## 1 Introduction  
Structural responses to earthquakes, winds, traffic, and other dynamic forces can endanger structural safety and disrupt comfort. Consequently, research into reducing the structural response and vibrations under the action of dynamic forces has increased in recent years. The control systems developed in these studies consume the energy entering the structure by providing additional damping. Such systems can be installed during construction or added to existing structures. Control systems are generally divided into active and passive types, but also have other classifications depending on the design and equipment used. Tuned mass damper (TMDs) are passive control systems, which are implemented in several famous structures like Taipei 101 in Taipei (Figure 2a) and seismic retrofitted LAX Theme Building in Los Angeles [1]. In addition to these systems, it is possible to treat semi-active and hybrid control systems as a separate category. Active tuned mass dampers (ATMDs), a type of active system, can be defined as a system derived by adding an active control mechanism (sensor, controller, and actuator) to the TMD system to increase its applicability at variable frequencies (Figure 1). As seen in Figure 1, the response of the top story (top story velocity in the numerical example) is used as the feedback of the controller to generate the time-varying control force linear dynamic actuators. In applications, different and multiple feedbacks for the sensors and different types of actuators can also be used. There are several practical examples of ATMDs, such as Shinjuku Park Tower (227 m) in Tokyo, Japan, Incheon International Airport ControlTower (100.4 m) in Incheon, Korea, Air Traffic Control Tower (57 m) in Edinburgh, UK, and Shanghai World Financial Center (492 m) in Shanghai, China (Figure 2b) [2]. In this section, ATMD system studies are presented chronologically. [PERSON] and [PERSON] designed an ATMD for the vibration control of tall buildings exposed to wind loads. In that study, wind loads were modeled with white noise and a full feedback (displacement, velocity, and acceleration) control algorithm was used for the control of the ATMD system [4]. [PERSON] et al. positioned ATMDs atop two tall structures to provide first-mode vibration control for wind effects, and found that the control algorithm using acceleration feedback was successful in reducing structural responses [5]. [PERSON] et al. used a norm control technique using root mean square responses (H\({}_{\text{rms}}\)) in an optimum ATMD design and tested the sensitivity of numerical expressions derived by [PERSON] and [PERSON] [4] for optimum ATMD design under more complex wind effects. Tests have determined that the method proposed by [PERSON] and [PERSON] [4] was sufficient for finding the optimum parameters under  
Figure 1: General component of structure with an active tuned mass dampers (ATMD) system. Figure 2: (a) Taipei 101 with a sphere-shaped tuned mass damper [3] (b) Shanghai World Financial Center in Shanghai, China. along-wind excitations, whereas for under-wind excitations, it was revealed that the optimum frequency ratio could not be achieved, requiring a modification to the frequency ratio [6]. [PERSON] et al. suggested the use of a dynamic condensation method, which is an iterative method. It is necessary to use a low-order control on the ground, but placing a sensor on each floor is not a practical solution [7]. [PERSON] and [PERSON] compared the performances of fuzzy logic controller (FLC) and linear quadratic regulator (LQR) control algorithms using five-story structure models to ATMD [8]. Similarly, [PERSON] et al. applied an ATMD system with an FLC control algorithm to a 76-story reinforced-concrete office tower with a height of 306 m in Melbourne, Australia, and the performance of the control system under the wind load was compared with an ATMD system with a linear quadratic Gaussian control algorithm [9].