## 4 Simulation Analysis  
In order to verify the feasibility of the strategy proposed in this paper, simulation experiments are carried out. The generalized super-twisting backstepping sliding mode controller based on a generalized super-twisting disturbance observer (GSTDO-GSTBSMC) proposed in this paper is compared with the sliding mode controller based on a nonlinear disturbance observer (NDO-SMC). NDO is the most basic and commonly used disturbance observer. SMC is a commonly used method in the control of electro-hydraulic servo systems in recent years, which is robust regarding systems with external disturbances and parameter uncertainties. Therefore, it is a good choice for comparing with NDO-SMC to see whether the proposed control method is effective. The parameters of the simulated hydraulic motor are shown in Table 1, which are from the real experimental platform. The parameters of the controller designed in this paper are shown in Table 2. The parameters of GSTDOs and GSTBSMC are selected according to dynamic and stability constraints. First, the sinusoidal signal \(\frac{5}{9}\pi\mathrm{sin}\,t\) is selected as the control target, the mismatched disturbance \(d\) is \(0.5\mathrm{sin}\,t+1\) and the matched disturbance \(q\) is \(\cos t\). The tracking results of the above two controllers under the same conditions are shown in Figure 3, and the tracking error curves are shown in Figure 4. It is obvious that GSTDO-GSTBSMC has the better tracking performance. Compared with the initial tracking error of NDO-SMC of \(+0.09\)\(\sim\)\(-0.06^{\circ}\), the initial tracking error of GSTDO-GSTBSMC is \(+0.03\)\(\sim\)\(-0.03^{\circ}\), which can converge to the desired curve in a shorter time of \(0.5\) s, and the error is almost \(0\). In the presence of disturbances, the error of NDO-SMC will increase significantly, and the proposed controller can still guarantee good tracking performance. The control input of the GSTDO-GSTBSMC is normalized as shown in Figure 5 below. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Viscous damping coefficient (\(B\)) & \(40\,(\mathrm{N\cdot m\cdot s})/\mathrm{rad}\) \\ Moment of inertia of the swing motor (\(J\)) & \(0.25\,(\mathrm{kg\cdot m^{2}})\) \\ Displacement of the swing motor (\(D_{m}\)) & \(8.7\times 10^{-5}\,\mathrm{m^{3}/rad}\) \\ Effective oil bulk modulus (\(\beta_{c}\)) & \(7\times 10^{8}\) \\ Total flow gain (\(k_{t}\)) & \(2.16\times 10^{-8}\)\(\mathrm{m^{3}/(s\cdot V\cdot Pa^{1/2})}\) \\ Total controlled volume (\(V_{t}\)) & \(1.4\times 10^{-4}\,\mathrm{m^{3}}\) \\ Pressure of oil source (\(P_{s}\)) & \(4\,\mathrm{MPa}\) \\ Leakage coefficient (\(C_{t}\)) & \(1\times 10^{-12}\)\((\mathrm{m^{3}/s})/\mathrm{Pa}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System Parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline \(\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{4}\) & \(0.1,\,0.1,\,0.1\) \\ \(\gamma_{1},\gamma_{2}\) & \(4,\,50\) \\ \(\mu_{41},\mu_{22},\mu_{41},\mu_{q2}\) & \(1,\,1,\,1,\,1\) \\ \(\rho_{1},\rho_{2}\) & \(1.5,\,1.5\) \\ \(c_{1},c_{2}\) & \(12 Figure 4: Comparison of the tracking error between GSTDO-GSTBSMC and NDO-SMC in Experiment 1. Figure 5: Control input for GSTDO-GSTBSMC u in Experiment 1. Figure 3: Comparison of the tracking results of GSTDO-GSTBSMC and NDO-SMC in Experiment 1. The observation performance of the observers in the above two control methods is shown in Figures 6 and 7. In the experiments, \(x_{2}\), \(x_{3}\) as well as the mismatched disturbance \(d\) and the matched disturbance \(q\) are observed, respectively. From the observation results, it can be seen that the proposed GSTDOs in this paper have better observation performance. In the observation of \(x_{2}\), the initial maximum observation error of NDO reaches +1.15\(--\)1.75 and gradually stabilizes to +0.08\(--\)0.08, while the error of GSTDO is almost 0.