## 6 Simulation and Test Results
### Flight Mission Path Simulation  
The Simulink platform is used to validate flight mission paths, energy consumption, and execution time through simulation tests. Figure 13 shows the simulation model. The model consists of five modules: path command, position controller, attitude controller, rotor motor hybrid controller, and flight dynamics. The path command module converts the input FPTLIR flight path command into the current position; the position control module transforms the current position of the FPTLIR into an attitude control command; the attitude control module employs a traditional PID control algorithm to control the attitude of the FPTLIR; the rotor motor hybrid control module decodes the output of the attitude control module into individual rotor motor control commands; and finally, the flight dynamics module includes a dynamic model representing the FPTLIR's behavior during flight as discussed in the previous sections. The simulation model uses the optimized path parameters, which are obtained from the improved speed curve, to generate the corresponding task path and energy consumption-time curves.  
The flight mission paths of the FPTLIR for the on-line and off-line missions are shown in Figures 14a and 14b, respectively, in the inertial reference system. The simulation model generates corresponding 3D trajectories by recording trajectory points at 0.5 s intervals, thereby representing the magnitude of velocity through the density of trajectory points. Initially, the FPTLIR hovers at Point (#1) with coordinates (0,0,0), then rises vertically to reach Point (#2) with coordinates (0,0),49.9058). It then transitions to horizontal forward flight and finally arrives at Point (#3) with coordinates (5.9655,0),49.9058). The FPTLIR then performs a horizontal backward flight from Point (#4) with coordinates (6.0000,0.50.0000) to Point (#5) with coordinates (0.0361,0.50.0000), before finally reaching its destination at Point (#6) with coordinates (0.0361,0.0.0764). The results show that the FPTLIR effectively responds to input commands and successfully completes flight missions while meeting stability, safety, positional accuracy, and other relevant indicators and constraints.  
Correspondingly, Figure 15a,b depict the energy consumption profiles of the optimized flight during on-line and off-line simulations, respectively. The results indicate that the FPTLIR completes the on-line mission in a total time of 17.81 s with a corresponding energy consumption of 1.3188 \(\times\) 10\({}^{5}\) J. Compared to the actual numerical calculations, we observe a time error of only 0.22% and an energy consumption error of only 1.31%. Similarly, for the off-line mission, the FPTLIR achieves it within a total time of 28.92 s while consuming approximately 1.2735 \(\times\) 10\({}^{5}\) J of energy, resulting in negligible errors compared to the actual numerical calculations (time error: 0.49%, energy consumption error: 0.19%). The  
Figure 13: The simulation model of FPTLIR.  
proposed energy model and optimization method demonstrate consistency and accuracy in predicting and optimizing the energy consumption and mission execution time of the FPTLIR during a mission, closely matching the actual observations.