# Novelty in Intelligent Controlled Oscillations in Smart Structures
## 5 Conclusions  
This study combined H\({}_{2}\) and H-infinity control to achieve complete vibration reduction in intelligent structures. Specifically, in vibration suppression applications, the resilience of the H-infinity controller to parametric uncertainty is emphasized. This studyprovides an excellent example of the benefits of active vibration suppression and robust control in the dynamics of intelligent structures. H-infinity control considers the modeling uncertainties that are difficult to introduce using different techniques. To do this, we used advanced programs written by the authors. The novelty of our work lies in the application of the H-infinity control theory specifically for oscillation damping, combined with its implementation using the finite element method. In our work, we managed to fully suppress the oscillations using the controller H-infinity. The piezoelectric material was inserted along the entire length of the beam. Reliable control systems can benefit from the many advantages of H-infinity control, which minimizes oscillations even when actuator placements vary. Numerical modeling validates that the suggested techniques are successful in lowering vibrations in piezoelectric smart structures. Herein, the benefits of robust control in intelligent structures are explored through the application of H-infinity regulation in both state and frequency domains.  
The following are the key aspects of this work:  
1. H\({}_{2}\) and H-infinity control are combined to achieve comprehensive vibration reduction in smart structures.
2. Demonstrating the resistance of H-infinity control to parametric uncertainties.
3. Highlighting the benefits of robust control and active vibration suppression in intelligent structures.
4. Showing that H-infinity control can minimize oscillations regardless of actuator placement.
5. Validating the effectiveness of the proposed vibration reduction methods through numerical modeling.
6. H-infinity regulation was used to investigate the advantages of strong control in intelligent structures in both state and frequency domains.
7. Results in the frequency domain and time-space domain: The study presents results in both the frequency domain and time-space domain, providing a comprehensive understanding of the system's dynamic behavior and control performance.  
This study significantly advances the understanding and application of control methods in intelligent structures, thereby demonstrating the effectiveness of robust control techniques. In our research, we successfully managed to fully eliminate oscillations by employing the H-infinity control method. To achieve this, we incorporated piezoelectric elements along the entire beam length to ensure comprehensive coverage for optimal control. The modeling and simulation of the system were performed using custom codes, specifically compiled and developed by the authors, to accurately represent the dynamics of the system. A detailed description of the experimental setup, as well as the outcomes of the physical tests, will be presented in future work and publications.  
A.M. and M.P.: software, formal analysis, writing review, and editing; G.E.S.: methodology; A.P.: investigation and software; N.V.: validation. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The data presented in this study are available upon request from the corresponding author.  
The authors are grateful for the support from the Hellenic Mediterranean University and the Technical University of Crete.  
The authors declare no conflicts of interest.