# Sliding Mode Control of Servo Feed System Based on Fuzzy Reaching Law
## 6 Conclusions  
1. A two-degree-of-freedom flexible body model reflecting the dynamics of the servo-feed system was developed, and a conventional exponential sliding mode controller was designed based on this model. For the problems of jitter and poor tracking performance caused by fixed exponential convergence parameters, an adaptive sliding mode control method based on the fuzzy convergence law is proposed and the stability of the method is demonstrated.
2. The overall simulation model of the system is built by Simulink, and the fuzzy convergence law sliding mode controller is simulated and compared with the traditional PID control and sliding mode control. From the simulation results, it can be seen that the optimized controller effectively suppresses the jitter phenomenon, improves the tracking accuracy of the control system, and eliminates the steady-state error in the uniform speed section.
3. The trajectory tracking test of servo feed system with different control algorithms was completed with the help of parallel moving platform. The experimental results show that the sliding mode control algorithm based on the fuzzy convergence law can meet the dynamic and steady-state performance of the servo-feed system better than the PID algorithm and the sliding mode control algorithm, which effectively weaken the jitter in the control signal and reduce the trajectory tracking error of the table.  
Conceptualization T.W. and C.-L.H.; methodology, T.W.; software, T.W. and M.L.; validation, T.W. and Y.Y.; formal analysis, T.W.; investigation, T.W.; resources, C.-L.H.; data curation, T.W.; writing--original draft preparation, T.W.; writing--review and editing, C.-L.H.; supervision, C.-L.H.; project administration, C.-L.H.; funding acquisition, C.-L.H. All authors have read and agreed to the published version of the manuscript.  
This research is funded by Shaanxi Provincial Key Laboratory of Industrial Automation and Shaanxi Provincial Engineering Research Center for Landing Gear and Aircraft Structural Parts Manufacturing and Testing in Universities; Funded by Shaanxi Provincial Two Chain Integration Project, Approval No. 2022 KJ-139; Funded by Shaanxi Provincial Key Industrial Innovation Chain Project, Approval No. 2023-ZDLGY-28; Funded by Shaanxi Provincial Science and Technology Department Key Project \"The key technology research and equipment development of sensor parameter calibration integration\", Grant No. 2020 GY-120.  
Not applicable.  
The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions. The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c} \hline
**Control Method** & **Maximum Tracking Error** & **Reduction/\% Compared to PID, Sliding Mode** \\ \hline PID control & 0.065 & 43.1\% \\ Sliding mode control & 0.054 & 31.5\% \\ Fuzzy convergence law sliding mode control & 0.037 & - \\ \hline \end{tabular}
\end{table}
Table 7: Comparison of experimental results of PID, sliding mode, and fuzzy convergence law sliding mode controllers.