## 3 Control of the APIVI Platform
### Simulation of APIVI Platform  
In order to verify the effectiveness of the controller of APIVI platform, single-frequency sinusoidal excitation signals with frequencies of 5 Hz, 40 Hz, 80 Hz, and 150 Hz were applied to the lower platforms of APIVI platform. The acceleration response at the upper platform centroid is shown in Figure 9. The simulation results show that when the excitation signal frequency is 5 Hz, the APIVI platform demonstrates no isolating effect no matter whether the controller is on or off. When the excitation signal frequency is 40 Hz, passive vibration isolation amplifies the excitation signal. With active control, the system can attenuate the excitation signal, indicating that 40 Hz has entered the effective vibration isolation band of active control. When the frequency of the excitation signal is 80 Hz, the passive control demonstrates no isolating effect. With active control, the effective attenuation of the excitation signal by the active and passive integrated control can reach 60%. When the frequency of the excitation signal is 150 Hz, there is little difference between the passive control and the active and passive integrated control, the vibration attenuation reaches 80%, and the passive control in the high-frequency region plays a major role. Passive isolation fails to suppress low-frequency vibrations. In the frequency band of \(\left[\sqrt{2}\omega_{n}/2,\sqrt{2}\omega_{n}\right]\), the vibrations are amplified. There is a conflict between resonance suppression and high-frequency suppression. The passive vibration isolation performs well in the high-frequency region. The simulation results verify the superiority of the proposed APIVI platform in vibration isolation performance, the active control of the isolation action, and the high-frequency vibration isolation performance of the passive structure itself is excellent, which solves the problem where the effective frequency band of active control is limited by the bandwidth and power of the piezoelectric ceramics. A composite single-frequency sinusoidal excitation signal composed of 20 Hz, 80 Hz, and 180 Hz was applied to the lower platform of the APIVI platform, and the acceleration response at the centeroid of upper platform was obtained, as shown in Figure 10. APIVI platform can effectively reduce vibration transmission. A random excitation signal was applied to the lower platform of the APIVI platform. The acceleration response at the centeroid of upper platform is shown in Figure 11. With  
Figure 10: The time domain vibration isolation effect of the six-dimensional orthogonal vibration isolation platform under a vertical composite-frequency sine signal disturbance. Figure 9: The vibration isolation effect of the APIVI platform under vertical sine signal disturbance with different frequencies: (**a**) 5 Hz; (**b**) 40 Hz; (**c**) 80 Hz; and (**d**) 150 Hz. the hybrid active and passive control, the APIVI platform under the integrated active-passive control can significantly and effectively attenuate the random disturbances, with the vibration attenuation reaching more than 80%. The vertical sweep signal was applied to the lower platform of APIVI platform for comparing the transmission characteristics of the system with different control strategies, as shown in Figure 12. When the controller is off, APIVI platform presents the transmission characteristics of a passive vibration isolation system, and the first-order resonance peak appears at 73 Hz. The effective isolation frequency band of passive vibration isolation ranges above 105 Hz. PID controller with appropriate feedback coefficient can attenuate the first-order resonance peak of the system, but the high-frequency vibration isolation effect is slightly worse. The vibration isolation performance of H\({}_{\infty}\) robust controller is obviously better at resonant peak or high-frequency band. \(\upmu\) synthesis-based robust controller performs the best vibration isolation effect in middle, resonant, and frequency.