# Adaptive Deterministic Vibration Control of a Piezo-Actuated Active-Passive Isolation Structure
## 5 Conclusions  
An adaptive active deterministic vibration control approach is applied to a piezo-actuated active-passive isolation structure as part of the Stewart platform. Experimental results illustrate that the piezo-actuated active-passive isolation system with the proposed adaptive controller can effectively suppress the deterministic vibration disturbance. The main contributions of this paper are:  
Figure 16: Time-domain residual vibration with step changes at frequencies [60; 61; 62; 63; 64; 65] Hz \(\rightarrow\)[55; 56; 57; 58; 59; 60] Hz in open loop (black) and closed loop (red) of the adaptive active vibration control system.  
Figure 17: Time-domain \(\hat{\theta}\) of the residual vibration with step changes at frequencies [60; 61; 62; 63; 64; 65] Hz \(\rightarrow\)[55; 56; 57; 58; 59; 60] Hz in open loop of the adaptive active vibration control system.  
Figure 15: Time-domain \(\hat{\theta}\) of the residual vibration with frequency [35-70-105] Hz in closed loop of the adaptive active vibration control system.  
A piezo-actuated active-passive vibration isolation system with active adaptive vibration control and passive vibration isolation is proposed, which integrally combines the advantages of active and passive vibration suppression.  
A Youla (\(Q\)) parameterized adaptive vibration control approach is developed. Firstly, an optimal LQG central controller is designed to shape the band-limited local loop of the closed-loop system. Then the central controller is further augmented to formulate a Youla parameterized outer-loop controller that can be designed to satisfy the internal model principle for the external deterministic disturbances.  
An online adjustable adaptive algorithm is developed to tune the \(Q\) parameter to the desired values so that the interpolation condition for the internal model principle can be satisfied when the external disturbances are unknown and time varying.  
The proposed vibration control method is experimentally evaluated in a piezo-actuated active-passive isolation structure. The experimental results illustrate that the proposed adaptive vibration controller can effectively attenuate the unknown and time-varying deterministic vibrations with a more than 20 dB suppression on average.  
In the future, the proposed control approach will be further tested on the Stewart platform with the multi-DOF piezo-actuated active-passive isolation structure and applied in the satellite vibration isolation platform.  
Conceptualization, Z.W., H.P., F.L. and Y.S.; methodology, F.L., Y.S., F.Q., M.W., J.D. and Y.S.; software, F.L., Y.S. and F.Q.; validation, F.L. and Y.S.; formal analysis, F.L. and Y.S.; investigation, Z.W., H.P., F.L. and Y.S.; resources, Z.W. and H.P.; data curation, F.L. and Y.S.; writing--original draft preparation, F.L.; writing--review and editing, Z.W., H.P. and Y.S.; visualization, F.L., S.Y. and F.Q.; supervision, Z.W. and H.P.; project administration, Z.W. and H.P.; funding acquisition, Z.W. and H.P. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (grant numbers 52075315, 51675321, 91748116, 61922053).  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.