## 2 Materials and Methods  
### Object of Research  
The object of the study is a unique drone known as FIXAR-007. This belongs to the VTOL class, although it has fundamental differences from other drones under this classification. As it can be seen in Figure 1, FIXAR-007 combines a multicopter scheme with an airplane scheme, using 4 motors, mounted at the fixed angles \(\phi_{1}-\phi_{4}\) to the symmetry axis at distances \(r_{1}-r_{4}\). This ensures that the motors generate both \(x\) axis thrust and lift. The ratio of the lift force of the wings to that of the motors varies with speed and can be as high as 65% at cruising mode according to the model simulation. For hover mode, the aircraft changes its orientation, starting to bring the propellers to a horizontal position. In this mode, the aerodynamic surfaces operate at extreme angles of attack, creating significant drag that requires compensation from the control system.  
The system described above eliminates all actuators except the motors. This, according to the manufacturer, increases the reliability of the system because of its simplicity. The manufacturer also indicates that using the motors in conjunction with the wing increases maneuverability and payload capacity. This is supported by the fact that the manufacturer of FIXAR-007 declares a flight speed of up to 20 m/s in winds of 12-15 m/s and a payload of up to 2 kg (28% of maximum takeoff weight) with a climb rate of 4 m/s, for a maximum takeoff weight of 7 kg and wingspan of 1.6 m. The system's parameters are described in Table 1. The values in this table, as well as the diagram shown in Figure 1, are approximate and are based on the author's assumptions about the components that could be applied to the described system.  
The object has a very wide range of nonlinear disturbances, mostly caused by aerodynamic forces. In [2], [PERSON] provides detailed analysis of the forces disturbing the VTOL drone of similar characteristics. The paper indicates that aerodynamic forces increase significantly at extreme angles of attack. In the system studied by [PERSON], this occurs during the transition processes between flight and hovering. In the case of FIXAR-007, operation at extreme angles of attack is expected during the entire hover due to the specific design.  
Thus, the object of study is a system with a kinematically simple basis and a nonlinear disturbance varying over a wide range as a function of several variables. The objective of the design is to develop a control system that will control the object over the entire range of disturbances.  
For accurate control of the drone, a control system with precise and controllable characteristics is required. It is necessary to guarantee the consistency and dependability of flight results, which in turn enable the work to be completed with the highest level of accuracy and to ensure the safety of those nearby. It should also be noted that the VTOL FIXAR-007 described in the paper has special properties, including the absence of a distinct mechanical separation between the fast \"airplane\" and \"position-hold\" flight modes. Autopilot systems are typically embedded software for microcontrollers. Examples  
Figure 1: Motor forces kinematics scheme: (**a**) top projection; (**b**) side projection.  
include the Ardupilot [3] and the PX4 [4], which are the most popular software in the hobbyist and civilian professional environments. Autopilots interact with the user via a control station, which can be either an onboard computer performing complicated functions like SLAM or a ground computer performing as a user interface.