Study of Tiltrotor Oscillations in a Vertical Longitudinal Plane

Purpose of research.The article provides mathematical simulation and a study of the motion of the tiltrotor, constructed according to the quadcopter scheme, in transient modes. Under these modes, the moment of transition of the device from the vertical flight to the horizontal flight and back, performeddue to changing the direction of the thrust vector of the rotorsis meant.Theseissuesarenotsufficientlystudied, includingthefactthat, whenperformingsuchmaneuvers, asignificantdeviationofthetiltrotorfromthegiventrajectorycanoccur, andundercertainconditions, thelossofitscontrollabilityandfallcanhappen.Therefore, the purpose of this paper is to study the basic patterns of motion in transient modes and features of control algorithms based on mathematical models describing the controlled motion of small unmanned tiltrotors.

Methods.To solve these problems, methods of theoretical mechanics and mechanics of robots, a matrix approach to the determination of the radius-vectors and their derivatives for the main points of the mechanism pieces were used.The advantages of the matrix method are simplicity, universality ofthe rules for selecting coordinate axes for transition matricesgeneration. Studying the patterns of the motion of the tiltrotor, methods of mathematical simulation of dynamic systems considering the properties of electric drives, kinematics of rotation of the body, algorithms for the formation of control voltages, and external periodic disturbances,were used.When developing control algorithms, methods of the automatic control theory were applied;the control was performed applying software, using PID control allowing minimization ofthe actual and required values of the controlled variable.

Results.It is revealed that in case of the deviation of the rotor,coupled oscillations occur; the range of parameters of the control, at which these oscillations in the transition period are damped and the tiltrotor recovers equilibrium, are determined. Also, there were revealed dependences of deviations of the actual position of the device from the set position in coordinates OH, OY, when the values of the coefficient of differential and proportional components of the ACS control change respectively.The pattern of the change of the diagrams indicates a significant influence of thecontrol coefficients on the pattern of the transition process in terms of the amplitude values of the error and the time of the transition process.

Conclusion. A mathematical model is developed and mathematical simulation of the tiltrotor motion in transient modes is performed.It is shown that the control of the pitch angle, as well as the motion in the vertical plane consist of several loops of proportional-differential control, so it is necessary for each loopto have a circuit that prevents a significant deviation of the controlled parameters from the specified values, at which a stable transition of the tiltrotor to the horizontal position is provided. The parameters of the mean square error minimization are determined.

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