## 5 Simulation and Analysis  
The simulation of a 6-DOF RLV dynamic is conducted in this section. The parameters of RLV are \(J_{xx}=130700\) kg\(\cdot\) m\({}^{2}\), \(J_{yy}=1507000\) kg\(\cdot\) m\({}^{2}\), \(J_{zz}=1493000\) kg\(\cdot\) m\({}^{2}\), and \(J_{xz}=116000\) kg\(\cdot\) m\({}^{2}\). The cross-section area and reference length are \(S_{\text{ref}}=73\) m\({}^{2}\) and \(L_{r}=40\) m, respectively. The initial state variables in the simulation are given as follows: \(r=6457\) km, \(\theta=-17.32^{\circ}\), \(\varphi=105.01^{\circ}\), \(\sigma=0.01^{\circ}\), \(\beta=0.49^{\circ}\), \(\alpha=45.01^{\circ}\), \(p=0.0007\) rad/s, \(q=0.0\) rad/s, \(r=0.0698\) rad/s, \(v=2916\) m/s, and \(m=23000\) kg. Moreover, the parameters of PTPPF are set as \(\rho_{10}=0.2\)rad, \(\rho_{iso}=0.005\)rad, \(k=1.6\), and \(T_{f}=1\). The parameters of the controller are \(a=-1.2\), \(T_{c}=0.5\), \(n=0.5\), and \(T_{p}=0.5\). The parameter uncertainties of aerodynamic coefficients in the simulation are set to \(20\%\) bias, while \(10\%\) bias is set for the moment of inertia. Then, two different control simulations are conducted for comparison; one is for the fixed-time nonsingular fast terminal sliding mode control (FxNFTSMC) [14], and the other is for active disturbance rejection controller (ADRC) [36]. For FxNFTSMC, let \(v_{1}=1.1\), \(v_{2}=3.2\), \(\lambda_{1}=1.6\), \(\lambda_{2}=1.3\), \(\gamma_{1}=1.3\), \(\gamma_{2}=0.38\), \(\chi=1.5\), and \(\lambda=2.0\). In the ADRC, there is \(\mathbf{\beta}_{1}=(150,\,160,\,160)\), \(\mathbf{\beta}_{2}=\Big{(}9.09\times 10^{3},\,9.09\times 10^{3}\Big{)}\), \(\mathbf{\beta}_{3}=\Big{(}1\times 10^{5},\,2\times 10^{3},\,2\times 10^{3}\Big{)}\), \(\mathbf{c}=(0.4,\,0.4,\,0.4)\), \(\mathbf{r}=(810,\,830,\,305)\), and \(\mathbf{h}_{0}=(0.1,\,0.1,\,0.1)\). In Figures 5-8, we can see that the attitudes of RLV can track the time-varying guidance command \(\mathbf{\Lambda}_{\text{C}}\) in the desired time \(1.0\) s, and the deviation from guidance commands is less than the predefined value \(\rho_{iso}=0.005\) rad. Figure 5 shows that the proposed controller has an excellent control effect taking into account the parameter uncertainties, state constraints, and external disturbances. In contrast, the attitude tracking errors of the FxNFTSMC are eliminated to be near zero within \(1.45\) s, and the convergence time of ADRC is about \(1.5\) s. Meanwhile, the FxNFTSMC needs a complex calculation of design parameters to obtain the desired convergence time. The proposed controller can directly give the actual convergence time, which avoids the process of obtaining the convergence time of the system through constant iteration and repeated testing in the FxSMC. Figure 5: Attitude tracking curves of \(\sigma,\ \beta,\ \alpha\): (**a**) the roll channel; (**b**) the yaw channel; (**c**) the pitch channel. Figure 6: Time responses of angular velocity: (**a**) the roll channel; (**b**) the yaw channel; (**c**) the pitch channel. Figure 7: Sliding mode surface of three channels: (**a**) the roll channel; (**b**) the yaw channel; (**c**) the pitch channel. Figure 8: Control moment of three channels: (**a**) the roll channel; (**b**) the yaw channel; (**c**) the pitch channel. **Author Contributions:** Conceptualization, M.W., C.W. and J.P.; methodology, M.W. ; software, M.W. ; validation, C.W. and J.P.; resources, N.C.; data curation, J.P.; writing--original draft preparation, M.W. ; writing--review and editing, C.W. ; visualization, C.W. ; supervision, N.C.; project administration, J.P. All authors read and agreed to the published version of the manuscript. This research was funded by the National Defense Basic Scientific Research (JCKY2019208C017) and National Natural Science Foundation of China (Grant 52232014). Not applicable. **Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The authors would like to thank the editors and anonymous reviewers for their constructive comments and suggestions.