# Driving Safety Improved with Control of Magnetorheological Dampers in Vehicle Suspension
## Vehicle Model and Its Coupling with Road and Environment  
The presented results refer to the actual, commercially available ATV-Sweden that is shown in Figure 1a, manufactured by CF-Moto. According to the vehicle approval documents, it is 2.185 m long, 1.17 m wide, 1.23 m high, and its mass is approximately 393 kg. Original shock-absorbers have been replaced with MR suspension dampers. It is also worth noting that each part of the suspension operates independently, which allows for only adapting a selected MR damper to the road unevenness. The vehicle is equipped with a measurement and control system in order to generate appropriate control currents for MR dampers. The measurement part of the system includes numerous sensors. Mainly, three-axis accelerometers are used. Five of them are located in the vehicle body and additional accelerometers are located in the vicinity of each wheel. Furthermore, the deflection of each suspension part is measured while using an LVDT (linear variable differential transformer). Pitch and roll motion of the body, as well as acceleration of the driver's seat, are measured by the additional IMU (inertial measurement unit). The angular velocity of each wheel can be roughly measured while using a Hall effect sensor and numerous neodymium magnets that are attached to the wheel rim. Regardless of this, the speed of the vehicle is measured by the standard sensor. The study is focused on the analysis of longitudinal behaviour of the vehicle model during accelerating, braking or driving with a constant speed. Thus, simulation was performed for a half-car model which describes the major behaviour of the vehicle during road manoeuvres mentioned above, i.e., longitudinal and vertical motion as well as body pitch. The parameters that were used for the model simulation were carefully estimated and listed further in Table 1 in Section 4. The proposed half-car model exhibits seven degrees of freedom (DoFs) and its graphical representation is shown in Figure 1b. First four DoFs are related to wheel vertical and angular motion, denoted as \(z_{uf}\) and \(\phi_{uf}\) for the front wheel, respectively, as well as \(z_{ur}\) and \(\phi_{ur}\) corresponding to the rear wheel. Further two DoFs, denoted as \(z_{s}\) and \(\phi_{sp}\), describe the heave and pitch motion of the body, respectively. For the simplification of the model, an assumption was made that longitudinal displacements of all vehicle components are the same and they are depicted by the last DoF, denoted as \(x_{s}\). This model describes the dynamics of the half of the vehicle. Thus, selected vehicle parameters, e.g., mass or moment of inertia of the body as well as the torque of the drive system need to be scaled down. The wheel weights were measured as \(m_{uf}\) = 10 kg and \(m_{ur}\) = 15 kg for the front and rear wheel,  
Figure 1: The experimental all terrain vehicle with magnetorheological (MR) dampers: (**a**) actual vehicle, (**b**) graphical representation of the implemented half-car model with 7 DOFs. respectively. Half of the body weight is \(m_{s}=171.5\) kg while taking the weights of the wheels into account. Longitudinal location of the body centre of gravity (CoG) was estimated and defined by \(l_{f}=0.609\) and \(l_{f}=0.681\) m, which show that CoG is slightly shifted toward the front of the vehicle. The height of the vehicle CoG \(h_{s}=0.554\) m was taken from the literature [42], where the selected parameters of the CF500 vehicle are listed. Any data related to the body moment of inertia are hardly available for this type of vehicle, while experimental identification is not a trivial task for such weight.