## 1 Introduction
### Functionality of Semi-Active Suspension Systems
As knowledge and technology advance, cab seats for operators and drivers are being developed to limit transmitted vibration frequencies to the lowest possible range (below 20 Hz). Despite this, vibration syndrome remains a significant contributor to the overall incidence of occupational diseases,with research indicating that the use of newer suspension technologies for both machines and vehicle operators' work seats can help to prevent these effects [17; 18; 19]. The objective of semi-active seat suspension systems is to enhance ride comfort by combining the features of passive and active systems. In contrast to passive systems, which rely primarily on springs and dampers, and active systems that utilise sensors and actuators to continuously adjust the suspension, semi-active systems facilitate straightforward control of the vehicle. These systems provide an enjoyable driving experience while simultaneously affording the driver control over the stability of the vehicle. This represents the optimal solution, offering the best of both worlds: comfort and control. Consequently, semi-active suspensions are commonly employed in contemporary vehicles. Furthermore, these systems facilitate reductions in vehicle vibration, which contributes to a more comfortable journey. Vibrations can be generated as a result of the unevenness of the road and the operation of the engine and gearbox combined with the dynamics of the tyres. These vibrations are not only displeasing to the passengers but also damaging to their health. Nevertheless, semi-active seat suspension systems enable a vehicle to adapt to varying frequencies and amplitudes, thereby adaptively enabling the dissipation of vibrations. The detection of vibrations and the subsequent adjustment of the seat suspension following these findings ensures a comfortable ride and avoids the negative effects of prolonged exposure to vibrations. The utilisation of semi-active seat suspension systems has been identified as a pivotal factor in the evolution of modern vehicles [20]. In recent times, vehicle manufacturers have placed a greater emphasis than ever before on two key aspects of driving: safety and comfort. The two most commonly utilised technologies in semi-active seat suspension systems are magneto-rheological and electromagnetic dampers [21]. Magneto-rheological dampers regulate the damping force by employing magnetic fields to alter the viscosity of the fluid, thereby enabling the suspension system to swiftly adapt to varying road conditions. Semi-active seat suspension systems have been lauded for their capacity to adapt to diverse driving styles and preferences. Some drivers may opt for a stiffer suspension to enhance the road feel, whereas others may select a softer suspension to better absorb bumps and potholes. Nevertheless, semi-active systems permit the seat suspension to be calibrated to align with drivers' disparate preferences, thereby offering flexibility to personalise the driving experience without compromising on quality and safety [22]. In addition, semi-active seat suspension systems are capable of alleviating driver fatigue, a further benefit of their use. Long periods of driving can result in discomfort and fatigue due to the vibrations and shocks caused by a non-level road surface. Nevertheless, by reducing these vibrations and providing a more comfortable ride, semi-active seat suspension systems can assist in maintaining the driver's alertness and focus. This can then result in a markedly enhanced driving experience for all, particularly for professional drivers who are required to spend extended periods behind the wheel. Furthermore, semi-active seat suspension systems have been empirically demonstrated to enhance safety [23]. By reducing vibration, these systems make it more difficult for factors that could lead the driver to lose control of the vehicle or prevent a rapid response in emergencies due to discomfort.