# State-of-the-Art Review of Structural Vibration Control: Overview and Research Gaps
## 5 Control Algorithms Used for Different Semi-Active Control Systems
### Classification of Control Algorithms  
The key factor in determining the overall performance of an innovative adaptive structure is the implementation of a control algorithm that can effectively counteract both known and unknown external excitations by providing additional force input through control devices. This control algorithm should be robust, versatile, and easy to design and implement. Furthermore, it should allow flexibility in selecting performance objectives to ensure a comprehensive and effective response reduction. The issue of modeling for  
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controllers is a complex and ongoing challenge because no established theory offers a model ideally suited for control design, primarily due to the complexity of modeling the system and designing the controller. After all, no established theory offers a model ideally suited for control design, primarily because modeling the system and designing the controller are inherently interconnected problems. The optimal choice of a control algorithm may hinge on factors such as the specific nonlinearity exhibited by the semi-active device, the accessibility of the feedback measurements, or the number of devices intended for incorporation into the structure. Furthermore, the specific structural feedback data, such as acceleration, velocity, and displacement, are of great importance in determining the control strategy for a feedback control system. Control algorithms are classified based on various factors or criteria in different literature sources. Control algorithms can be classified as linear and nonlinear based on the measured response and the control signal. Additionally, control algorithms can be classified as open-loop, closed-loop, or open-closed-loop, depending on the type of information used to determine their output control signals (Figure 3). Another common practice among researchers in classifying control algorithms is to categorize them as optimal, stochastic, adaptive, intelligent, and hybrid. Figure 4 shows this classification and the sub-classification for this type. Some of the commonly used algorithms and their features are discussed below. The linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) algorithms are the most widely used optimal control algorithms, appreciated for their simplicity [29]. Neither of these control approaches require prior knowledge of the external excitation, as they are based solely on the system's state variables. However, they are primarily suitable for linear systems [160]. Additionally, the LQG control requires accurate feedback or structural models, and its primary flaw is that the uncertainty is modeled as white noise, which is not ideal [161]. Sliding mode control (SMC) is a form of nonlinear control that generates intermittent control signals to modify a system's dynamic behavior. Sliding mode control (SMC) operates on the concept of switching between various independent structural configurations. The control approach drives the system to follow a trajectory along predefined behavioral surfaces. The design ensures that system trajectories are continually directed toward a nearby region of this surface, with varying control intensities, rather than remaining confined to a single control regime [162; 163]. As a result, the system navigates the boundaries of different control structures while minimizing errors. SMC stands out for its robustness and ability to handle both linear and nonlinear systems without requiring precise models [164], although it suffers from issues like the chattering effect and limited optimization capabilities. A robust control algorithm is a frequency-domain strategy designed to effectively handle uncertainties.