# Sliding Mode Control of Electro-Hydraulic Position Servo System Based on Adaptive Reaching Law
## 4 Simulation Analyses  
Some parameters of the electro-hydraulic position servo system studied in this paper are shown in Table 1, the parameters of the adaptive reaching law SMC algorithm are shown in Table 2, and the parameters of the exponential reaching law SMC algorithm are shown in Table 3. The nonlinear electro-hydraulic position servo system model was used with AMESim in the AMESim/Simulink co-simulation. The sampling time in the simulation was 0.001 s.  
Figure 3: AMESim/Simulink co-simulation block diagram. Figure 2: Schematic diagram of SMC system based on adaptive reaching law. The paper uses the co-simulation function of AMESim and Simulink to simulate the system. Giving a sinusoidal signal, the SMC algorithm based on the exponential reaching law and the SMC algorithm based on the adaptive reaching law were used for the simulation and the obtained curves were compared and analyzed. Figure 4 is the tracking characteristic curve of the SMC system based on the exponential reaching law, and Figure 5 is the tracking characteristic curve of the SMC system based on the adaptive reaching law. Compared with the SMC algorithm based on the traditional exponential reaching law, the SMC algorithm of the adaptive reaching law has a great improvement in the control accuracy, and the following effect is obviously better than that of the SMC system using the traditional exponential reaching law algorithm. As shown in Figure 6, compared with the exponential reaching law SMC algorithm, the adaptive reaching law SMC algorithm can adaptively adjust the system control variables, so that the final displacement tracking effect is better. \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Parameter** \\ \hline Maximum stroke of hydraulic cylinder \(L\) & 0.4 m \\ Hydraulic cylinder inner diameter \(D\) & 63 mm \\ Piston rod diameter \(d\) & 45 mm \\ Servo valve rated voltage \(u\) & 10 V \\ Servo valve flow \(q\) & 60 L/min \\ System working pressure \(p_{s}\) & 15 MPa \\ Oil return pressure \(p_{0}\) & 0 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of electro-hydraulic position servo system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Parameter** \\ \hline System open loop gain \(K_{\text{sys}}\) & 1.86 \\ Parameter \(c_{1}\) & 29,258 \\ Parameter \(c_{2}\) & 68.8 \\ Parameter \(\xi\) & 5 \\ Parameter \(\xi\) & 20 \\ Valve-controlled cylinder natural Frequency & 296 rad/s \\ Valve-controlled cylinder damping ratio & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of adaptive reaching law SMC algorithm. \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Parameter** \\ \hline System open loop gain \(K_{\text{sys}}\) & 1.86 \\ Parameter \(c_{1}\) & 29,258 \\ Parameter \(c_{2}\) & 68.8 \\ Parameter \(\xi\) & 5 \\ Parameter \(\xi\) & 20 \\ Valve-controlled cylinder natural Frequency & 296 rad/s \\ Valve-controlled cylinder damping ratio & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of exponential reaching law SMC algorithm. Figure 4: Displacement tracking trajectory of SMC algorithm using exponential reaching law. Figure 5: Displacement tracking trajectory of SMC algorithm using adaptive reaching law. A bounded white noise interference signal was added to the given sinusoidal signal, and the exponential reaching law and the adaptive reaching law SMC controllers were used for the simulation, respectively. It can be seen from Figures 7 and 8 that the displacement tracking effect of the adaptive reaching law SMC algorithm is obviously better than that of the exponential reaching law SMC algorithm, after being disturbed. The proposed adaptive reaching law SMC controller improves the robustness of the system. Figure 6: Curves of control variables under different reaching laws. Figure 7: Displacement tracking curve of adaptive reaching law SMC algorithm after disturbed signal.