## 4 Simulation Results  
The actual parameters of the electrohydraulic lifting mechanism of the launcher system can be observed from Table 1. The lifting mechanism is drove by the hydraulic cylinder. The function is defined as \(S_{f}(x_{2})~{}=~{}2\arctan(1000x_{2})/\pi\) The sample time is set as 0.5 ms. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(m\) (kg) & 10,000 & \(B\) (N\(\cdot\) m \(\cdot\) s/rad) & \(2.5\times 10^{5}\) \\ \(J\) (kg \(\cdot\) m\({}^{2}\)) & \(1.5\times 10^{5}\) & \(A_{f}\) (N\(\cdot\) m) & \(3\times 10^{3}\) \\ \(P_{s}\) (Pa) & \(2.1\times 10^{6}\) & \(k_{1}\) (m\({}^{4}\)/(s\cdot\) V \(\cdot\) v \(\sqrt{\text{N}}\)) & \(7.937\times 10^{-8}\) \\ \(P_{r}\) (Pa) & 0 & \(\beta_{c}\) (Pa) & \(7\times 10^{8}\) \\ \(A_{1}\) (m\({}^{2}\)) & \(3.14\times 10^{-2}\) & \(C_{t}\) (m\({}^{5}\)/(s\cdot\) N) & \(9.6\times 10^{-13}\) \\ \(A_{2}\) (m\({}^{2}\)) & \(1.6\times 10^{-2}\) & \(d_{1}\) (m) & 1.6 \\ \(V_{01}\) (m\({}^{3}\)) & \(3.1416\times 10^{-4}\) & \(d_{2}\) (m) & 2 \\ \(V_{02}\) (m\({}^{3}\)) & \(3.04\times 10^{-2}\) & \(d_{3}\) (m) & 3.5 \\ \(g\) (m/s\({}^{2}\)) & 9.8 & \(d_{4}\) (m) & 3 \\ \(\theta_{0}\) (rad) & 0.2648 & \(\beta_{0}\) (rad) & 0.2618 \\ D (mm) & 200 & \(d\) (mm) & 140 \\ \(L_{c}\) (mm) & 1900 & & \\ \hline \hline \end{tabular} Where \(D\) and \(d\) stand for the cylinder diameter and the piston rod diameter, respectively; \(L_{c}\) stands for the cylinder stroke.  
\end{table} 
Table 1: Physical parameters of the EHA system. Four controllers are compared to validate the effectiveness of the developed controller in the article. (1) NRC: The nonlinear robust controller is proposed in Section 3, whose controller parameters are provided by \(k_{1}=100\), \(k_{2}=50\), \(k_{2s}=10\), \(k_{3}=50\), \(k_{3s}=30\), \(c_{1}=10\) and \(c_{2}=30\). In addition, \(b_{1}(t)=b_{2}(t)=\frac{1}{t^{2}+500}\). (2) FLC: This is the feedback linearization controller introduced in [11], whose control law is  
\[\left\{ \begin{array}{l}x_{3d}\ =\ \Big{(}\frac{2\chi_{c}}{\delta x_{1}}\Big{)}^ {-1}(x_{3 da}+x_{3 ds})\\ x_{3 da}\ =\ mgd_{4}\cos(\beta_{0}+x_{1})+A_{f}S_{f}(x_{2})+Bx_{2}+j\dot{x}_{2d}- \xi_{1},x_{3 ds}\ =\ -k_{2}\xi_{2}\\ u\ =\ \frac{(u_{a}+u_{s})}{\varphi_{1}},u_{a}\ =\ \varphi_{2}+\dot{x}_{3d}- \frac{\partial x_{s}}{\partial x_{1}}\xi_{2},u_{s}\ =\ -k_{3}\xi_{3}\end{array} \right. \tag{30}\]  
The deference between NRC and FLC is that the nonlinear feedback terms are not introduced into FLC. That is, \(k_{2s}=0\) and \(k_{3s}=0\) in FLC. The other control parameters are same as NRC. (3) RC: This is the robust controller, whose control law is  
\[\left\{ \begin{array}{l}x_{3d}\ =\ \Big{(}\frac{\partial x_{s}}{\partial x_{1}} \Big{)}^{-1}(j\dot{x}_{2d}-k_{2}\xi_{2})\\ u\ =\ \frac{(\dot{x}_{3d}-k_{3}\xi_{3})}{\varphi_{1}}\end{array} \right. \tag{31}\]  
The deference between FLC and RC is that the model-based compensation terms are not introduced into RC. The other control parameters are the same as FLC. (4) PI: This is a proportional-integral controller that is widely applied in practice. The controller parameters are set as \(k_{p}=10\) and \(k_{i}=10\), in which \(k_{p}\) and \(k_{i}\) stand for proportional gain and integral gain, respectively. **Case 1:** First the reference tracking signal presented in Figure 3 is employed to test the control performance of the developed contr ol method. As seen from Figure 3, the reference tracking signal is a point-point tracking trajectory, whose velocity and acceleration values are at most \(2^{o}/\)s and \(2^{o}/\)s\({}^{\text{2}}\), respectively. The tracking trajectory of NRC can be found in Figure 3. The corresponding control errors of the four controllers is collected in Figure 4. It is easy to observe that NRC proposed in this paper can attain the best control performance among the four controllers in terms of the transient and steady-state tracking performance.