## 1 Introduction  
Conventional wind power systems, a representative renewable energy source, generate electricity using blade rotations driven by wind energy, producing at a relatively high efficiency. However, large-scale wind power systems have significant disadvantages, such as high construction costs, a large area required for the installation site, and high noise. Furthermore, wind power systems have an adverse visual impact on the aesthetic environment and pose a threat to birds [1; 2]. Furthermore, these systems comprise rotating mechanical parts, such as bearings and blades [3], with a short life cycle that requires frequent maintenance and high operating costs. To solve these major disadvantages of conventional wind power systems, new approaches have been proposed for wind turbines. In this sense, blackless wind turbines (BWTs) are a new and promising concept. A small-scale cylinder-type BWT was first proposed in [4]. This pioneering concept is designed using a simple cylinder on a flexible rod that resonates with the vortex-induced vibration (VIV). Its inner structure features a simple design without rotational mechanical parts, thereby reducing manufacturing and maintenance costs. Furthermore, this design is compact, offering a relatively high energy density per area, and it can be installed on rooftops, allowing more freedom at the installation sites. Vortex-induced vibration (VIV) occurs due to a Karman vortex, which is formed when wind passes through a cylindrical body [5]. The Karman vortex forms a low periodic pressure on the body of the cylinder, which exerts a periodic lifting force on the body perpendicular to the wind velocity. If the vortex-shedding frequency is close to the structural frequency of the BWT, the vortex enters the lock-in range of the resonance, causing the BWTto oscillate [6]. The vibration energy of the BWT's resonance can be converted into electrical energy with electric generators or smart materials. It is preferable to maintain the BWT's resonance for maximum vibration when generating energy by keeping the vortex-shedding frequency in the lock-in range. However, the vortex-shedding frequency is proportional to the wind speed, which depends on the weather conditions. When the wind speed changes, causing the induced vortex frequency to be outside the structural resonance, it decreases the vibration level and consequently dramatically lowers power generation [7]. A solution to increase the efficiency of power generation is to widen the operating lock-in range to expand the wind velocities of the BWT operation. Several studies have attempted to widen the lock-in range by modifying the aerodynamic design and material. [PERSON] et al. [8] designed a mast shape to expand the aeroelastic resonance range to improve power generation. [PERSON] et al. [9] attached fin-shaped rods to the mast surface and demonstrated that their innovation could expand the frequency band to harvest vibration energy. Furthermore, [PERSON] et al. [10] altered the roughness of the mast surface to widen the vortex frequency band and amplitude. However, these surface design approaches have limitations in actively responding to varying wind speeds [11]. Another approach to expanding the operating lock-in range is to actively tune the BWT's resonant frequency. A resonance-tuning system is proposed to tune the frequency of the BWT structure to closely match the frequency of the varying input vortex [4; 12]. These tuning systems are designed to control the equivalent stiffness of the system, which affects the resonant frequency of the system. A magnetic-force-based tuning module for VIV BWTs was proposed in [4]. This system is composed of two pairs of circular magnets with identical poles facing each other. The first magnet is attached to a flexible rod, whereas the other magnet is fixed to the ground. Additionally, the magnetic repulsion force is proportional to their relative distance, which varies proportionally to the magnitude of the oscillation.