# Optimization of Damping in a Semi-Active Car Suspension System with Various Locations of Masses
## 1 Introduction  
The wheels are connected to the vehicle through the suspension system. In real vehicle suspensions, the relative movement of the wheels in relation to the vehicle body is used for vibration control and for the transmission of force and torque between the wheels and body. Vibration control helps hold good and uninterrupted contact of the tires with the road and ensures driving safety and ride comfort regardless of the quality of the road surface [1]. Depending on vibration control, the suspension types are passive, semi-active, and fully active. Semi-active suspension can smoothly change the damping coefficient and can be nearly as effective as a fully-active suspension for increasing ride quality [2]. It combines the advantages of both the other suspension types. Various systems are discussed in reference [3] noting their strengths, weaknesses, and relative performance or equipment requirements. The semi-active suspension system becomes a suitable choice due to its small power consumption, low expense, and fewer parameters [4]. The main element of semi-active suspensions is a variable damper of a few possible types: the magnetorheological damper, the electrorheological damper, the electrohydraulic damper, and the electromagnetic damper [5, 6]. Road conditions often alter during driving. Different emphasis is placed on ride comfort and handling stability under different road conditions or driving styles [7, 8, 9]. The properties of the suspension should also change depending on the road conditions [10, 11, 12]. When ride comfort is the priority, a semi-active suspension system using a variable damper can have an effectiveness close to that of an active suspension [3, 13, 14, 15, 16]. However, the variable damper in a semi-active suspension system can only change the rate of dissipating energy without receiving energy, and it has major restrictions when one requires controlling the height and attitude movement of a vehicle. The semi-active suspension system with variable stiffness can solve this problem [17, 18, 19]. Meanwhile, some authors use both a variable damper and stiffness [20, 21, 22, 23]. Therefore, semi-active suspension systems are veryhelpful in enhancing ride comfort and vehicle handling capabilities. One of the main problems is to determine the control signal for the semi-active suspension. Various control strategies [6; 24; 25; 26] have been developed in which the control signal is determined by the measurement of different parameters. Real-time control strategies such as skyhooks or groundhooks are common for semi-active vibration damping based on road statistical properties, i.e., an optimal damping ratio control [26]. In addition, a preview strategy was implemented to improve the behavior of semi-active systems. Therefore, the system needs information about road conditions. At present, researchers have carried out many studies of models and methods of road recognition. Some of them are difficult to realize or are very expensive. Various methods and equipment for measurement of the road properties are briefly discussed in [27; 28; 29]. Different, inexpensive response-based road profile identification methods are reviewed and presented in [30]. Several vehicle models with semi-active suspension systems have been commercially developed in recent years [6]. The usage of road profile information before a wheel hits road unevenness, investigated in [13; 31; 32; 33; 34; 35], has been applied to mass production cars as well. The early attempts were made by Nissan in 1990 using Super Sonic Suspension [36] and, recently, the Magic Body Control feature [37] used in Mercedes Benz. [PERSON] and [PERSON] in [38] state, \"the next advances in active and semi-active suspension design will mainly come from two thrust areas.