5.1. Simulation of Direct Switching
100 m height, 19 m/s cruise speed, and 16 m/s switching speed are selected as simulation environment to realize the process of switching from fixed-wing mode to switching mode, and from switching mode to rotary-wing mode. The process maintains a fixed height, and the pitch angle command is zero to ensure the smallest possible pitch angle. After switching to the rotary-wing mode, it decelerates and prepares for the subsequent hovering landing.
The nominal simulation of direct transition was conducted first. Direct transition refers to the process of switching from fixed-wing mode to rotary-wing mode without going through the switching mode (that is, reducing the switching mode duration to 0 s) and keeping the fixed height and airspeed command unchanged.
Figure 13 displays the simulation results after entering the rotary-wing mode by direct transition.
Here, the commands , , and are dimensionless: 0 means none and 1 means the full speed of the corresponding rotor/front-mounted propeller, which are 0 RPM and 8000 RPM, respectively.
Although the direct transition from fixed-wing mode to rotary-wing mode can be achieved under the current control framework, there are large fluctuations in pitch angle and altitude in the subsequent rotary-wing mode. It is preliminarily speculated that adverse situations may occur under the influence of model uncertainty, so Monte Carlo (MC) shooting simulation with model uncertainty is needed.
Simple and practical MC shooting simulation is often used to verify the robustness of controllers with model uncertainties. By setting the disturbance range of all model parameters, randomly forming them, and assigning them to the simulation system, it is a direct nonlinear robustness verification method that is suitable for almost all control systems. In order to compare different switching mode designs and prevent a small amount of data from affecting the accuracy of the conclusion in parameter random perturbations, a random number sequence of 100 random numbers is generated, and the subsequent biased simulations use this group of random seeds, which can facilitate the inspection and reproduction of the simulation results, and also compare different transition phase designs under the condition of variable control.
The perturbation ranges of all model parameters of the longitudinal channel designed in this manuscript are shown in
Table 3.
The results of 100 times of MC shooting simulations are drawn into images, as shown in
Figure 14. For the transition phase without switching mode design, although mode switching is basically realized in the nominal simulation, problems such as pitch angle oscillation and drastic change, loss of altitude maintenance, throttle saturation and rotor speed saturation occurred in all 100 MC target shooting simulations with 20% model uncertainty. Therefore, the transition phase without switching mode may pose a serious threat to flight safety and it is more vulnerable to model uncertainty and shows relatively poor robustness.
Therefore, a soft transition design is needed to address issues caused by mode switching, such as loss of altitude tracking, drastic changes in pitch attitude, and poor robustness.
5.2. Simulation with 5 s Switching Mode
In the nominal simulation, it was observed that the UAV basically reached a steady state within 5 s after entering the switching mode, as shown in
Figure 15. Therefore, the soft transition design of the 5 s switching mode was introduced for comparison.
Similarly, MC shooting simulation with 5 s switching mode uses the same random seeds with the same main parameter perturbations, and the simulation results are shown in
Figure 16.
It can be observed that in the 100 MC shooting simulations, the mode switching task was completed well under most conditions, but there were also a few cases with perturbation of main parameters, resulting in poor altitude holding, throttle, and rotor speed saturation. As shown in
Figure 17, details of the simulation results in
Figure 16 are provided, and it was observed that, at the moment of switching to the rotary-wing mode (at the 5th second), the altitude channel had not yet entered a steady state. It was preliminarily judged that more time was needed to complete the altitude tracking, so it was considered to extend the duration of the mode switching for comparison.
5.4. Compilation and Comparison of the Results of Three Transition Phase Designs
The deceleration process of fixed height, which is 12 s after switching to rotary-wing mode, is shown in
Figure 20 and the three design methods of transition phase are compared.
The nominal simulation results under three transition phase designs are summarized and the distribution ranges of each parameter are shown in
Table 4.
The comparison results in
Table 4 show that:
A soft transition design with switching mode, after switching to rotary-wing mode, reduces the maximum pitch angle from 20.5° to 1.1°, by about 94%. In addition, the maximum pitch angle rate is reduced by about 72%. Therefore, it can inhibit the sudden change in pitch angle and pitch angle rate.
The soft transition design reduces the height fluctuation from 24 m to 1.1 m, which is a reduction of about 95%, so it has an enhanced effect on height maintenance.
The soft transition design reduces throttle usage by approximately 17% and therefore predictably withstands greater uncertainties, reducing the risks of saturation.
When model uncertainty is excluded, the nominal simulation results of the soft transition design with a 5 s switching mode show little difference compared to the design with 10 s switching mode. Therefore, when UAV modeling is accurate, the soft transition design with 5 s switching mode is relatively ideal.
The comparison results in
Table 5 show that:
The design of the transition phase with 5 s has passed 100 MC shooting simulations with 20% model uncertainty. However, the design of the 10 s switching mode and the direct switching design have failed in some cases.
Under the random seed condition with poor pitch angle and height control in the 5 s switching mode design, good command tracking is obtained for the 10 s switching mode design. Therefore, the design of the transition phase with switching mode can effectively reduce the impact of model uncertainty and improve the robustness of the UAV transition phase, and the longer the duration of the switching mode within a certain limit, the better the flight stability.
Under the design of the 10 s switching mode, the occurrence of throttle and rotor speed saturation in a few extreme cases can be avoided. Therefore, extending the switching mode duration within a certain limit can reduce the possibility of extreme cases caused by mode switching, thereby improving the safety of the UAV transition phase.
Therefore, considering the uncertainty of the model, the MC shooting simulation results of the soft transition design with 10 s switching mode show greater advantages than those of the design with 5 s switching mode. For this type of UAV with inaccurate modeling, in order to achieve better robustness and safety, a 10 s switching mode is relatively more suitable.
Figure 20.
Comparison between three designs for the transition phase.
Figure 20.
Comparison between three designs for the transition phase.
5.5. Quality Comparison of Mode Switching
The normal overload of an aircraft is the overload in the pitch direction perpendicular to the flight speed, which is the ratio of the centripetal acceleration to the gravitational acceleration. The aircraft will generate normal overload when performing pitch maneuvering flight. Normal overload will affect the equipment safety of the aircraft and the physiological condition of the pilot and passengers, such as excessive normal overload will also cause passenger comfort reduction and energy loss of the aircraft, and in serious cases even cause pilot loss of consciousness or black eye phenomenon and structural and airborne equipment damage of the aircraft.
Therefore, normal overload can be used as an important indicator to reflect the smoothness of mode switching. In UAV VtolA7, we believe that the limit normal overload within −1.5~3.8 can ensure the safety of the UAV and airborne equipment; considering the future manned scenario of air cars, a normal overload outside the range of −1~2.5 is considered unacceptable.
Figure 21 draws the normal acceleration diagram under three modes of switching in nominal simulation, which can intuitively and clearly outline the contrast between them, and also reflect the significance of normal overload as a soft switching indicator. The ranges of normal acceleration for the three modes are −0.29~0.23, −0.04~0.04, and −0.04~0.02, respectively, which imply ranges of normal overload of 0.71~1.23, 0.96~1.04, and 0.96~1.02, respectively. Therefore, in the nominal simulation, the soft switching design can decrease the maximum normal acceleration by about 86%, and the maximum normal load by about 17%.
As shown in
Figure 22, the design of the transition segment can significantly reduce the overload limit caused by mode switching, which is manifested in:
In the case of model uncertainty, there is a greater risk without a transition segment. Although the limit normal overload in 70% of cases is distributed between 0 and 2, it can reach −6 and 10 in extreme cases. Considering the future requirements of UAM vehicles for passenger comfort and equipment safety, direct switching is obviously a dangerous and fatal practice.
Under the soft switching design, the 5 s switching mode design can control the limits of the normal overload between 0.45 and 2, and about 90% of them are distributed between 0.9 and 1.1; in other words, the limit of the normal acceleration is within 0.1 to 1 times the gravitational acceleration. Therefore, the soft switching design of the 5 s switching mode can reduce the normal overload by about 80% and the limit of the normal acceleration by about 90% under the condition of 20% model uncertainty.
The 10 s switching mode design can control the limits of the normal overload between 0.92 and 1.08, and about 90% of them are distributed between 0.93 and 1.06, that is, the limit of the normal acceleration is within 0.06 to 0.08 times the gravitational acceleration. Therefore, under the condition of 20% model uncertainty, the soft switching design of the 10 s switching mode can reduce the normal overload by about 55% and the limit of the normal acceleration by about 90% compared with the 5 s switching mode design.
The soft switching design adopted in this paper can reduce the limit of the normal overload by about 17% under the condition of accurate model, and by about 89% under the condition of 20% model uncertainty. Therefore, especially for eVTOL aircraft with inaccurate modeling, there is a higher demand for soft switching, and a smooth switching design is needed to improve passenger comfort and solve the safety hazards caused by mode switching.