# Advancements in Semi-Active Automotive Suspension Systems with Magnetroheological Dampers: A Review
## 1 Introduction  
The evolution of automotive technology has continuously pushed the boundaries of vehicle performance, comfort, and safety. One of the most critical systems contributing to these advancements is the suspension, which acts as the interface between the vehicle's frame and wheels. It plays a pivotal role in ensuring a smooth and stable ride by mitigating the impact of road irregularities and enhancing vehicle handling. With the increasing demand for enhanced vehicle performance, the significance of ride comfort and safety, closely associated with the suspension system, has become increasingly pronounced. Suspension systems have undergone significant development, transitioning from traditional passive systems to more advanced active and semi-active configurations. Passive suspension systems, renowned for their simplicity and reliability, have historically dominated the automotive market. However, their inability to adapt to varying road conditions restricts their effectiveness in optimizing both ride comfort and handling stability simultaneously. This constraint has propelled the development of active suspension systems, which utilize actuators to dynamically adjust damping forces in real time, thereby offering superior performance across diverse driving conditions [1; 2]. Despite their advantages, the complexity and high energy consumption associated with active suspensions have hindered their widespread adoption. Semi-active suspension systems have emerged as a promising alternative, striking a balance between the simplicity of passive systems and the adaptability of active systems [3; 4]. These systems operate withintelligent control strategies to adjust damping forces based on real-time driving conditions, thus enhancing ride comfort and handling stability without high energy demands as active suspensions. Among the array of semi-active suspension technologies, magnetorheological dampers (MRDs) have gained substantial attention due to their rapid response, excellent reversibility, compact size, low energy consumption, continuous damping force adjustment, and high reliability. MRDs function by altering the viscosity of magnetorheological fluid (MRF) through the application of a magnetic field [5]. They have found widespread applications in the automotive industry, aerospace, and construction, reflecting their versatility and effectiveness in various fields. The design of MRDs involves intricate interactions among fluid dynamics, magnetic fields, and structural mechanics. Researchers have made significant strides in optimizing MRD structures and enhancing their performance. Notable developments include the introduction of twin-coil MRDs [6], twin-tube MRDs [7], self-inductive and self-powered dampers [8], and advanced controllers to improve response speed and damping efficiency [9]. These innovations have laid a solid foundation for the widespread use of MRDs in various sectors. Semi-active suspension systems, particularly those utilizing MRDs, are complex nonlinear systems influenced by multiple factors. Optimizing suspension control strategies is essential for enhancing vehicle ride comfort and overall performance. Control strategies for semi-active suspensions can be broadly classified into classical, modern, and intelligent categories. Classical control strategies include skyhook [10], groundhook [11], and hybrid controls [12]. Skyhook control aims to reduce vibrations by theoretically connecting the vehicle body to an \"absolutely stationary\" point. Groundhook control focuses on improving road adherence and vehicle stability. Hybrid control strategies integrate the advantages of both skyhook and groundhook methods. Modern control strategies encompass optimal control [13; 14], model predictive control (MPC) [15], robust control [16], and adaptive control [17]. Optimal control, such as linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) methods, involves formulating system state equations and optimization functions.