# Driving Safety Improved with Control of Magnetorheological Dampers in Vehicle Suspension
## 1 Introduction
### Highlights  
The studies presented in the literature and related to vehicle vibration control using magnetorheological dampers are commonly limited to stationary vehicle suspension model, which does not take the longitudinal motion of the vehicle, more complex wheel model, or tire to road friction into account. Typically, description of tire-road interaction is limited to their contact in a single point. Admittedly, sophisticated models of vehicle and tire dynamics are well known; however, they are rarely related to semi-active suspension and semi-active control algorithms, in particular with regard to the analysis of road holding and vehicle handling. The presented study discusses the interaction between the road surface and half-car vehicle model equipped with MR dampers and controlled with standard semi-active control algorithms. The most important phenomena that may occur while driving are taken into account, such as tire slip, body heave and pitch motion, wheel vibration, rolling resistance, and aerodynamic drag. It was shown how the suspension control influences the vehicle behaviour during the typical driving phases, i.e., accelerating, driving with constant speed, and braking. The results were obtained for a vehicle model, which is, in detail, referred to an actual, commercially available, and real-size all-terrain vehicle (ATV), which was additionally equipped with suspension MR dampers. The road profile was generated according to the norm ISO 8608 describing road surface profiles with respect to mechanical vibration [41]. Furthermore, the influence of road profile on the vehicle wheel was evaluated while assuming the actual parameters and dimensions of the ATV's wheels. The methodology of road holding and vehicle handling was proposed while road holding was further analysed with respect to susceptibility of the wheels to separation from the road surface and fluctuations of the normal force exerted by the ground. It was also shown that driving-safety-related studies, like other research areas, require statistical analysis and averaging operation performed over several realizations. It is caused by the fact that the effective influence of the road on wheels depends on many factors, including applied control algorithms, tire and suspension deflection, or vehicle speed, despite the fact that the same road profile was used. The paper is organized, as follows. Section 2 presents the description of the vehicle model, including the method of generating the road profile, a half-car submodel of vehicle suspension, and the MR damper model, which is based on a hyperbolic tangent function. The distributed model of tire takes into account the averaged normal force exerted by the ground and damping related to the tire deflection. Further, the interactions of the vehicle with the road and slipping effect are described by the Burckhardt model of tire-road friction. The description of wheels dynamics includes their moment of inertia, which has influence on effective torques that are generated by the rear drive system and disc brake on the front wheel, similarly as in the real vehicle. The model of wheels also includes rolling resistance while the whole vehicle is subjected to aerodynamic drag. Section 3 is dedicated to semi-active suspension control algorithms in which three control approaches are compared. First, a case of MR dampers controlled by different values of constant current is defined, which reflects different soft and hard configurations of passive suspension. Further, two variants of Skyhook control are presented, where the former is based on separate control of suspension parts, while the latter emulates different damping forces that are exerted on heave and pitch velocities of the vehicle body. Section 4 presents the results obtained for implemented semi-active control approaches with respect to road holding and vehicle handling.