# Sliding Mode Control of Servo Feed System Based on Fuzzy Reaching Law
## 4 Simulation Analysis
From Figures 10 and 11, it can be seen that the maximum tracking error of PID control is 0.541 mm, and there is a steady-state error of 0.046 mm in the stage of uniform travel of the table, and the response to the control voltage signal is also slow. The maximum tracking error of the sliding mode control is 0.101 mm, and there is obvious chattering in the control voltage signal during the table acceleration and deceleration phase. With the fuzzy convergence law sliding mode controller designed in this paper, the voltage signal is significantly smoother and less chattering, and the maximum tracking error is reduced to 0.051 mm, the comparison results are shown in Table 6. Compared with the previous two, the fuzzy convergence law sliding mode controller has better speed and stability, and the position tracking performance of the table is significantly improved. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Control Method** & **Maximum Tracking Error** & **Reduction/\% Compared to PID, Sliding Mode** \\ \hline PID control & 0.541 mm & 90.6\% \\ Sliding mode control & 0.101 mm & 49.5\% \\ Fuzzy convergence law Sliding mode control & 0.051 mm & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of simulation results for PID, sliding mode, and fuzzy convergence law sliding mode controllers. Figure 11: Control voltage signal. Figure 10: Trajectory tracking error of the table. Considering the influence of the interference term on the precise positioning of the table, adding d\({}_{1}\) = d\({}_{2}\) = sin(\(\pi\)t) in the simulation, the simulation results are shown in Figures 12 and 13. From Figures 12 and 13, it can be seen that the maximum tracking error of all three control methods increases after adding the perturbation term to the simulation model. The maximum tracking error of PID control is 1.10 mm, which is 1.054 mm higher than that without disturbance. The maximum tracking error of sliding mode control is 0.615 mm, which is 0.514 mm higher than that without disturbance. However, after the table stops moving, the steady-state errors of 0.304 mm and 0.234 mm exist for the PID control and sliding mode control, respectively, and the tracking accuracy is significantly reduced. Compared with the previous two, the maximum tracking error of the fuzzy convergence law sliding mode control is 0.268 mm, which only increases 0.217 mm. The tracking error curve does not change much from before the disturbance was added, and it can still track the reference trajectory accurately. Combining the above simulation results and analysis, the fuzzy convergence law sliding mode controller designed in this paper can effectively improve the position tracking accuracy of the servo feed system and suppress the chattering phenomenon of the control voltage signal. Its good robustness can effectively eliminate the steady-state error of the system and achieve high accuracy position tracking of the table when there is disturbance in the system. Figure 12: Position tracking error of the table after adding interference. Figure 13: Voltage control signal after adding interference.