deflection should be constrained to \(\pm 20^{\circ}\). Apart from this, the nominal values of the parameters related to the flight vehicle are listed in Table 1.  
The flight vehicle initially locates at \( \begin{bmatrix}0&15000&0\end{bmatrix} ^{T}(\text{m})\) in the Inertial reference frame and the initial values of the roll, yaw, and pitch angles are set to be \(\gamma(0)=0.3634^{\circ}\), \(\psi(0)=0.2955^{\circ}\), and \(\vartheta(0)=1.4261^{\circ}\). The initial velocity, flight path angle, and heading angle of the flight vehicle are assumed as \(V(0)=1000(\text{m}/\text{s})\), \(\vartheta(0)=0^{\circ}\), and \(\psi_{v}(0)=0^{\circ}\). The initial angular rate vector is \(\mathbf{\omega}(0)= \begin{bmatrix}0.2&-0.1&-0.12\end{bmatrix} (^{\circ}/\text{s})\). The control parameters are selected as follows: \(\omega_{0}=5\), \(\tau_{2}=\tau_{3}=0.1\), \(K_{11}=1.25R\), \(K_{12}=-1.25R\cos q_{z}\), \(\lambda_{1}=10\), \(K_{2}=2.5\text{E}_{3}\), \(\lambda_{2}=2\), \(K_{3}=5I\), \(\lambda_{3}=10\). The simulation includes three cases with the same control parameters but different actuator fault models for fixed or moving objects. **Case1. ** No actuator fault happens. In other words, \(\rho_{x}(t)=\rho_{y}(t)=\rho_{z}(t)=1\). **Case2. ** The actuator healthy factors are all constants, which are set as \(\rho_{x}(t)\)\(=0.8\), \(\rho_{y}(t)\)\(=0.7\) and \(\rho_{z}(t)=0.6\). **Case3. ** The actuator healthy factors are not constants, which are set as  
\[\rho_{i}(t)\text{=}0.7+0.15\text{rand}(t)+0.1\sin(0.5t+0.2\pi)\]  
where \(\text{rand}(\cdot)\) refers to the random function distributed on the open interval \((-1,\,1)\). Furthermore, to verify the robustness of the proposed FTGC, the parameter perturbations are also considered in the simulation.