# Sliding Mode Control of Laterally Interconnected Air Suspensions
## 1 Introduction  
The vehicle suspension plays an important role in reducing the body vibration transmitted from the road excitations and ensuring handling stability of vehicles [1; 2]. With the increasing demand on ride comfort and road handling, various control technologies and structures of suspensions are emerging continuously. Vehicle suspensions can be classified into three types: active [3; 4; 5; 6], semi-active [7; 8; 9; 10; 11; 12], and passive [13; 14; 15; 16]. Active suspension systems with appropriate control strategies can greatly improve both the comfort and handling, but they are expensive and consume large amounts of energy. Thus, energy-regenerative structures are proposed to reduce power consumption, resulting in more complex structure and costs [17; 18; 19; 20]. Passive suspension systems with constant spring stiffnesses and damping coefficients only perform well under limited conditions, but new structures have also recently been proposed to improve the overall performance [20; 21]. Meanwhile, semi-active suspension systems can reach a balance between cost and performance, thus the research of semi-active suspensions attracts lots of attention. In terms of the semi-active suspension, the air spring has been widely used because of its significant advantages of low vibration-transfer coefficient and adaptive load-capacity ability [22; 23; 24]. In addition,the air spring is applicable for adjusting the body height or tuning the stiffness, which brings more control flexibility to the semi-active suspension [25; 26; 27; 28]. Some new structures of the air spring have been proposed, such as the air suspension with an additional air chamber and the interconnected air suspension [29; 30; 31]. Generally, connecting the air spring to an additional chamber can soften the air spring. Similarly, the interconnected air suspension system connects springs with a pipeline, and each connected spring plays the role of the others' additional chamber. However, different from the additional-chamber design, the sum gas volume of all the springs remains constant in the interconnected suspension system. Therefore, the vertical stiffness of the vehicle stays the same and only the roll and pitch dynamics are affected [31; 32]. Besides, the pitch and roll dynamics affect the bounce response of the vehicle body [33; 34; 35], which brings the opportunity to improve the suspension performance via interconnection. Interconnected suspension can be classified based on the transferred media, for example, mechanical, hydraulically, pneumatic, and hydro-pneumatic interconnected suspension [36; 37; 38; 39; 31]. The interconnected air suspension was proposed by [PERSON] in BHL in 1961 [40], which can be interconnected laterally and longitudinally. The longitudinally interconnected air suspension is mainly used in heavy trucks to achieve better road friendliness and ride comfort [41; 42]. Hence, many studies can be found in the literature, such as modeling, characteristics analysis, structural optimization, and the corresponding control strategies [28; 42; 43]. Similarly, the laterally interconnected systems can also improve the road friendliness and comfort. On the basis of previous studies [22; 31], the effect of the interconnection mostly depends on the diameter and length of the interconnection pipelines. The lateral interconnection structure significantly reduces the pipeline length compared with the longitudinal one. Thus, the laterally interconnected suspension system has a quicker response and achieves better comfort and road friendliness than the longitudinal one when using the same diameter of the pipelines. However, the current studies on laterally interconnected air suspension system only focus on its modeling and characteristic analysis. To achieve a better use of laterally interconnected suspension system, an appropriate control method should be developed. Several methods have been proposed to overcome different shortcomings.