## 5 Conclusions  
In this paper, a novel data-driven model-free adaptive nonsingular fast integral terminal sliding mode control algorithm is proposed to solve the problems of difficult to establish an accurate model and unknown disturbance in a WWTP. The proposed method doesn't need a precise mathematical model and prior knowledge of WWTP, only real-time 1/O data, and has fast error convergence, nonsingular control law, and global robustness. Furthermore, the error convergence and BIBO stability of the closed-loop system have been proven through theoretical analysis. The simulation results in three cases indicate that compared with other control strategies, the MFA-NFITSMC has a higher control accuracy and stronger robustness in the control of WWTP and can effectively suppress the impact of unknown interferences on the WWTP system. In addition, the proposed method provides a new solution for the tracking control problem of a class of nonlinear slow time-varying and difficult to establish models for complex systems under multiple operating conditions.  
Although the proposed method MFA-NFITSMC has achieved excellent results for the control of WWTPs, there are still some problems that need to be addressed urgently. For example, the selection of controller parameters was only obtained through a large number of experiments and further research work is focused on optimizing controller parameters and designing controllers for MIMO systems.  
Conceptualization, Supervision, B.X.; Methodology, Writing--original draft, Z.W.; Project administration, Z.L.; Writing--Review & Editing, Y.W.; Software, Validation, Y.C. All authors have read and agreed to the published version of the manuscript.  
Figure 8: \(S_{O,5}\) and \(S_{NO,2}\) tracking effect in rainy weather. (**a**) Control effect of \(S_{O,5}\) and \(S_{NO,2}\); (**b**) Tracking error of \(S_{O,5}\) and \(S_{NO,2}\).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Control Strategy**} & \multicolumn{3}{c}{\(S_{O,5}\)} & \multicolumn{3}{c}{\(S_{NO,2}\)} \\ \cline{2-7}  & _ISE_ & _IAE_ & _Dev\({}_{max}\)_ & _ISE_ & _IAE_ & _Dev\({}_{max}\)_ \\ \hline MFA-NFITSMC & 0.00058 & 0.0013 & 0.0128 & 0.0016 & 0.0782 & 0.0571 \\ ASMC [9] & 0.00493 * & 0.035 * & 0.49 * & 0.00527 * & 0.046 * & 0.42 * \\ SMC [9] & 0.00552 * & 0.030 * & 0.61 * & 0.00562 * & 0.046 * & 0.44 * \\ PID & 0.0143 & 0.072 & 0.74 & 0.0081 & 0.056 & 0.53 \\ \hline \hline \end{tabular}
* The data originates from the corresponding articles.  
\end{table}
Table 5: The comparison of the performance of different control algorithms in Case 3.  
**Funding:** This research was funded by Research on the National Key Research and Development Program of China, Grant Number: 2019 YFA0708304 and the Strategic Cooperation Technology Projects of CNPC and CUPB, Grant Number: ZLZX2020-03 and the National Natural Science Foundation of China, Grant Number: 52374015.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
**Acknowledgments:** Acknowledgements to [PERSON] for providing funding acquisition, data calculation, and contributions during the article revision process. Acknowledgements to [PERSON] for providing funding for this project. Acknowledgements to [PERSON] for providing data support for this project. Acknowledgements to [PERSON] for analyzing on-site data. Acknowledgements to [PERSON] for investigating the data required in the experiment.  
**Conflicts of Interest:** The authors declare no conflict of interest.