State-of-the-Art Review of Structural Vibration Control: Overview and Research Gaps

Abstract

This paper comprehensively reviews structural vibration control systems for earthquake mitigation in civil engineering structures. Structural vibration control is vital for enhancing the resilience and safety of infrastructure subjected to seismic activity. This study examines various control strategies, including passive, active, and hybrid methods, with a focus on the advantages of semi-active systems, which offer a balance of energy efficiency and adaptive capabilities. Semi-active devices, such as magnetorheological dampers, are highlighted for their ability to offer adaptive control without the high energy demands of fully active systems. The review discusses challenges like time delays, sensor placement, and model uncertainties that can impact the practical implementation of these systems. Experimental studies and real-world applications demonstrate the effectiveness of semi-active systems in reducing seismic responses. This paper emphasizes the need for further research into optimizing control algorithms and addressing practical challenges to enhance the reliability and robustness of these systems. It concludes that semi-active control systems are a promising solution for enhancing structural resilience in earthquake-prone areas, offering a practical alternative that strikes a balance between performance and energy requirements.

1. Introduction

1.1. General

Structural vibrations in civil engineering have a significant impact on the performance, safety, and serviceability of various infrastructures, including buildings, bridges, and towers. Seismic vibrations pose a significant threat to the safety and performance of civil structures, particularly in regions prone to earthquakes. Structural vibration control has recently emerged as an effective technology for earthquake mitigation. Over the years, extensive research has been conducted to develop effective approaches for mitigating seismic vibrations and minimizing the adverse effects of earthquakes on structures. Researchers have studied different passive, active, semi-active, and hybrid control methods for the seismic response control of structures. Comprehensive, state-of-the-art reviews on structural control in general [1,2,3,4] and specific controls [5,6,7] are presented, providing an overview of the various control strategies and their applications. A list of all state-of-the-art review papers is presented in

Table 1. List of publications on the state of the art of structural control.

List (40)	Publications
General (13)	[4,8,10,12,14,18,19,20,21,22,23]
Passive (4)	[15,16,24,25]
Active (3)	[11,12]
Active and Semi-active (3)	[2,26,27,28]
Semi-active (3)	[13,28,29,30]
MR Damper (7)	[6,31,32,33,34,35,36]
Hybrid (2)	[3,5]
Control Strategies (5)	[27,29,32,37,38]

. Housner et al. [8] presented an in-depth review covering diverse control systems, sensors, and research requirements from 1990 to 1996. Notably, this study pioneers the Physical Design Problem (PDP) concept, subsequently becoming a fundamental principle in various research endeavors. The authors advocate for prioritizing specific topics, including energy-efficient strategies for control devices and algorithms, integrating intelligent sensors for distributed sensing and control in dispersed systems, and addressing concerns related to near-field strong earthquake ground motion that influences structural control applications. Their recommendations set the stage for subsequent research, shaping the trajectory of advancements in the field during the specified period. Regarding active structural control, recent influential papers by Soong [4,9,10] offer a comprehensive overview of the various active structural control systems developed up to 1990. Additionally, Datta [11] provides a thorough review of the active control of structures subject to earthquake excitations. This review discusses different types of active control and their theoretical foundations, highlights key findings from parametric studies on various control strategies, addresses the limitations and practical challenges of active control systems, briefly examines the more promising semi-active control methods, and concludes with an outline of several active control strategies implemented in practice. Korkmaz [12] provides a comprehensive review of active control, delving into the challenges posed by engineering informatics. The review emphasizes the imperative for multi-objective control strategies, highlighting their dual focus on ensuring the structure’s safety and serviceability while enhancing the robustness of the control system. Reviews on semi-active control are also reported [13,14]. Other notable review papers include state-of-the-art reviews on the base isolation of structures [15,16,17].

The development of active, hybrid, and semi-active control systems has reached the stage of full-scale applications in actual structures. Nevertheless, every structural control system and its applications encounter challenges and limitations across various aspects. The challenges in implementing control strategies have hindered their expected applications.

To maximize effectiveness, the controller must be designed with consideration for the issues and should be robust, stable, reliable, and simple to design and implement. This paper presents a comprehensive examination of these challenges and limitations, providing insights into future research requirements and directions.

Structural control constitutes a vast and interdisciplinary research domain within civil engineering systems, making it impractical to discuss or reference all relevant publications and applications comprehensively. Therefore, the initial section of this paper provides an overview of various structural control systems, outlining their general limitations and challenges. Upon reviewing the literature, it becomes evident that semi-active control systems have emerged as promising techniques, offering the versatility and adaptability of active control systems without the need for a substantial energy supply while retaining the reliability characteristic of passive control systems. The following section provides a comprehensive examination of various semi-active control devices and their associated advantages. The practical implementation of a semi-active control system crucially depends on the chosen control strategy, presenting a foundational challenge. The following section provides a systematic review of the control theories and algorithms for semi-active control systems.

This section summarizes the advantages and disadvantages of each control algorithm, highlighting efforts to address the distinct challenges associated with each. In discussions related to control theory, emphasis is placed on issues directly tied to the physical behavior of civil structures, rather than delving into intricate developments in control system theory. The subsequent section explores the ongoing efforts of various researchers to refine control strategies tailored to specific issues and requirements, outlining different approaches to modify algorithms for enhanced system performance. The final section consolidates the research findings, offering a conclusion and outlining potential avenues for future research. This structured approach thoroughly explores the diverse aspects of structural control, ranging from devices to theories and strategies, and provides valuable insights for researchers and practitioners.

1.2. Research Significance

Numerous surveys have explored vibration control strategies for civil structures, with a predominant focus on distinct control system categories. Most of these review papers emphasize the limitations of control systems, impeding their anticipated implementation. Unfortunately, none comprehensively address the experimental challenges of implementing semi-active control for structures. This study presents a state-of-the-art review paper to address this research gap, offering a broader perspective on research efforts to overcome practical implementation challenges in semi-active control systems.

The contributions of this review include studying and summarizing the various types of semi-active control devices and control algorithms in civil structures, identifying key challenges and limitations in the application of control systems, and reviewing emerging trends in semi-active control strategies to address these challenges and ensure robust performance. This paper provides a realistic evaluation of semi-active control systems, discussing practical issues such as delays, uncertainties, algorithm selection, and system integration. It emphasizes methods to mitigate these undesirable effects and highlights the advantages of semi-active systems in seismic applications. Additionally, it highlights the increasing importance of multi-objective adaptive control algorithms, which address multiple challenges, such as optimizing control parameters, mitigating uncertainties, managing sensor and actuator configurations, facilitating decentralized control, and minimizing time delays.

2. Overview of Structural Control Systems

It is crucial to recognize that the control system and the structure do not operate as isolated dynamic entities; instead, they significantly interact and mutually influence each other. The control system, integrated with the structure, manages seismic forces by providing counteracting forces or dissipating seismic energy, thereby preventing a catastrophic failure of the structural system. Structural control class selection depends on various factors, including budget constraints, desired performance, specific structural characteristics, and project requirements. Each class has its advantages and limitations, and informed choices are to be made based on the type of structure, control goals, and constraints. This section presents the classification of the control systems and their critical features.

Structural control can be broadly classified based on the amount of external energy required; the different control systems can be categorized as passive, active, semi-active, hybrid, and passive control systems (Figure 1) [13]. Based on the mathematical modeling of the control systems, active and semi-active systems are further classified according to their mathematical modeling [11], as shown in Figure 2.

2.1. Passive Control System

Passive control systems are the basic structural control systems that do not need any external power to operate. The passive systems do not generate energy within the structure, thereby maintaining the stability of the control system. Passive energy-dissipating systems are external add-on damping devices commonly used to dissipate energy from structural vibrations. Passive devices generate control forces in response to the structure’s motion. Passive control devices are broadly classified into two categories: passive isolation devices and energy-dissipating devices [22]. Some of the most widely used passive devices are viscoelastic dampers, viscous fluid dampers, friction dampers, metallic dampers, tuned mass dampers, liquid column dampers, and base isolators. Researchers have conducted state-of-the-art reviews on the application of passive isolation [15,16,17]. Rahimi et al. [7] presented a critical review of the application of tuned mass dampers for the structural vibration control of structures subjected to wind and earthquakes, providing a comparison of their efficiency and the comparative advantages and disadvantages. The potential of TMDs for improving the wind and seismic behaviors of prototype civil structures was also reviewed by Elias et al. [24]. The review highlights the dynamic characteristics and unique features of different systems, namely single-tuned mass dampers (STMDs), multiple-tuned mass dampers (MTMDs), and spatially distributed MTMDs (d-MTMDs), which have been explored both theoretically and through experimental investigations.

2.2. Active Control System

Active control systems are more sophisticated and require a significant power source for operation. These control systems use sensors to measure structural responses. Based on feedback from the sensors, the control forces are computed according to a prescribed controller and are then applied to the structure through actuators. These systems have the advantage over passive systems in adapting to varying load conditions [8]. However, it can also destabilize the structure if the control forces are not applied in the proper position and at the appropriate time. Some control devices are active mass dampers, active tuned mass dampers, and active tendon systems. Fisco et al. [2] presented a review of active and semi-active devices for structures since 1997 and identified that research in recent years has moved toward semi-active and hybrid control systems. Ikeda [28] provided a report on the application of active and semi-active devices in Japan, which discusses the practical application of active control devices in structures.

2.3. Semi-Active Control System

These systems require low power supplies for their activation compared to typical active control systems. These systems generate counteracting forces by reactive devices with variable damping and/or stiffness characteristics. These systems are also referred to as controllable passive systems. These systems can operate during large earthquakes, as they require a minimal magnitude of external energy, which can be supplied with the help of battery power. Semi-active systems do not impart energy into the structure and therefore do not cause structural instability. The semi-active control devices include hydraulic dampers, electrorheological and magnetorheological dampers, semi-active stiffness control devices, friction control devices, semi-active tuned mass dampers, and tuned liquid dampers [13]. It is noted that these control systems are adaptable to active systems and possess fail-safe features similar to those of passive systems. A detailed review of dynamic models of MR dampers and control algorithms is presented by Jung et al. [6]. The MR-fluid-based dampers are shown to be highly effective for full-scale civil engineering structures. Gkatzogias et al. [30] presented a current state-of-the-art review of semi-active control in bridges, focusing on some full-scale applications of semi-active control devices and relevant benchmark studies. Among the semi-active control devices, the MR damper is suggested to be a promising alternative due to its reduced adaptability and reliability compared to passive and active devices.

2.4. Hybrid Control System

Hybrid control systems are developed by combining a passive system with an active or semi-active one. Hybrid systems employ multiple control devices, meaning both active control devices and passive devices are installed within the same structure. Hence, combining the systems can eliminate some of the limitations and disadvantages of each system that arise when they are used separately, thereby achieving better performance. Some of the combinations studied include base isolation and active actuators, tuned mass dampers and base isolation, and viscoelastic dampers and base isolation, among others. Fisco et al. [3] provided a review of the hybrid control systems and the control algorithms for the structures. The authors also noted that most research on smart structures is concentrated in the US, Japan, Taiwan, China, and Korea, with lesser attention given to Europe.

Passive and semi-active controls have better preference than active control due to their reliability and inherent stability. An active control system may develop asynchronous control forces due to time delays, which can render the structure unstable. Out of semi-active, passive, and hybrid control, semi-active control has garnered more attention because it can offer a more effective reduction in seismic responses. Therefore, this paper reviews the advancement in semi-active control applications for earthquake mitigation. The following section presents a review of semi-active control systems for structures.

3. General Limitations of Structural Control Systems

Although the structural control of civil engineering structures has emerged as a notably efficient method to mitigate the potentially devastating effects of earthquakes, most papers report that the limitations of the control system have hindered the expected implementation of the systems. Jiang and Wang [5] state that while structural control has advanced significantly, three major concerns still impede the application of active or hybrid control techniques to full-scale structures: system complexity, reliable measurements, and the capacity of the actuators. One of the most challenging aspects of active control research in civil engineering is its interdisciplinary nature [4]. It requires integrating knowledge from various fields beyond traditional civil engineering, including computer science, data processing, control theory, material science, sensing technology, stochastic processes, structural dynamics, and wind and earthquake engineering.

The successful implementation of structural control systems is not without its intricate challenges that demand careful consideration and resolution. For the practical implementation of structural control systems, aside from the availability of ample power sources for implementing control schemes, several intricate real-time application challenges require careful consideration. These challenges encompass a broad spectrum of issues that engineers and researchers face when designing and deploying effective strategies to mitigate structural vibrations and enhance the resilience of buildings and infrastructure. This section discusses the challenges associated with implementing structural control.

3.1. Modeling Errors

The accuracy of structural control depends on the ability to model the actual structure effectively. However, limitations in modeling, often arising from a reduced number of degrees of freedom, can introduce errors. Consequently, control algorithms based on idealized models may struggle to effectively manage the actual structure’s dynamic behavior. The modeling errors are classified into four types: parameter errors, model order errors, neglected disturbances, and neglected nonlinearities. No controller can treat all four at once [8]. Disregarding various errors and concentrating solely on one category may result in inaccurate conclusions. Most hardware and design suggestions and results are based on satisfactory computer simulations. It is challenging to draw clear conclusions about hardware and design recommendations because the research papers heavily rely on numerous referenced hardware tests. The available results predominantly stem from computer simulations, which are effective in conservative systems where errors in design parameters cannot destabilize the system. However, active feedback control can introduce instability or suboptimal performance if significant modeling errors and control energy are substantial. Relying solely on computer simulations may not offer sufficient evidence for a robust design. Simulations may or may not encompass enough modeling errors to assess the stability of the actual system. The lack of addressing the interdependency between modeling and control design is one of the severe issues in control systems. The study by Housner et al. [8] stated that robust control theories, such as adaptive control and H_∞ can treat the errors and stabilize the system if the unbounded error is known. However, such systems usually trade performance for robustness.

3.2. Time Delay

A standard structural control system for civil engineering structures comprises multiple components, including sensors, filters, controllers, and control devices. Since each element requires a finite amount of time to function, there is always a delay between measuring response quantities and applying control forces. In seismic control systems, these delays stem from the time required to measure state vector responses during earthquakes and to process this data using digital computer units. Furthermore, time delays are introduced when calculating active forces through control algorithms, activating control devices, and applying them to the plant or system.

Experimental studies have shown that time delay is inevitable in operating control systems, which can deteriorate control performance. The existence of a time lag between sensing structural responses and applying control forces is a critical issue. From previous studies [39,40,41], it is observed that time delay can cause degradation in control performance. These time delays can occur in control system inputs, outputs, or states, and their characteristics can vary from being discrete to distributed, constant, time-varying, known, or unknown, and from deterministic to stochastic, depending on the specific features of the system [42].

Study [39] demonstrated that the decentralized output feedback polynomial controller, the Lyapunov controller, and the simple passive controller are highly robust to time delay issues, even without implementing any compensation to mitigate the effects of the delays. Also, various compensation methods have been proposed to address the instability and performance degradation caused by these delays. Extensive real-scale semi-active tests and simulations were conducted [43] to estimate the time delay effects in the control electronics and the mechanical and electrical parts of the MR damper within a closed control loop using a Bingham model of 50 kN MR dampers. They identified three distinct time delays in the real-scale 50 kN MR damper: Control Electronics Time Delay, which included signal acquisition, processing of the acquired signal, and power supply operations; Electrical Time Delay, which pertains to the electrical part of the damper or its electromagnetic circuit; and Mechanical Time Delay, which is the interval between the moment the current to the device starts changing and the moment the device begins to adjust its mechanical behavior.

3.3. Sensor and Controller Placement

The practical constraints of installing sensors at all critical points for comprehensive feedback collection are formidable. Balancing the optimization of sensors and controller locations with limited resources can be a complex task, and using observers to construct a state vector from sparse measurements may introduce additional challenges. The strategic positioning of actuators and sensors not only enhances energy efficiency and cost-effectiveness but also plays a crucial role in influencing the stability and reliability of a control system. The methods for designing optimal damper placement can be categorized into three primary groups: evolutionary, analytical, and heuristic. A review of these methods has been outlined by Kookalani et al. [44]. The authors recommend that more studies be conducted on damper placement for algorithms such as the artificial bee colony algorithm (ABCA) and the firefly algorithm (FA). Soto and Adeli [45] presented a review of placement control devices for structural control techniques, stating that most of the available literature on semi-active control focuses on MR dampers. The study also states that the research on the optimal placement of control devices in semi-active and hybrid control systems remains largely unexplored. While structural control systems show promise in effectively mitigating external dynamic forces, such as those induced by winds and earthquakes, the precise optimization of device placement has not received extensive investigation.

3.4. Parametric Uncertainties

Structural parameters, such as material properties and nonlinear behaviors, often exhibit uncertainties. Additionally, online identification complicates the management of time-dependent degradation and further complicates maintaining the effectiveness of control schemes in the face of evolving structural conditions. The mathematical model of a system is typically an approximation of its actual dynamic behavior, with differences arising from unmodeled and uncertain parameters. These uncertainties can significantly affect the performance and stability of the control system. These uncertainties can be classified into structured and unstructured categories.

Navigating these multifaceted challenges is crucial for successfully implementing structural control systems, ultimately enhancing the safety and resilience of civil infrastructure. In summary, the structural control of civil engineering structures presents a promising solution for earthquake mitigation. However, it encompasses intricate challenges related to control strategy, mathematical modeling, sensor networks, input variables, and parameter uncertainties. Successfully addressing these challenges is crucial for designing effective control systems that safeguard structures and enhance their resilience against seismic events. These efforts are crucial in enhancing the overall safety and longevity of critical infrastructure. Experimental studies form the basis for studying these challenges. This paper emphasizes the significance of experimentally assessing semi-active control systems. It illustrates how numerous issues that may arise in real-world applications are also evident during the experimental testing of these systems. The following section presents experimental studies on the semi-active control of structures and discusses how the issues related to these studies are addressed.

4. Semi-Active Control Systems

The introduction of structural control in civil engineering is widely acknowledged on a global scale, attributed to the groundbreaking article authored by Yao [46] and the subsequent promotion of its implementations by Kobori [47]. Despite the successful application of numerous structural control strategies, their widespread adoption has been hindered by challenges related to cost, dependence on external power sources, and the complexity of mechanical aspects throughout the structure’s lifespan. Although active control effectively reduces structural responses, its requirement for an extensive external power source and its potential to destabilize the structure are significant concerns regarding its applicability. Semi-active control systems offer the advantages of versatility and adaptability of active control systems, without requiring an ample energy supply, while maintaining the reliability of passive control systems [41]. Comprehensive state-of-the-art reviews on active and semi-active control [2,26,27,28] and MR are notable [6,13,29,31,32]. Symans and Constantinou [13] conducted an extensive literature review that examined dynamic characteristics and distinctive attributes of various semi-active systems. The review presents the control systems experimentally tested at the component level and within scaled-down structural models, and it considers semi-active systems, including stiffness control devices, electrorheological dampers, magnetorheological (MR) dampers, friction control devices, fluid viscous dampers, tuned mass dampers (TMDs), and tuned liquid dampers.

Table 2. Critical features of semi-active control devices.

Control Systems	Key Features
Stiffness control devices	Used to alter the stiffness and, consequently, the natural vibration properties of the structure to which they are connected. The system mainly regulates the rigidity of a structure to achieve a non-resonant state during earthquakes. The semi-active stiffness devices are activated or deactivated to incorporate or remove, respectively, the stiffness of the structure’s bracing system.
Electrorheological dampers	Comprise a hydraulic cylinder that holds micron-sized dielectric particles dispersed in a fluid (typically oil). In a strong electric field, the particles align and polarize, thereby providing greater resistance to flow. Altering the electric field can adjust the dynamic performance of an ER damper.
Magnetorheological (MR) dampers	MR dampers generally comprise a hydraulic cylinder filled with micron-sized, magnetically polarizable particles dispersed in a fluid (commonly oil). The behavior of MR fluid is managed by applying a magnetic field to the fluid. Without a magnetic field, the MR fluid moves freely; however, when subjected to a magnetic field, it behaves like a semi-solid. MR fluids can withstand a maximum yield stress in the range of 50–100 kPa [35,43]
Friction control devices	Employed either as energy dispersers in the lateral bracing of a structure or as elements in sliding isolation systems.
Friction-controllable sliding bearing	The pressure between the two sliding surfaces can be adjusted to manage the friction between the bearing and the ground.
Tuned mass dampers	Tuned mass dampers essentially comprise a single-degree-of-freedom mass–spring–damper arrangement usually positioned on the uppermost floor of a multi-story building. The dynamic traits of the system are adjusted to manage the movement of the structure to which it is connected.
Tuned liquid dampers	An effective control approach for managing a variety of dynamic loading scenarios.
Semi-active slip bracing system	Commonly used when the lateral force-resisting consists of braces. It slips at the interface when the brace’s axial forces reach a predetermined threshold (the friction coefficient multiplied by the clamping force). Installing this type of device allows for the adjustment of a brace’s strength without changing its stiffness. Another benefit of this device over a passive one is its ability to operate effectively under minor forces (such as small earthquakes or winds) while still delivering effective performance under greater demands.
Electro-inductive device	Key factors in utilizing electro-inductive devices rather than fluid dampers include the following: The behavior is essentially unaffected by outside temperature, as the device’s operating temperature consistently exceeds the air temperature and is achieved in just a few seconds. Maintenance of the device is minimized due to the absence of aging or leakage issues, which are present in fluid dampers.
Air-jet actuators	They were introduced as an effective solution to the traditional concern that power would not be available when needed unless it was stored in advance. The flow of compressed air supplies the actuator force, to be transmitted to the structure through the principle of momentum preservation.
SMA actuators	They are commonly adopted to realize passive devices, while the different (and long) reaction times for cooling and heating prevent their adoption in semi-active devices.

lists the different semi-active control devices and their salient features.

Semi-active systems offer a strong alternative to both passive and active systems, as they outperform the former in terms of structural performance and the latter in terms of power consumption. This has been demonstrated in several scaled-down experimental investigations involving bridges and framed structures, e.g., [44,45,46,47,48,49].

Table 3. List of publications on the semi-active control of structures.

List	Publications
Buildings	[29,35,36,39,45,48,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120]
Bridges	[20,41,49,55,96,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157]

lists publications on semi-active control for buildings and bridges. It has been observed that most of these studies focus on the controller’s efficiency in mitigating seismic vibrations. However, little attention is given to addressing the practical issues in implementing the systems.

Experimental studies with controllable devices demand focused efforts to address distinct aspects within the three stages of the semi-active control loop: acquisition, processing, and command. Additionally, the control system’s efficiency is dramatically dependent on the control algorithm. Dyke et al. [158] examined the effectiveness of different control strategies for MR dampers, illustrating that the performance of the control system is significantly influenced by the algorithm selected for implementation. The subsequent section offers a comprehensive overview of the control algorithms employed in semi-active vibration control.

5. Control Algorithms Used for Different Semi-Active Control Systems

Semi-active control systems employ various control algorithms to achieve their intended purposes. These control algorithms are designed to adaptively regulate the damping or stiffness properties of structural components, thereby mitigating vibrations and enhancing the overall performance of structures. Creating an accurate mathematical model of the structure–controller system for real-world structures, while accounting for the various uncertainties associated with process parameters, is a challenging endeavor. Nonetheless, these issues must be addressed to create and develop controllers that operate effectively in these complex systems. Various control strategies have been documented in the literature, including fuzzy logic, neural networks, instantaneous optimal control, the sliding mode technique, linear quadratic Gaussian (LQG) controllers, and linear quadratic regulators (LQRs). Jansen and Dyke [29] examined and assessed the effectiveness of different semi-active control techniques for MR dampers, including the Lyapunov controller, decentralized bang-bang controller, modulated homogeneous friction algorithm, and a clipped optimal controller. Numerous recognized algorithms in control engineering have been applied to manage systems, including optimal control, LQR or LQG, pole placement, sliding mode control, the H₂ and H₁ methods, fuzzy control, and various additional techniques. Soong [4] and Casciati et al. [159] detail the most appropriate algorithms for structural applications and the practical factors that need consideration. The selection of a control algorithm relies on the unique features of the semi-active control system, the type of structural vibrations, and the goals of control. Engineers and researchers select the most suitable algorithm based on the application and desired performance outcomes.

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 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. These uncertainties—arising from external excitations or inaccuracies in structural response measurements—can degrade control system performance. Robust control addresses these challenges during the design phase to maintain reliable operation. Among the prominent methods are the H_∞ and H₂ controllers. The H_∞ controller uses a combination of time- and frequency-domain approaches to tackle a wide range of control problems. It excels in disturbance rejection and guarantees system stability under diverse operating conditions [165]. Its popularity stems from its flexibility—performance goals can be incorporated as weighting functions during the design process. The H_∞ framework also includes process and measurement noise, making it robust to model uncertainties. It is suitable for both single-input single-output (SISO) and multi-input multi-output (MIMO) systems. The H₂ controller is a specific subset of the H_∞ approach. It minimizes the H₂ norm, aiming for optimal performance while stabilizing the system. Like H_∞, the H₂ controller typically follows a two-input, two-output configuration and is particularly effective for systems where the emphasis is on minimizing overall energy or variance in the output. Robust control is favored for its ability to function without a structural model and handle system uncertainties, but its complex design poses practical challenges. One of the limitations of a robust control system is that time-domain constraints cannot be integrated easily.

Adaptive control algorithms are designed to respond to changes, uncertainties, and the random nature of control systems, whether in the controller itself or the feedback and feedforward signals. In recent years, adaptive control strategies have been widely explored both numerically and experimentally in the field of structural control for various civil engineering applications [166,167,168]. Adaptive control demonstrates strong real-time adaptability and robustness under both linear and nonlinear conditions by dynamically responding to uncertainties, albeit at the cost of increased design complexity. This comparison underscores the importance of selecting control algorithms based on specific structural needs, performance criteria, and implementation feasibility [169].

The accuracy of nonlinear system modeling has a significant impact on the effectiveness of traditional control algorithms. While conventional control strategies account for uncertainties in measuring both input excitations and system responses, their success still largely depends on the specific control law used. In contrast, intelligent control systems enhance these algorithms by incorporating elements such as reasoning, computation, and decision-making, while also addressing uncertainties in system identification and modeling. This makes intelligent controls a more realistic approach, offering a wider range of solutions. Intelligent systems are influenced by human input, which introduces the potential for error due to reliance on the designer’s experience. Intelligent control methods are typically classified into three main types: (a) fuzzy control, (b) neural network control, and (c) genetic algorithms. Neural network control and fuzzy logic control both eliminate the need for predefined structural models, relying instead on data-driven or rule-based approaches [122,170,171,172,173]. While they offer flexibility for nonlinear systems, they face challenges related to training complexity, stability, and design intricacy. These algorithms do not consider feedback from the actuator and rely solely on the structural responses, which can be difficult to obtain during seismic events.

The effectiveness of a specific controller can vary for different structures, indicating that the performance of control algorithms relies on the characteristics of the structural system and the earthquake data it experiences. It is crucial to compare structural responses using ground motions with the same hazard level. For example, the performance of a controller on the first floor may decrease as the number of building stories increases, making it more suitable for lower floors. Therefore, it is crucial to investigate the optimal number and placement of dampers based on the specific structures. To achieve a more robust performance evaluation for semi-actively controlled structures using MR dampers, it is necessary to expand the dataset by including more seismic ground motions, building more comprehensive models, and developing more advanced control algorithms. The most effective way to demonstrate the robustness of the control algorithms is through experimental testing. The review shows that several novel control algorithms have been developed to enhance the efficiency of the control systems [117,134,158,159,160,161,162,163,164,165,166]. However, most of them are not tested experimentally. Experimental testing of semi-active control systems in structures requires addressing specific aspects to achieve a more realistic evaluation of their effectiveness in controlling earthquake-induced vibrations [174]. The practicality of a semi-active control system in mitigating the seismic impact on structures is studied through experimental testing at both the component level and with small-scale model structures affixed to a shake table [165]. It has been observed from the literature that control systems are developed to address specific challenges, such as uncertainty, time delay, and sensor optimization. The following section reviews the controllers developed to address specific issues.

6. Optimized Control System Designed to Tackle Practical Implementation Challenges

Upon reviewing the literature, it becomes evident that each control algorithm exhibits strengths and weaknesses. Researchers have consistently focused on enhancing control system performance by taking various factors into account [28,39,42,56,61,122,169,170,171,175,176,177,178,179,180,181,182,183]. The overall effectiveness of the control system can be improved by considering a range of factors, which are elaborated in this section.

To successfully apply control systems to structures, a balance must be found between reliability and robustness. Reliability, as a crucial concept, depends on the control system’s sustained efficiency over time, encompassing all aspects of frequent system use, regardless of whether it is used for controlling minor, major, near-field, or far-field earthquake ground motions. However, increasing the reliability of a system does not automatically ensure optimal performance under varying earthquake conditions.

In contrast, system robustness is crucial for preventing failure, malfunction, or counterproductive effects in structural response during exposure to a wide range of ground motions, including extreme earthquakes. While enhancing reliability ensures consistent system operation, enhancing robustness guarantees effective performance under more substantial seismic events.

The subsequent section discusses research-driven strategies to elevate seismic control performance. These strategies are tailored to enhance the robustness of semi-active control systems. Notable approaches include minimizing the impact of uncertainty, time delay, and the optimal placement of sensors and actuators. This paper aims to shed light on how advancements in robustness can strengthen the effectiveness of active and semi-active control systems under seismic conditions.

6.1. Control Systems to Ensure Robustness to Uncertainties

This review observes that most control algorithms developed are investigated for their robustness and stability in response to system uncertainties, such as stiffness and mass. Conventional control algorithms rely on nominal models and may not work well in uncertain models [42]. Various methods, including H_∞, H₂, H_∞/H₂, μ-synthesis, and linear matrix inequalities, are employed for robust controller design.

Table 4. Robust control algorithms for uncertainties.

Publication	Method Used	Issues Addressed
(Amini and Ghaderi) [184]	Discrete Wavelet Transform and particle swarm optimization	Uncertainty in structural damping and earthquake
(Bagheri and Amini) [185]	Wavelet analysis and pattern search method	Uncertainty in the frequency content of earthquakes
(Amiri et al.) [186], (Bitaraf and Hurlebaus) [187]	Fuzzy logic-based control algorithm	Nonlinearity
(Oliveira et al.) [188]	Predictive control	Uncertainty and time delay
(Nguyen et al.) [189]	New fuzzy sliding mode controller Adaptive neuro-fuzzy inference system	Uncertainty and time delay
(Ghaderi and Amini) [190]	Adaptive block backstepping	Unknown parameters
(Ramezani et al.) [104]	Fuzzy type-1 and type-2	Uncertainties
(Shan et al.) [191]	Model reference adaptive backstepping control algorithm	Structural nonlinearity, structural uncertainty, and the influence of actuator saturation
(Zabihi-Samani and Ghanooni-Bagha) [101]	Adjustable cuckoo search wavelet-based fuzzy logic controller (ACSWBFLC)	Nonlinear modeling of MR damper Optimization of placement and number of MR dampers
(Darbanian et al.) [170]	Fuzzy-LQR Algorithm	Uncertainties of Structural Parameters

presents a comprehensive overview of advanced control algorithms specifically designed to address various types of uncertainties commonly encountered in structural systems. These uncertainties may include variations in structural damping, changes in frequency content due to ground motion characteristics, the nonlinear behavior of materials and components, and inherent time delays in sensing, computation, and actuation.

To manage these complex and dynamic challenges, the following table highlights several sophisticated control strategies that have shown promising results in both theoretical and experimental studies. Among these, the Discrete Wavelet Transform (DWT) stands out for its ability to decompose non-stationary signals and extract relevant features in both time and frequency domains, making it suitable for real-time monitoring and adaptive control during seismic events. Fuzzy logic control is another method, known for its effectiveness in handling imprecise or ambiguous input data. This approach does not require a precise mathematical model of the system; instead, it relies on rule-based reasoning, making it particularly suitable for systems that are uncertain or nonlinear in nature.

Additionally, Adaptive Neuro-Fuzzy Inference Systems (ANFISs) are employed as a hybrid method, combining the learning capabilities of neural networks with the interpretability of fuzzy logic. This approach enables the controller to adapt to changing system dynamics by updating its rule base and membership functions over time, resulting in enhanced control accuracy and robustness.

It is observed that the use of frequency domain control methods involves analyzing and designing control systems in the frequency domain, where the behavior of a system is examined in terms of its response to different frequencies. H_∞ control is one such method that is often used for robust control system design, particularly in the presence of uncertainties and disturbances. Robust H_∞ control seeks to minimize the impact of disturbances on the controlled system while maintaining stability and optimal performance. It provides a framework for handling uncertainties and disturbances to optimize the system’s response in the presence of these factors. Studies have also shown that the use of frequency-shaping filters incorporated into the control system influence or shape the system’s frequency response. These filters allow us to tailor the system’s behavior at specific frequencies, making it more responsive or less sensitive to specific input frequencies. Narasimhan and Nagarajaiah [165] developed a novel control algorithm based on H_∞ for a variable friction-based semi-active control system. The controller was designed to determine the optimal control force for reducing responses to near-fault earthquakes. The study’s results, considering stiffness uncertainty, indicate that both active and semi-active H_∞ controllers demonstrate robustness and effectiveness in reducing responses for intelligent base-isolated structures in the face of near-fault earthquakes.

Loh et al. [192] conducted an experimental validation of wireless communications for real-time structural control, assessing the control performance of the wireless system in comparison to a conventional tethered control system. The efficacy of the wireless control system is evaluated through a shaking table test performed on a three-story steel frame equipped with an MR damper on each floor. The study demonstrates that wireless sensor networks represent a promising technology capable of operating in real-time environments. Additionally, the study highlights the advantages of decentralized control approaches due to their robustness against failure, ensuring that the control system can still operate even if one damper fails to function correctly.

Wang et al. [107] studied the mechanical performance of a piezoelectric ceramic friction damper installed on a three-story structure. An adaptive fuzzy neural network controller (FNNC) is proposed, and its performance is compared with the LQR optimal control. To study the robustness and stability of the proposed controller in the presence of model uncertainties, a stiffness adjustment of ±10% is considered. The results indicate that FNCC exhibits good robustness and stability, particularly in the face of uncertainty, and can effectively reduce the responses.

6.2. Control Systems to Handle Time-Delay Issues

The existence of a time lag between sensing structural responses and applying control forces is a critical issue. Research focused on mitigating time delays in control systems has been reviewed, and it is seen that control algorithms such as the time-delay compensation method based on Newmark’s method decentralized output feedback polynomial control (DOFPC), Lyapunov control, the Taylor series expansion of the control force, the decentralized H₁ controller, adaptive control, and the Proportional–Integral–Derivative (PID) controller demonstrate robustness to time delay. Wang [40] conducted a study employing decentralized dynamic output feedback controllers to reduce the H_∞ norm of the closed-loop system. The formulation of the problem considers the impact of feedback time delay, which is consequently addressed in the design of the controllers. The controller’s performance is found to be more efficient when compared to a time-delayed LQG controller. Di Paolo and Pirrotta [193] studied the effect of time delay under random excitation. Comparing three approaches, the study suggests that the Taylor expansion method can serve the dual purpose of assessing both the critical time delay at which control effectiveness diminishes and of evaluating the response with variance. Cha et al. [39] studied the effects of time delay on large-scale semi-active control strategies. This study explored the impact of time delay on the performance of a structure equipped with a large-scale MR damper. The study utilized numerical simulations for earthquakes occurring in both near-field and far-field scenarios. The MR damper operates via four unique semi-active control methods: simple passive control (SPC), decentralized output feedback polynomial control (DOFPC), Lyapunov control, and clipped-optimal control (COC). The findings reveal that all controllers, except for COC, exhibit significant robustness in the face of time delay. In contrast, the clipped-optimal controller requires integration with a compensator to enhance performance when dealing with time delays. An experimental verification of the adaptive neuro-fuzzy inference system (ANFIS) and a novel fuzzy sliding mode controller (FSMC) was demonstrated in the study by Nguyen et al. [189] to mitigate the effects of time delay and uncertainties.

6.3. Control Systems for Optimal Placement and Number of Control Devices

Strategically positioning dampers optimally enhances control performance and reduces the system’s reliance on external power sources, thus lowering the overall cost of the control system and creating additional available space. Furthermore, an optimally placed, compact set of dampers can deliver the same level of performance as a complete set, typically requiring less energy to generate control forces. Ideal locations for these dampers may include the lower floors and other vulnerable areas of civil structures, where seismic excitations often induce significant nonlinear deformations [51,194,195,196].

An overview of the optimal damper distribution as a passive energy dissipation system for retrofitting structures against earthquakes is presented in [44]. Ribakov and Agranovich [197] introduced an algorithm for determining damper locations based on their maximum contribution to total seismic energy dissipation. Chat et al. [4,198] proposed a multi-objective genetic algorithm to optimize the placement of control devices and sensors, considering cost and seismic control performance when designing structural control systems. To study the optimal placement of devices, the linear quadratic Gaussian (LQG) algorithm emerges as the most employed in the studies reviewed, as seen in the works of [4,5,197,198,199] and [44].

7. Research Gaps and Future Directions

Research in the field of structural control systems has made significant progress; however, challenges to practical implementation require further investigation. In theory, structural control offers significant potential for enhancing the performance and safety of structures, particularly under dynamic loading such as earthquakes. However, its practical implementation often presents challenges that are not fully addressed in academic research. Therefore, greater emphasis should be placed on translating theoretical advancements into practical solutions. Future research should prioritize the development of control systems that are not only technically effective but also feasible and straightforward to implement from the perspective of builders and engineers in the field. Bridging this gap between theory and practice is essential to facilitate the broader adoption of structural control technologies in real-world construction projects.

Several significant gaps remain in the existing literature on adaptive control systems for structural engineering applications. One key area lacking sufficient research is the use of adaptive and intelligent controllers for mitigating seismic responses in structures employing control systems. This topic warrants further study to develop robust strategies suited for time-varying systems with inherent uncertainties. Another underexplored area is the use of indirect adaptive control, which is especially useful when the system model is either unknown or subject to change. Despite its potential to enhance performance and seismic resilience, its application remains limited. Addressing these shortcomings is crucial for advancing adaptive control technologies that aim to mitigate seismic impacts on structures.

To address these challenges and close the existing research gaps, several directions for future work can be considered. First, there is a need for the development of robust, multi-functional control systems that combine intelligent and adaptive control strategies. Such systems could offer more flexible and responsive solutions to structural vibrations. Second, the formulation of multi-objective control schemes that optimize both vibration mitigation performance and cost-efficiency would be highly beneficial, particularly for practical implementation. Third, since ensuring a stable energy supply during earthquakes is a significant challenge, future research should explore energy harvesting techniques and their seamless integration with vibration control systems to enable autonomous or semi-autonomous operation. Lastly, combining vibration control systems with structural health monitoring technologies can create a more holistic and responsive approach to managing structural performance, especially in post-earthquake scenarios.

8. Concluding Remarks

An overview of seismic vibration mitigation systems for structures has been provided in this review. Based on the current research landscape, there is a preference for semi-active control systems in structural vibration control over other control systems. Both numerical and experimental studies consistently demonstrate the superior performance of semi-active systems compared to passive systems, which require significantly less external energy than active control systems. Amongst the semi-active control devices, MR dampers have emerged as the most extensively studied.

Despite advancements in research on structural control strategies, their widespread adoption has been hindered by practical implementation challenges. This paper outlines the limitations and challenges of implementing control systems, identifies critical issues in experimental execution, and proposes improved control systems tailored to address each challenge. The careful selection of a control algorithm is crucial in ensuring the effective and robust performance of these control systems. Various control algorithms have been investigated in the pursuit of effective response control, revealing that no single algorithm can be deemed optimal.

This paper makes a clear and valuable contribution by critically evaluating the current state of seismic vibration mitigation systems, with a strong emphasis on the growing prominence of semi-active control strategies. This paper highlights the advantages of semi-active systems and addresses the significant gap between theoretical development and practical implementation. Key challenges in real-world applications, including experimental limitations, algorithmic selection, and system integration, are identified. This paper offers a comprehensive assessment of existing limitations. This paper also reviews improved control strategies to address these challenges, emphasizing the importance of selecting the appropriate algorithm. Notably, multi-objective adaptive control algorithms are gaining increased attention in seismic control research. These algorithms target challenges such as optimizing various parameters, minimizing uncertainties, optimizing the quantity and distribution of sensors and actuators, establishing decentralized control networks, and reducing time delays. This paper provides an overview of existing structural vibration control systems and enhances their practicality and robustness for mitigating seismic vibrations.