Synthesis of a polynomial matrix controller that takes into account the inertia of the actuator

In this paper, we consider the synthesis of a quadcopter orientation control system with a small change in rotation angles (near hovering), taking into account the inertia of the propeller-motor groups. The feedback linearization of the orientation subsystem is shown, taking into account the inertia of the propeller groups. The controller is designed using a polynomial matrix synthesis method that provides a given location of the poles of the closed system. To evaluate the results, a comparison with a controller that does not take into account the inertia of the propeller-motor groups is made. Orientation and positioning control of a multirotor vertical takeoff and landing unmanned aerial vehicle (UAV) in space is inextricably linked with the formation of a motion control vector consisting of a combination of thrusts and aerodynamic moments created by each propeller-motor group. The accuracy and speed of formation of the motion control vector significantly affects the positioning and orientation errors of the UAV. In most studies devoted to the synthesis of UAV control systems, a motion control vector is used without taking into account the dynamics of the propeller-motor groups, which in some cases forces us to reduce the speed of the control system. It is shown that the increase in the control system performance can be limited by inertia, since oscillation occurs, and with further attempts to increase the performance by shifting the desired poles of the characteristic polynomial further into the negative region, the control system becomes unstable. To solve this problem, it is proposed to take into account the inertia of the propeller-motor group. It is shown that due to this, it is possible to increase the performance of the control system. It is also shown that the feedback linearization of the quadcopter orientation subsystem is also affected by the inertia of the propeller-motor group, so it is proposed to perform feedback linearization taking into account the inertia.