# Sliding Mode-Based Slip Control of Compact Electric Vehicle Truck for Varying Load and Yaw Rate
## 1 Introduction  
Application of control techniques for improved vehicle stability has captured the interest of researchers for a long time. In general, various control methods such as Electric Stability Control and Traction Control Systems are implemented for vehicle stability. With the advent of electric vehicles (EVs), stability controls such as an anti-lock brake system, a yaw stability system, a traction control system, and a roll stability system have been applied as extensions of existing studies [1, 2]. With the recent emergence of compact EVs that represent the low-speed and short-range market, statutory compulsory restrictions on existing stability controllers have been excluded and the vehicles have been mass-produced without considering stability control. However, in the case of compact EV trucks, vehicle stability controls are essential owing to the impact of weight of the cargo on vehicle characteristics. In this study, an improved target for stability control of compact EVs was developed for stability enhancement.  
Accurate vehicle body control aims to take actions according to the desired yaw rate which is used to control slip not only in EVs, but also in the chassis control of many vehicles [1, 3]. In addition, the desired yaw moment is used as a key reference for various types of vehicle control such as front steer control and torque vectoring [2, 4, 5].  
Although necessary for DY calculation, it is not realistic to consider the change in cornering stiffness in actual vehicle control because of several challenges such as the absence of a sensor. To estimate cornering stiffness, [PERSON] et al. proposed a Magic formula [6]. [PERSON] et al. simplified this formula by assuming a constant stiffness [7]. [PERSON] et al. and [PERSON] considered varying stiffness according to the road friction coefficient [8, 9]. [PERSON] et al. used an uncertain boundary term for constantstiffness [10]. [PERSON] et al., used the tire cornering stiffness by adding a scale factor to the constant for active front steering control [11]. [PERSON] et al. used a range of reference yaw rate instead of applying constant stiffness [12]. In most of the studies, stiffness was assumed to be or varied within a small range to calculate the desired yaw rate. Assuming a constant cornering stiffness does not accurately account for various changes in the system. A method using robust control to cope with the nonlinearity of constant cornering stiffness has also been proposed [13; 14; 15].  
However, in the case of trucks, the load varies according to the weight of the cargo and the cornering characteristics of the tires, so understeer or oversteer may occur in some situations, unlike general sedans and SUVs [16]. In particular, research on vehicle slip control under overload is required as it is known to cause numerous traffic accidents.  
In this study, the problem of cornering stiffness was solved by mathematically formulating the change in the understeer characteristics of an EV truck according to the vehicle cargo weight. A new reference for the yaw rate was designed based on the understeer gradient and the performance was verified through the slip controller. The overall configuration is shown in Figure 1. First, the existing method of estimating the desired yaw rate is examined, and the appropriate hypotheses in various tests are confirmed through ISO 3888-1 double lane change [17]. Second, by the ISO 4138 Steady State Circle test [18], the desired yaw rate is adjusted by formulating a variable mass understeer gradient (VMUG). Third, using the VMUG formula, the movement of the vehicle with heavy loads that cannot be examined by the Steady State Circle Test is investigated. Finally, a sliding mode slip controller that performs slip control according to the tire load is designed, and the performance of the VMUG is verified by comparing with the control of various desired yaw rate references.