## 4 Discussion  
The integration of active control, such as \(\mu\)-analysis technologies, into smart structures has been the subject of the present work [4; 36; 40]. When utilizing the Hifoo controller in tandem with non-parametric and non-convex optimization methodologies, it ensures that the control output does not surpass operational constraints despite the desirable characteristics of low steady-state errors, rapid recovery, minimal maximum uplift, and reduced vibration, as outlined in [34; 35; 45]. The steps were as follows: 1. Determining the damping and stiffness. Mass and matrices using the finite element method. 2. Introduction of electrical charge and mechanics to the dynamic oscillation (Equation (3)). Application of control theory for modeling displacement results for finite element models with and without robust control. 4. Derivation of stress results using piezoelectric patches as actuators. 5. Decreasing the controller rank leads to a reduction in the computational requirements of the model. Remarkably, the controller demonstrated effective operation even with a significantly lower system degree. Robust stabilization requires a self-stabilizing controller, whereas simultaneous stabilization requires the identification of a single controller. There are particular cases of multi-objective robust control challenges for stabilizing multiple plants [46; 47; 48; 49]. Many of the current techniques and heuristics employed to address these issues often result in excessively high-order controllers. The results show the significant benefits of the proposed model and approach, and the control behavior of the beam aligns with our expectations. \(\mu\)-Analysis is a technique used for analyzing and designing controllers for linear time-invariant systems. It deals with the frequency domain and helps to assess the robustness and performance of a control system. The goal is to find a controller that can handle uncertainties and variations in the system while maintaining stability and desired performance. By contrast, Hifoo control is a method used in control theory that involves the design of controllers to achieve optimal performance in the presence of disturbances and uncertainties. Hifoo controllers are designed to minimize the impact of disturbances and uncertainties on the system output while meeting certain performance specification bounds [7; 18; 19; 45]. In essence, \(\mu\)-analysis is a broader technique for system analysis and controller design, while the Hifoo control is a specific approach within that broader framework, focused on  
Figure 10: The four nodes of the beam rotations with and without \(\mu\)-analysis: displacement. achieving optimal performance in the presence of uncertainties. Control theory uses synthesis approaches to create controllers that provide guaranteed stability [48; 49]. In the context of smart structures, \(\mu\)-synthesis is a valuable tool for designing robust controllers that can effectively control the behavior of these structures, particularly when faced with uncertainties, variations, or disturbances. Smart structures typically involve the integration of sensors and actuators to respond actively to external stimuli and optimize their performance. In this context, \(\mu\)-synthesis can be applied in the context of smart structures, which are often subjected to external disturbances such as wind, vibrations, or other environmental factors. We use \(\mu\)-synthesis to design controllers that can reject these disturbances and maintain the desired structural performance. A control designer can use \(\mu\)-analysis approaches to formulate the control issue as a mathematical optimization problem and then determine the controller that overcomes this optimization. One benefit of reduced-order approaches over conventional control methods is their ease of adaptation to multivariate systems with channel cross-coupling.