## 1 Introduction  
The suspension system plays an important role in the overall performance of a vehicle, influencing aspects such as ride comfort, handling stability, and safety [1; 2; 3; 4; 5; 6]. Vehicle suspension systems can be classified into three main categories: passive, semi-active, and active. Passive suspension systems typically comprise springs and dampers, which serve to absorb impacts and control spring motions, respectively. It is important to be aware that passive suspension systems have inherent limitations in their ability to provide an optimal balance between road holding and ride comfort [7]. To remedy this problem, an active or semi-active suspension can be employed. An active suspension system includes various actuators which pull down or push up the vehicle body to suppress the vibrations produced by road irregularities [8; 9]. The principal disadvantage of active suspensions is their complexity, the elevated cost of manufacture and maintenance, and the associated customer service expenses [10; 11]. Semi-active suspensions do not add energy to the suspension system but can change suspension parameters such as the damping coefficient of the shock absorber in real time, depending on the road profile and the vehicle dynamic state [12; 13]. In light of the aforementioned considerations, it can be inferred that the most adequate solution can be a semi-active suspension system, which displays superior performance in comparison to a classical (passive) system. Furthermore, it offers a more straightforward and cost-effective alternative to an active system. With regard to semi-active suspensions, magnetorheological (MR) dampers have been the subject of considerable interest over several decades [14]. An MR damper is a semi-active device that employs a MR fluid with adjustable viscosity, which is controlled by an external magnetic field. The fluid within MR dampers comprises micron-sized particlesthat are magnetisable and suspended in an oil-based medium. When exposed to magnetic fields, the particles align with the field, resulting in a notable increase in the fluid's viscosity and enhanced damping capabilities [15]. MR dampers possess the following beneficial characteristics: variable damping force, rapid response time, fault safety, and low power consumption [16; 17]. One of the primary challenges associated with integrating MR dampers for semi-active suspensions is their highly non-linear behaviour, which is inherently difficult to model [18]. For that purpose, a variety of models have been proposed to characterize the dynamic damper behavior. These include the Bingham model [19], the bi-viscous hysteresis model [20], and the phenomenological Bouc-Wen model [21]. While all of these models are capable of capturing the post-yield behavior of MR dampers, the modeling of nonlinear hysteretic damper behavior presents a significant challenge. For that purpose, the Bingham and Bouc-Wen models can be considered as two extremes. While Bingham is the simplest model, only accounting the magnitude and sign of the deflection rate of the damper [22], Bouc-Wen uses differential equations that depend on 14 experimental parameters [23]. The bi-viscous model represents a middle ground, utilizing a set of six equations based on piston velocity to estimate damper force [24]. Despite the fact that a higher-order model, such as the Bouc-Wen, has the potential to more accurately represent the actual behavior of a damper, several factors act as obstacles to its acceptance as a viable alternative. These include adjusting a large set of experimental parameters, which implies a complex and time-consuming identification process, as well as the difficulty in achieving a real-time implementation of such a complex model [25].