# Single-Parameter-Tuned Attitude Control for Quadrotor with Unknown Disturbance
## 4 Training and Testing in the Simulation
### Performance in the Simulation and Details
#### 4.2.4 Performance of the Full Controller  
The quadrotor attitude controller combined RL with ADRC in this paper has excellent performance, including a fast convergence rate, nearly no overshoot and steady-state error, a high robustness for different platforms, and a strong disturbance rejection ability. In Figure 9, the quadrotors with different CGPs perform well in the step response test with the same external disturbance.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Generation number \(g_{max}\) & 100 \\ Initial standard deviation \(\sigma_{max}\) & 60 \\ Number of sample points \(\lambda\) & 100 \\ Number of offspring points \(\mu\) & 25 \\ Learning rate of evolution path update \(c\) & 0.1 \\ Learning rate of rank 1 update \(c_{1}\) & 0.2 \\ Learning rate of rank \(\mu\) update \(c_{\mu}\) & 0.5 \\ Time step & 0.01 s \\ \hline \hline \end{tabular}
\end{table}
Table 3: CMA-ES training hyper parameters in simulation.  
Figure 8: The performance of the controller with ESO in different episode.  
The disturbance is a square wave, but the final performance compensates for the disturbance completely in a timely manner. The overshoot angle and final steady-state errors are less than 0.001 degrees, which can be ignored. The 30 degrees step-response take less than 0.35 s, which show great convergence rate. In conclusion, the performance in Figure 9 meet our demand for a quadrotor attitude control system. The performance of these quadrotors also indicate that the convergence rate and the disturbance rejection ability of a quadrotor can be improved with a larger CGP value.  
We designed a traditional PID controller for comparison. The PID parameters are also optimized with the CMA-ES algorithm, and this controller can be considered as a near-optimal PID controller. In Figure 10, the PID controller is not as good as that of our RL controller. The control quality of the PID controllers is limited due to the conflict between rapidity and stability, and the RL controller can solve the problem with enough exploration during training. When compared to the traditional PID controller, the RL controller in this paper only has one parameter to tune, which is a great advantage.  
Notably, parameter I in the PID controller converges to 0 during the CMA-ES optimization process. However, the integral controller can also compensate for disturbance over time. We manually set parameter I as a small value in the next experiment. As Figure 11 shows, if the external disturbances  
Figure 10: The performance of automatically tuned traditional proportional-integral-derivative (PID) controller without outer disturbance.  
Figure 9: The performance of the controller in this paper with severe external disturbances.  
are added to the system, then the PID controller is unable to compensate for these errors in a timely manner, and the compensation efficiency of integral controllers is not sufficient.  
In conclusion, the controller in this paper has shown greater advantages than the traditional PID controller in control performance, robustness for system models, and external disturbance.