The mathematical model of UAV vertical take-off and landing

This paper aims to present a mathematical model of the dynamics of the unmanned aerial vehicle (UAV) vertical take-off and landing (VTOL). It will be used to develop control laws to a multirotor that is inherently unstable. Also, the model will be used to design algorithms to estimate the attitude of an object.

The physical model of UAV assumes that it is a rigid body with six degrees of freedom acted by forces generated by the propellers, motors, aerodynamic forces, gravity and disturbance forces. The mathematical model was described by differential equations. However, drive system (propeller, BLDC motor and BLDC motor controller) was described by six transfer functions. These transfer functions were demarcated with Matlab/Simulink identification toolbox from data received from a specially designed laboratory stand. Moments of inertia of the platform have been analytically determined and compared with empirical results from the pendulum. The mathematical model was implemented in Matlab/Simulink.

The paper confirms the need of designing mathematical models. Moreover, mathematical models show that some parts of the object are better to be replaced by experimental results than by equations, which is proved by the data. The paper also shows advantages of using Matlab/Simulink. What is more the simulation of the model proves that multirotor is an unstable object.

The test results show that drive units are strongly dependent on ambient conditions. An additional problem is the different response of the drive set to increasing and decreasing the control signal amplitude. Next tests will be done at different temperatures and air densities of the environment, also it is need to explore drag forces.

The mathematical model is a simplification of the physical model expressed by means of equations. The results of simulation like accelerations and angular rate are noise-free. However, available sensors always have their errors and noise. To design control loops and attitude estimation algorithms, there is a need for identification of sensors’ errors and noise. These parameters have to be measured.

The paper describes a solution of correct identification of drive unit, which is a main component of the UAV.