## 5 Simulation Analysis
When the flexible vibration suppressor proposed in this paper is closed and controlled by IFSM-NV, the amplitude of the base gradually increases from 0.015 m and diverges beyond the actual value at 7 s. When ISM-NV control is adopted, the amplitude of the base reaches 0.05 m at 2.5 s, and the vibration tends to be irregular and uncontrollable. From Figures 7 and 8, the IFSM and ISM controllers can suppress the amplitudes of the 1 and 2 joints of the fully flexible Space robot to within 0.2 rad and 0.05 rad, respectively. Using IFSM-NV controller, the amplitude of 1 joint reaches 0.5 rad at 4.5 s, and the amplitudes of 1 joint and 2 joint diverge around 7 s. With the IFSM-NV controller, both joint 1 and joint 2 vibrated violently at 2.5 s and finally caused control failure. The simulation results show that the amplitude of the base truss guide rail is about 0.015 m and the amplitude of the base gradually increases from 0.015 m to 0.015 m. The amplitude of the base gradually increases from 0.015 m and the amplitude of the base gradually increases from 0. From Figures 9 and 10, it can be seen that by using IFSM and ISM controllers, the first-order mode of the link B\({}_{1}\) can be suppressed within 2 mm and 5 mm, respectively, and the second-order mode of the link B\({}_{1}\) can be suppressed within 0.05 mm and 0.4 mm, respectively. If the flexible vibration suppressor proposed in this paper is closed, under the control of IFSM-NV, the initial amplitude of the first mode of the link B\({}_{1}\) is 0.01 m, reaching 0.4 m at 7 s, and the initial amplitude of the second mode of the link B\({}_{1}\) is 0.2 mm, reaching 0.15 m at 7 s. Under ISM-NV control, the initial amplitude of the first mode of the link B\({}_{1}\) is 0.02 m, reaching 0.04 m at 2 s, and the initial amplitude of the second mode of the link B\({}_{1}\) reaches 6 mm at 2.7 s. From Figures 11 and 12, it can be seen that by using IFSM and ISM controllers, the first-order mode of the link B\({}_{2}\) can be suppressed within 1 mm and 2 mm, respectively, and the second-order mode of the link B\({}_{2}\) can be suppressed within 0.  
link B\({}_{2}\) is 2 mm and reaches 0.6 m in 7 s, the initial amplitude of the second-order mode of the link B\({}_{2}\) reaches 0.06 m at 7 s. Under ISM-NV control, the first modal amplitude of the link B\({}_{2}\) is 0.04 m, and the initial amplitude of the second modal of the link B\({}_{2}\) reaches 0.04 m at 2.7 s. The simulation results show that the flexible vibration suppressor proposed in this paper can suppress the flexible vibration of the flexible link of the manipulator. In addition, in order to compare and verify the robustness of IFSM to external interference, external disturbance is introduced to make \(\mathbf{d}=\text{diag}(5,5,5)\). Simulations were carried out separately using IFSM and ISM to observe the error convergence rates of the two control algorithms in the presence of the effect of \(\mathbf{d}\). Error conversion rates are calculated by \(\log\|\mathbf{q}-\mathbf{q}_{\text{d}}\|\), the unit is \(\log(\text{rad})\). Therefore, the smaller the error convergence rate, the higher the control accuracy of the controller. From Figure 13a, it can be seen that the total error convergence rate of the fully flexible space robot base, links and joint is within \([-2.5,\,-1.6]\), when no external perturbation d is considered under the IFSM controller condition, and within \([-2.5,\,-1.6]\) when the effect of the perturbation d is considered, the disturbance d can hardly affect the system control accuracy under IFSM control. From Figure 13b, it can be seen that the total error convergence rate of the fully flexible space robot base, links and joints is within \([-1.7,\,-1.6]\) when the external disturbance d is not considered under the ISM controller condition; when the effect of the disturbance d is considered, the error convergence rate is within \([-1.5,\,-2]\) and the control accuracy is significantly reduced, the disturbance d significantly degrades the system control accuracy under ISM control.