# Control Methods Comparison for the Real Quadrotor on an Innovative Test Stand
## 3 Experimental Setup and Results
### Evaluation of Controllers
#### 3.4.5 Controllers Comparison  
Various quality indicators were chosen to discuss the efficiency of the control algorithms, such as the integral of absolute error \(I_{AE}\), integral of absolute desired torque \(I_{AM}\) and maximum absolute variation of the quaternion \(O_{q}\). The performance of all attitude controllers is summarized in tables that can be found in Appendix A. Chosen quality indicators are identified separately for each section of the desired sequence. Table 4 shows the total number of the best and also the worst performances related to the particular quality indicator. The best value of each quality indicator for entire sequence is indicated by green color and the worst value is indicated by red color. The evaluation of the performed sequences of chosen controllers can be done in two different ways. The first approach is focused mainly on the reaching the desired orientation in the shortest possible time omitting the importance of the efficiency of power supply. The integral of total absolute quaternion error and the maximal absolute quaternion variation are decisive quality indicators used in this approach. The backstepping controller indicates the smallest value of the sum of all parts of the \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**PD**} & \multicolumn{2}{c}{**LQR**} & \multicolumn{2}{c}{**Backstepping**} \\ \cline{2-7}  & **Best** & **Worst** & **Best** & **Worst** & **Best** & **Worst** \\ \hline \(I_{AE}\) & **—** & & & & **—** & \\ \(I_{AM}\) [N:m\(\cdot\)s] & & & **—** & & **—** & \\ \(I_{AEa}\) & 5 & 7 & 1 & 5 & 12 & 6 \\ \(I_{AEx}\) & 6 & 5 & 9 & 2 & 3 & 11 \\ \(I_{AEy}\) & 4 & 5 & 10 & 2 & 4 & 11 \\ \(I_{AEz}\) & 3 & 6 & 5 & 6 & 10 & 6 \\ \(I_{AMx}\) [N:m\(\cdot\)s] & 5 & 8 & 11 & 3 & 2 & 7 \\ \(I_{Amp}\) [N:m\(\cdot\)s] & 5 & 7 & 9 & 1 & 4 & 10 \\ \(I_{AMz}\) [N:m\(\cdot\)s] & 7 & 0 & 9 & 4 & & 14 \\ \(O_{q\alpha}\) & 13 & 3 & 13 & 2 & 7 & 9 \\ \(O_{q\alpha}\) & 6 & 4 & 11 & 4 & 5 & 11 \\ \(O_{q\beta}\) & 6 & 7 & 13 & 2 & 5 & 11 \\ \(O_{qz}\) & 10 & 4 & 11 & 7 & 7 & 9 \\ Sum & 56 & 70 & 102 & 38 & 61 & 105 \\ Total & 3 & 2 & 8 & 2 & 2 & 8 \\ \hline \end{tabular}
\end{table} 
Table 4: Overview of quality indicators of controllers’ (\(I_{AE}\)—the integral of absolute error, \(I_{AM}\)—the integral of absolute desired torque, \(O_{q}\)—the maximum absolute variation of the quaternion). Figure 19: Desired torques of the quadrotor when using backstepping controller. quaternion error and it also shows the best control around \(z\) axis. However, when it comes to control around the \(x\) and \(y\) axes this controller exhibits the worst results. The best attitude control around the \(x\) and \(y\) axes was achieved by LQR controller. The PD controller shows average performance when only the integral of total absolute quaternion error and maximal absolute quaternion variation as quality indicators is considered. To sum up, the LQR attitude controller is considered to be the best option when taking into account only the importance of reaching the desired quaternion as fast as possible. The second approach is focused not only on reaching the desired orientation, but it also takes into account the efficiency of the power supply. The second approach expands the quality indicators from the first approach with the total absolute desired torque. The most energy efficient controller was the LQR controller, which consumed the least energy during the whole sequence. When the movement is divided into various rotations related to the particular axis, the LQR controller is the most efficient controller around the \(x\) and \(y\) axes, while around \(z\) axis the most efficient controller is the PD controller. The backstepping controller consumes the most from power supply among implemented controllers. When taking into account the energy consumption and also the quaternion error, the best performance exhibits the LQR controller and the worst performance shows the backstepping controller. As in the previous case, the PD controller exhibits average performance.