# Novelty in Intelligent Controlled Oscillations in Smart Structures
## 3 Results
### Mathematical Modeling Results
The data provided a clear insight into how piezoelectric elements contribute to reducing vibrational movement, highlighting the effectiveness of the smart beam design in mitigating oscillatory behavior through targeted stress generation. Next, sinusoidal loading was applied while utilizing the H-infinity control theory. The results are highly impressive, as there is a noticeable reduction in oscillations. Figure 19 shows the displacement of the structural free end with and without the installed control system. These findings were remarkable, showing a complete reduction in oscillations when the control system was implemented. This highlights the efficacy of the H-infinity control theory in managing and mitigating vibrational movements and ensuring the structural stability and performance of smart structures under sinusoidal loading conditions. A comparison between the controlled and uncontrolled scenarios underscores the significant impact of the control mechanism on achieving optimal structural behavior. Figure 20 shows the displacement of the 3 rd node of the structure with and without the control system. The results are remarkable, revealing the complete elimination of oscillations when the control system is active. This underscores the efficacy of the H-infinity control theory in reducing vibrational movements and ensuring the performance and stability of the smart structure under sinusoidal loading conditions. The comparison between controlled and uncontrolled scenarios highlights the crucial role of the control mechanism in optimizing the structural behavior. The control voltages under sinusoidal disturbances for all the nodes of the smart structures are shown in Figure 21. These voltages are crucial for counteracting disturbances and maintaining structural stability. By applying these control voltages, the system effectively mitigates the impact of sinusoidal disturbances, ensuring optimal performance and reducing oscillatory behavior in smart structures. A detailed analysis of these control voltages highlights their significance in achieving precise and efficient control over structural responses. Figure 21 shows the generated piezoelectric stresses, which are essential for damping oscillations. The data offer a clear understanding of how piezoelectric elements help reduce vibrational movement, emphasizing the effectiveness of smart beam design in mitigating oscillatory behavior through precise stress generation. Figure 18: Control voltages for each smart structure node. The numbers 1, 2, 3, and 4 correspond to the four piezoelectric actuators (voltages) present in the smart beam. Figure 22 presents a Bode diagram of the smart structure, which illustrates the frequency response of the system. This diagram provides critical insight into the gain and phase shift of a smart structure over a range of frequencies. By analyzing the Bode diagram, one can assess the performance and stability of the control system and identify how effectively it mitigates disturbances and responds to various frequencies. The Bode plot  
Figure 19: Smart structure’s free end displacement with (H-infinity) and without control (open loop, OL). Figure 20: Displacement of the 3 rd node of the smart structure presented with (H-infinity) and without control (open loop, OL). highlights key characteristics such as resonant frequencies and bandwidths, which are essential for understanding and optimizing the dynamic behavior of a smart structure. Figure 21: Control voltages for all the nodes of the smart structures under sinusoidal disturbances. The numbers 1, 2, 3, and 4 correspond to the four piezoelectric actuators (voltages) present in the smart beam. Figure 15:0 The Bode diagram of the smart structures. \(\Upsilon\) axis is the magnitude (dB).