## 1 Introduction  
With its large transportation capacity and low transportation cost, the liquid tank semi-trailer has become the main vehicle for transporting liquid chemical products. Compared with ordinary freight cars, liquid tank semi-trailers not only have the characteristics of a high center of mass position and large cargo weight but also are more prone to instability than ordinary semi-trailers, because of the coupling relationship between the lateral sloshing of the liquid in the tank and the tank body [1]. The dangerous working conditions of liquid tank semi-trailers are mainly divided into yaw instability and roll instability. When a vehicle is running on a low-adhesion road, due to the small adhesion between the tires and the road, the lateral force of the tires is easy to become saturated, which leads to the occurrence of yaw instability; when driving on a high adhesion road, a vehicle is prone to roll instability [2]. At present, most scholars' research mainly focuses on the influencing factors and improved methods of the roll stability of liquid tank semi-trailers. [PERSON] [3] established a dynamic model of a liquid tank vehicle based on the trammel pendulum (TP) model and analyzed the influence of the liquid filling ratio and other influencing factors on the driving stability of the liquid tank vehicle. [PERSON] [4] established a volume of fluid (VOF) multi-phase flow model and a standard k-\(\varepsilon\) turbulence model to study the effects of transportation conditions, such as the liquid-filling ratio, the elliptical ratio of the tank section, and the number of baffles, on the vehicle's roll stability. [PERSON], [PERSON] [5] improved the roll stability of a liquid-carrying articulated vehicle based on the proposed two control methods to avoid rollover, shimmy, and folding accidents. These studies analyzed the influencing factors of the roll stability of a liquid tank semi-trailer on a good road and provided the corresponding improvement methods, but there were few studies on the yaw stability of vehicles turning on low-adhesion roads. In addition, most research on the path-following problem concentrates on the field of intelligent vehicles [6], while little research focuses on the field of heavy semi-trailers or liquid tank semi-trailers. Therefore, this paper studies the yaw stability and path-following performance of liquid tank semi-trailers when turning on low-adhesion roads. To study the yaw stability control method of liquid tank semi-trailers when driving on low-adhesion roads under turning conditions, it is necessary to study the liquid sloshing law in the tank. At present, the main research methods of liquid sloshing are hydrodynamics, the quasi-static model, the equivalent mechanical model, etc. [7]. With the ability to describe the large amplitude of liquid sloshing and the convenience of being coupled with the vehicle dynamic model, the equivalent mechanical model is widely used in practical engineering. The most commonly used equivalent mechanical models mainly include the spring-mass model, the simple pendulum model, and the TP model [8]. However, the spring-mass model is only suitable for small amplitude shaking; for the simple pendulum model, the motion track of it is a circular arc, which is only suitable for describing the liquid sloshing effect in a cylindrical tank but not for an elliptical cylinder tank. To solve this problem, [PERSON] [9] studied the liquid impact in the horizontal elliptical cylinder tank and proposed the TP model, which is suitable for simulating the liquid sloshing effect in the elliptical cylinder tank. In terms of vehicle yaw stability control methods, there are mainly active steering, active suspension, differential braking, etc. [10]. Among these methods, the actuator of active steering is complex and costly, the damping adjustment range of active suspension is small, and the suspension adjustment time is too long.