# Analytical Investigation of Vertical Force Control in In-Wheel Motors for Enhanced Ride Comfort
## 1 Introduction  
The rapid rise of electric vehicles (EVs) is transforming the automotive industry. Central to this transformation is the use of in-wheel motors (IWMs), a technology first proposed in 1900. Today, with the growing market potential of EVs, IWMs have emerged as a promising approach to revolutionize vehicle design and performance [1, 2]. Relocating the motor to the wheel brings numerous advantages. It reduces the overall vehicle weight, thereby increasing driving range, reducing running costs, and minimizing the frequency of battery charging. Additionally, IWMs improve handling due to precise torque control on each wheel, resulting in enhanced stability, traction control, and shorter stopping distances. This technology also offers more efficient production and flexible vehicle design, making it economically attractive for manufacturers. However, integrating IWMs into vehicle wheels increases unsprung mass, adversely affecting ride comfort and handling, especially at high speeds [3]. Each IWM adds 30-52 kg per wheel, significantly boosting unsprung mass and reducing the body-to-wheel mass ratio [4]. This imbalance compromises ride smoothness, particularly at high frequencies where dynamic load changes are more pronounced. The increased unsprung mass causes the wheels to react more intensely to road irregularities, resulting in greater vertical vibrations. When the dynamic load and dead load are equal but opposite, the vertical load drops to zero, causing the wheel to lose contact with the road. This loss of adhesion can make driving dangerous during high-speed driving or sudden maneuvers [3]. Furthermore,this situation stresses suspension components, increasing wear and potential damage. Maintaining tire contact with the road is crucial for safety and performance, as any loss of contact reduces stability and control [3; 5]. To address these challenges, vehicle suspension systems play a critical role in transmitting forces between the wheels and the vehicle frame, reducing shocks from rough roads, and ensuring driving smoothness and stability. Extensive research has focused on developing both active and passive suspension systems to enhance vehicle performance. One common solution involves applying passive suspensions with springs and dampers between the IWM and the wheel to improve comfort [1; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. However, these systems often fail to address the relative vertical displacement or vibration of the IWM, necessitating more advanced solutions. These challenges require advanced suspension systems, such as semi-active or active systems equipped with magneto-rheological (MR) [7; 9; 16], hydraulic (HA) [17], or electromagnetic (EMA) absorbers [18]. Numerous control techniques have been developed to enhance vehicle ride and handling, ranging from comfort-oriented sky-hook to handling-oriented ground-hook and multi-objective linear optimal control techniques [6]. Despite these advancements, traditional suspension systems cannot fully eliminate vibrations across all frequency ranges, necessitating a compromise between ride comfort and handling performance. This compromise is further exacerbated in IWM vehicles due to the increased unsprung mass, highlighting the need for more sophisticated suspension technologies to maintain optimal ride quality and vehicle control. Configurations using MR dampers showed low efficiency [9], with unchanged trade-offs between low- and high-frequency responses. Dynamic dampers like tuned mass dampers (TMDs) can partially reduce this issue. Ref. [8] reported a 31.2% improvement in ride comfort and a 2.2% increase in road holding. Ref. [19] introduced a compact electromagnetic TMD, achieving a 21.7% increase in comfort and a 5.7% improvement in handling. Refs. [5; 10; 13] demonstrated a two-stage optimization control reducing body acceleration by 11.34% and impulse force on the IWM by 88.57%. Despite these advances, implementation remains challenging due to limited wheel space and system robustness.