## 2 Differential Step-Scaling Antilion Algorithm
### Algorithm Idea and Specific Steps
It can be seen that, on the test function F1, the DSALO proposed in this paper has a relatively strong improvement in both convergence speed and accuracy. On the test function F2, the PSO algorithm falls into local optimum earlier. ALO can avoid falling into local optimum, but its optimization accuracy is not as good as DSALO. OEALO's effect is better than ALO but still has a disparity with DSALO. On the test function F3, both PSO and ALO fall into local optimum earlier. On the test function F4, DSALO and OEALO have similar performances and both of them are better than PSO and the origin ALO. From these results it can be concluded that DSALO has a significant performance improvement for multimodal functions, and has a similar performance with OEALO for unimodal and composite functions. Although DSALO has a similar effect to OEALO, it has a faster convergence speed. Since the four test functions in this section belong to different types of functions, so it can be shown that the DSALO algorithm has performs well in unimodal functions, multimodal functions, and composite functions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**The Function Name** & **Algorithm** & **Mean Fitness** &
\begin{tabular}{c} **The Standard** \\ **Deviation** \\ \end{tabular} & **Maximum Fitness** & **Minimum Fitness** \\ \hline \multirow{4}{*}{F1} & DSALO & \(6.19\times 10^{-1}\) & \(1.37\times 10^{1}\) & 2.27 & \(1.71\times 10^{-3}\) \\  & ALO & \(4.43\times 10^{1}\) & \(6.83\times 10^{2}\) & \(8.99\times 10^{2}\) & 9.32 \\  & PSO & \(3.73\times 10^{3}\) & \(1.12\times 10^{1}\) & \(6.64\times 10^{3}\) & \(8.93\times 10^{2}\) \\  & OEALO & \(8.34\) & \(2.64\times 10^{1}\) & \(7.38\) & \(1.67\times 10^{-3}\) \\ \hline \multirow{4}{*}{F2} & DSALO & \(5.28\times 10^{-15}\) & \(9.46\times 10^{-3}\) & \(4.89\times 10^{-14}\) & \(8.73\times 10^{-16}\) \\  & ALO & \(2.65\times 10^{-5}\) & \(5.34\times 10^{-2}\) & \(3.92\times 10^{-5}\) & \(1.35\times 10^{-5}\) \\  & PSO & \(1.79\) & \(8.32\times 10^{-2}\) & \(3.17\) & \(1.01\) \\  & OEALO & \(4.74\times 10^{-5}\) & \(7.39\times 10^{-2}\) & \(1.44\times 10^{-5}\) & \(8.39\times 10^{-6}\) \\ \hline \multirow{4}{*}{F3} & DSALO & \(1.06\times 10^{-15}\) & 3.48 & \(3.74\times 10^{-15}\) & \(8.88\times 10^{-16}\) \\  & ALO & \(9.15\times 10^{-2}\) & \(6.83\times 10^{1}\) & \(4.7\times 10^{-1}\) & \(7.63\times 10^{-2}\) \\  & PSO & \(4.36\times 10^{-2}\) & \(5.69\times 10^{-1}\) & \(7.97\times 10^{-2}\) & \(3.94\times 10^{-2}\) \\  & OEALO & \(3.47\times 10^{-9}\) & \(2.04\times 10^{-3}\) & \(2.56\times 10^{-9}\) & \(4.43\times 10^{-9}\) \\ \hline \multirow{4}{*}{F4} & DSALO & \(3.39\times 10^{-4}\) & \(2.71\times 10^{-1}\) & \(3.78\times 10^{-4}\) & \(3.14\times 10^{-4}\) \\  & ALO & \(7.76\times 10^{-4}\) & 1.04 & \(8.67\times 10^{-4}\) & \(6.77\times 10^{-4}\) \\ \cline{1-1}  & PSO & \(5.36\times 10^{-4}\) & \(5.82\) & \(7.08\times 10^{-4}\) & \(4.35\times 10^{-4}\) \\ \cline{1-1}  & OEALO & \(3.57\times 10^{-4}\) & \(3.85\times 10^{-1}\) & \(3.86\times 10^{-4}\) & \(3.03\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test results. Figure 4: Convergence curve of algorithm optimization test function F2. Figure 3: Convergence curve of algorithm optimization test function F1. ## 4 Parameter Optimization of ADRC

In this section, the effectiveness of the DSALO algorithm is illustrated by examples. The controlled object is assumed to be a tank in industrial manufacture. In the parameter optimization problem of a linear active disturbance rejection controller, the structure used is shown in Figure 7:

Figure 5: Convergence curve of algorithm optimization test function F3. Figure 6: Convergence curve of test function F4 optimized by the algorithm.