## 1 Introduction
### Functionality of Semi-Active Suspension Systems  
Semi-active seat suspension systems play a pivotal role in reducing vibrations and enhancing ride comfort in vehicles. Semi-active seat suspension systems are employed in contemporary automobiles to reduce vibrations and enhance ride comfort. For instance, the latest generation of vehicles is anticipated to offer elevated levels of ride comfort, expansive interiors, effective soundproofing, innovative seating arrangements, and optional semi-active seat suspension systems. The utilisation of semi-active seat suspension systems confers a plethora of advantages, including enhanced driving comfort and diminished vibration [10; 11]. The mechanism utilised in these systems enables the seat suspension to be dynamically modified during operation, responding directly to the immediate external conditions, including but not limited to road quality and vehicle speed. This entails adjusting the seat in a manner that mitigates the impact of shock and vibration, thereby enhancing the comfort of the journey for those occupying the vehicle. Furthermore, in the event of an emergency in which the vehicle must stop or turn abruptly, the adjustments made to the suspension ensure stability (and consequently safety) for all passengers in the various scenarios in which such a situation occurs. The principal advantage of such systems is their capacity to adapt to diverse road and road surface conditions. They are capable of automatically selecting the optimal level of damping without the need for driver intervention, based on the information provided by available sensors [12]. A pertinent illustration of this phenomenon is the suspension adjustment when traversing a rough road. This adjustment serves to mitigate the transmission of shocks and vibrations to each passenger, thereby preventing the perception of each bump in the road. Conversely, modifying the suspension when driving on a smooth motorway can provide greater stability, thereby enhancing the safety of passengers. The technology of a semi-active seat suspension system is based on sensors that are integrated into both the seat and the suspension system. The two components work in conjunction with one another, continuously monitoring the condition of the road surface and the vehicle's movement [13]. This enables the system to communicate effectively to make real-time adjustments to the suspension system for optimum support. Consequently, the system is capable of reacting promptly to alterations in road conditions, thereby ensuring a comfortable and secure journey for drivers. In addition to enhancing driving comfort and safety, semi-active seat suspension systems can also have a beneficial impact on the health and well-being of drivers and passengers. Long-term exposure to vibration and shock while driving can result in some health problems [14]. When driving on a smooth road, the suspension can be adjusted to provide a more stable ride, better support, and reduced lateral movement. Furthermore, semi-active seat suspension systems can also enhance vehicle handling and stability, particularly at high speeds or during cornering [15]. Individuals engaged in occupational activities requiring a seated posture, such as driving, operating machinery and construction site work, and tractor driving, are exposed to general vibration. This vibration is transmitted to the body from the ground via the pelvis and back. Those exposed to vibration experience disturbances of the nervous system, including decreased concentration and increased reaction time, sensory disturbances and lesions of the locomotor organs. Particularly adverse changes in the human body are caused by the resonant vibrations of internal organs [16]. The range of these frequencies depends on the individual's physique and position (sitting, standing) and ranges from 2 to 12 Hz for internal organs and the thorax. The resonant frequencies for the head are in the range of 20 to 30 Hz, while those for the visual organs are 60 to 90 Hz.