## 1 Introduction  
One of the main challenges of Internet of Things (IoT) technology is to find adequate power supply [1]. The current trend is integrating the IoT system with sensors and wireless communication components. Consequently, there are higher requirements for wireless communication, sensor miniaturization, and reduced power consumption of electronic devices. Energy harvesting is a promising technique that converts unused abundant environmental energy into electrical energy. Therefore, kinetic (or vibration) energy harvesting systems are considered potential candidates to supplement electrical energy sources for self-powered sensors, IoT technology, and wearable microdevices (MEMS). All harvesters use transducer mechanisms to convert mechanical energy into electricity. The most popular ones are electromagnetic, piezoelectric, and electrostatic. Electromagnetic harvesters (EHs) appear to be extremely promising in practice. One possible explanation for this is the high mechanical robustness of these mass-spring-damper constructions, which means that they can be installed with coils and magnets rather than with fragile piezoelectric crystals [2] and that they can be applied at low frequencies. Most EHs rely on magnets oscillating in a coil suspended by a spring or magnetic levitation. In the paper [3], various technologies were used for the fabrication of the harvester, and insights into the circuits used in real applications were given. That study primarily focused on design configurations, construction parameters, modeling, and experimental validation of transduction mechanisms and energy outcomes. [PERSON] et al. [4] demonstrated that an appropriate electromagnetic harvester architecture could improve efficiency by about 10%. Magnetic levitation energy harvesters are interesting due to their capacity for operation in a low-frequency bandwidth. Therefore, they can be effectively applied in pendulum vibration harvester/absorber systems [5; 6]. These harvesters have a simple and easy-to-maintain design, which eliminates the need for mechanical components such as springs. These systems have a non-linear stiffness profile due to magnetic forces producing a nonlinear frequency response, allowing more power to be collected over a larger frequency range. A comprehensive and systematic analysis of 21 design configurations of electromagnetic energy harvesters with magnetic levitation architectures is given in [7]. These are classified into four types based on the number of coils and permanent magnets: single coil and single levitating magnet [8; 9], single coil and multiple levitating magnets [10; 11], multiple coils and single levitating magnet [12; 13; 14], and multiple coils and multiple levitating magnets [15; 16]. Several studies have found that the amount of energy harvested greatly depends on the geometric optimization of the harvester [17; 18; 19]. Investigations have been made into magnetic levitation harvesters based on a single moving magnet in the coil. The magnetic restoring force is usually modeled as the Duffing hard characteristics [20]. A study [21] demonstrated that a magnetic levitation vibrational energy harvester exhibited features that were typical of chaotic dynamic systems. However, the state was more complicated than the Duffing equation, which was previously used to describe magnetic forces. [PERSON] et al. [22] proposed a two-degrees-of-freedom harvester based on magnetic levitation. The effects of the key variables, such as the distance between the lower spring and the suspended magnet, excitation acceleration, spring stiffness, and the copper cylinder mass on the generated properties, were investigated. In reference [23], a 2 DOF magnetic levitation harvester with two magnetic springs and a series connection of two induction coils was described. In one of the tested configurations, the harvester's performance improved by 10% compared to the 1 DOF system. [PERSON] and [PERSON] [24] studied the influence of resistance charge on the energy recovery in a 2 DOF magnetic levitation harvester.