Synthesis of Multicopter Stabilizing Control

The paper is devoted to the problem of analytical synthesis of control that stabilizes the position in space of an unmanned aerial vehicle (UAV) of a multi-rotor type a multicopter. An analysis of UAVs of this class has been carried out, features, place and differences among UAVs of various design schemes have been determined. The type of spatial mathematical model describing the translational and rotational motion of a multicopter is substantiated, which is considered to be  a model of a four-rotor UAV – a quadrocopter, since such UAVs are widespread and have the basic properties that are inherent in such aircraft devices. A transition was made to a linear simplified model of UAV movement by linearization and justification of the main assumptions made during the linearization of the mathematical model. The problem of determining stabilizing control is reduced to the classical form of analytical synthesis of control that minimizes a given integral quality functional. A feature of the considered quality functional is the justification of normalization coefficients, which make it possible to reduce the summable integrands of various physical natures to a dimensionless form and take into account the real  restrictions imposed by the technological and design features of a particular UAV on its maneuvering characteristics.  As a result of the analytical solution of the problem, expressions for optimal control have been obtained, which are changes  in time in the rotation speeds of the opposite quadcopter propellers, allowing to stabilize the position of the UAV in space, compensating for external undesirable effects on the UAV in the form of gusts of air flow or other factors. The executed computer simulation has confirmed the efficiency of the developed methodology. The given graphical dependences of the change in time of variables characterizing the control action and movement of the UAV in space clearly show the type of transient processes and allow us to evaluate the maneuver-ring capabilities of the UAV and formulate the basic requirements for its structural elements at the preliminary design stage.

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