# Research and Verification of Trajectory Tracking Control of a Quadrotor Carrying a Load
## 4 Simulation Verification  
In this paper, the QBall2 quadrotor carrying a load is used as the simulation object. The experimental platform consists of three parts: the hanging flight system composed of the QBall2 quadrotor and the hanging load produced by Quanser, the OptiTrack positioning system and the flight control system of MATLAB/Simulink environment. The experimental platform is shown in Figure 3. Table 1 below shows the parameters of each part of the quadrotor. The selected load is 0.2 kg, and the hanging rope is 0.4 m.  
The actual outdoor wind disturbance nonlinear model is more complicated. Considering the convenience of the research, the outdoor wind disturbance is generally simplified into a simple and practical engineering wind field model, and the complex parts of the model are simplified. The simplified model includes the main influencing factors in the wind field. It can be regarded as a real wind field model. In order to facilitate the research, this paper superimposes the Dryden turbulent wind field model with variable wind direction and the average wind with variable wind speed. The Dryden model is selected for the turbulent wind field. The structure of the model is relatively simple, and the time-frequency spectrum function can be conjugate decomposed. The input signal's Gaussian white noise is generated through the designed shaping filter to generate the numerical model of the atmospheric turbulent wind field to generate the turbulent wind field sequence. The transfer function \(G(s)\) of the shaping filter obtained by splitting and simplifying is: \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(M\) & 1.80 kg & \(I_{x}\) & 0.03 kg\(\cdot\)m\({}^{2}\) \\ \(l\) & 0.20 m & \(I_{y}\) & 0.03 kg\(\cdot\)m\({}^{2}\) \\ \(m\) & 0.2 kg & \(I_{z}\) & 0.04 kg\(\cdot\)m\({}^{2}\) \\ \(L\) & 0.4 m & \(M_{t}\) & 8.80 N \\ \(w\) & 15 rad/s & \(M_{y}\) & 0.40 N \\ \(g\) & 9.81 m/(s\({}^{2}\)) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Quadrotor parameters. Figure 3: Experimental platform of a quadrotor carrying a load system. \[ \begin{cases}\text{G}_{u}(s)=\frac{\sigma_{u}\sqrt{L_{u}/\pi V_{u}}}{(L_{u}/V_{u} )s+1}\\ \text{G}_{v}(s)=\frac{\sigma_{v}\sqrt{L_{v}/\pi V_{v}}}{\Big{(}2L_{v}/\sqrt{3}V_ {v}\ \Big{)}s+1}\\ \text{G}_{w}(s)=\frac{\sigma_{w}\sqrt{L_{w}/\pi V_{w}}}{\Big{(}2L_{w}/\sqrt{3} V_{w}\ \Big{)}s+1}\end{cases}  \tag{51}\]  
Among them, \(\sigma_{i}(i=u,v,w)\) represents the intensity of turbulence, \(L_{i}(i=u,v,w)\) represents the scale of turbulence and \(V_{i}(i=u,v,w)\) represents the flight speed of each axis. The average wind speed is 4.4 m/s, the median value of a level 3 breeze, as weak interference and the median value of level 4 wind, 6.7 m/s, is strong interference. The superimposed wind field model can indicate the change in the wind direction and intensity. Differently, it can be expressed as a real wind field model. During the experiment, the Qball2 quadrotor started to take off and began to ascend. At the fifth second, the quadrotor reaches an altitude of 0.5 m and starts to track according to: \( \begin{bmatrix}X&Y&Z\end{bmatrix} = \begin{bmatrix}2\cos(\frac{\pi}{10}t)&-2\sin( \frac{\pi}{10}t)+2&0.1t\end{bmatrix} \) orbit. At the 15 th second, add the superimposed wind field as interference to the eight-degree-of-freedom mathematical model of a quadrotor carrying a load, and compare two different strengths of interference according to the strength of the wind field. The Simulink simulations are compared with the adaptive integral backstepping algorithm and the backstepping algorithm for these two strength disturbances. The simulation time is set to 35 s. The simulation plots are shown below, the left column is (a) and the right column is (b). The simulation _Bks_ denotes the backstepping algorithm, _Adp_ denotes the adaptive integral backstepping algorithm and _Rbfibks_ denotes the neural network adaptive algorithm based on integral backstepping.