## 1 Introduction
[PERSON] proposed a lever-type ATMD/LT-ATMD to obtain a high-performance active control system in structures under a harmonic influence. In that study, the performance of the system was calculated by using the values of dynamic magnification factor [10]. [PERSON] and [PERSON] used multiple ATMDs (AMTMDs), which consist of ATMDs with the same damping and stiffness coefficients and different mass and control forces, in order to reduce the oscillations occurring due to ground vibrations [11]. [PERSON] et al. suggested using fuzzy logic control (FLC) and genetic algorithm (GA), which are metaheuristic algorithms, for the control of high-rise structures against earthquake effects with ATMD [12]. [PERSON] and [PERSON] suggested using an AMTMD to reduce the horizontal and torsional responses of asymmetric structure models simplified to two degrees of freedom (2 DOF) [13]. [PERSON] and [PERSON] designed an ATMD system that uses Proportional-Derivative (PD) and FLC control algorithms to limit structural vibrations [14]. PD controllers have only two actions. These actions, which are proportional action and derivative action, are defined by the parameters called proportional gain and derivative time, respectively. In PD, the error signal and the derivative of the error signal are used in the production of the control signal. By the addition of integral action defined with integral time to use the integral of the error signal, proportional-integral-derivative (PID) controllers are generated. In another study, [PERSON] and [PERSON] used a fuzzy proportional-integral-derivative (PID) controller with an ATMD system structure to limit the structural vibrations caused by the earthquake effect [15]. [PERSON] and [PERSON] also proposed the self-adjusting FLC for the active control of ATMD structures [16]. [PERSON] et al. suggested using the ATMD system to reduce the linear and torsional responses that may occur in asymmetric structures in an earthquake. In the study, optimum ATMD parameters are determined by using the minimum linear and torsional displacement minimization criteria and the gradient search method [17]. [PERSON], C. analyzed asymmetric structures with an AMTMD control system, in which the soil structure interaction (SSI) was taken into account. In that study, the optimum parameter criterion was defined as the minimization of the mean square root values of the horizontal and torsional displacements [18]. [PERSON] and [PERSON] have developed an active control method to reduce out-of-plane vibrations in the engine compartment of wind turbines. In that study, in which soil-structure and wing-tower interactions are also taken into consideration, an ATMD system with an LQR controller was used [19]. [PERSON] et al. used particle swarm optimization (PSO) and linear quadratic regulator (LQR) to find the optimum active control force in ATMD-controlled structures [20]. [PERSON] et al. investigated an ATMD system with a linear quadratic Gaussian (LQG) controller in order to reduce wind-induced responses in high-rise buildings [21]. In the study, ATMD parameters (tuning frequency and damping ratio) were found by a numerical optimization method developed by [PERSON] and [PERSON] [22]. [PERSON] et al. suggested using the interval type-2 FLC algorithm for the active control of structural systems modeled as single degree of freedom with ATMD systems [23]. Two identical ATMDs were used to reduce the wind-induced vibration of the Shanghai World Financial Center Tower in China [24]. [PERSON] and [PERSON] suggested using fuzzy logic control (FLC) and particle swarm optimization (PSO) to reduce vibrations in a structure experiencing an earthquake [25]. [PERSON] and [PERSON] suggested using a \"multi-objective adaptive genetic-fuzzy\" controller to control tall structures exposed to high earthquake activity and repeated wind load by ATMD [26]. [PERSON] and [PERSON] suggested using a hybrid active tuned mass damper (HATMD) to reduce vibrations caused by ground acceleration in the buildings.