# Novelty in Intelligent Controlled Oscillations in Smart Structures
## 3 Results
### Mathematical Modeling Results  
Figures 14 and 15 compare the rotations and translations of the nodes in the smart architectures with and without control, respectively. This analysis highlights the significant impact of the control system. Without control, the nodes exhibited substantial rotational movement, indicating a lack of stability and an increased susceptibility to oscillations. Conversely, the rotations were markedly reduced with the control system in place, demonstrating the effectiveness of the system in enhancing stability and minimizing unwanted movements. This comparison underscores the critical role of the control mechanism in retaining the structural integrity and performance of the smart structures. In Figure 14, the four nodes of the smart structure rotations are depicted for three different scenarios: with H\({}_{2}\) control, Heo (H-infinity) control, and without any control. The results clearly show that Heo control provides the best performance, as the rotations are nearly zero. This indicates that the Heo control method is highly effective in minimizing rotational movement systems [1; 6; 7; 25; 26; 27; 29; 30; 31; 35]. Similarly, Figure 15 illustrates the displacements of the four smart structure nodes under the same three scenarios: with H\({}_{2}\) control, with H\(\infty\) control, and without control. The comparison reveals that Heo control yields a superior outcome. The displacements were almost zero when the Heo control was applied, demonstrating its effectiveness in minimizing positional deviations. Thus, the Heo control proved to be the most effective method for reducing both rotations and displacements in smart structures. Figure 14: Comparing the nodes’ rotations in the smart structures both with and without control. The results are then provided in detail for the static loading of 12 N at the free end of the smart structure. In Figures 16-18, a concentrated force (12N) is applied to the edge of the carrier, and the displacement at the edge of the carrier quickly stabilizes at 0.015 sec. This shows the very good operation of the model. In addition, what is also the goal of the specific problem is achieved, i.e., a reduction in oscillation since with the blue line, we have a result with control where I is a reduction in distortion, while with the green line, I is the open loop in which the oscillation is much greater. Figure 16 illustrates the displacements for all the nodes of the smart beam, where the H-infinity control criterion is employed. The results are highly impressive because the displacements were negligible. This illustrates how the H-infinity control strategy effectively reduces the displacements while maintaining the stability and structural integrity of the smart beam under static loading scenarios. The near-zero displacement highlights the superior performance and robustness of the control system [6; 7; 26; 30; 31]. Figure 17 depicts the rotations for all the nodes of the smart beam using the H-infinity control criterion. The findings were exceptionally impressive as the displacements were nearly imperceptible. This underscores the efficacy of the H-infinity control approach in reducing displacements to a minimum, thereby ensuring the structural integrity and stability of the smart beam under static loading scenarios. The minimal rotations for all the nodes of the smart beam highlight the superior performance and robustness of the implemented control system. Figure 15: Analyzing and contrasting the smart structure node displacements with and without control. Figure 16: Results of displacements with and without control when applying static loading at the beam’s free end. Figure 17: Results of rotations with and without control when applying static loading at the beam’s free end. The results for the four smart beam nodes are shown in Figure 18. This figure shows the piezoelectric stresses produced, which are necessary for damping oscillations.