# Voltage-Based Braking Controls for Electric Vehicles Considering Weather Condition and Road Slope
## 1 Introduction
The main objectives of ABS are to prevent the wheels from locking in order to maintain the stability and steerability of the vehicle during heavy braking, as well as to maximally exploit the tire-road friction coefficient in order to achieve the shortest possible braking distance. There are many papers on ABS [15; 16; 17; 18]. In [15], an ABS system was performed on flat-surface driving environments. An ABS algorithm designed for such flat-surface driving environments encounters difficulties in slopes, since the effect of a slope cannot be sufficiently reflected in the calculation. Reference [2] derived the braking distance, considering the case where the vehicle exists on the slopes. However, [2] did not consider both weather condition and road slope. In [19], the vehicle's dynamic behavior during braking and steering input was investigated by considering a sport-utility vehicle (SUV) with the ABS. Regulating the wheel slip ratio in the optimal value for different conditions of the road surface (dry, wet, and icy) during braking was considered as the ABS control strategy in [19]. The authors of [19] showed that the Pacejka Formula has the most appropriate results for the full range of the wheel slip ratio than other tire models, such as polynomial model. However, ref. [19] did not consider the road slope, as in our article. The authors of [16] addressed adaptive neural control of ABS incorporated with passive suspension dynamics. The authors of [18] handled control and estimation problems in ABS. Other papers on ABS handled how to derive the braking torque (or braking pressure) for controlling the wheel angular velocity. However, heavy or prolonged braking can cause brake fade or wear and it can also be dangerous in certain situations, such as when driving on wet or icy roads. According to EURO 7 regulations, brake fade or wear is not desirable, since the regulations refer to the reduction in particles emitted from brake pads [20]. For avoiding heavy or prolonged braking, our paper does not use a brake unit, such as electro-mechanical brake units or hydraulic brake units, for vehicle stop. In other words, a brake unit is completely avoided in our paper. This can potentially simplify the braking system and reduce maintenance requirements. Considering an electric vehicle with DC motors, the voltage in the motors is used for controlling the wheel angular velocity. Considering an electric vehicle with DC motors, the angular velocity is controlled using the voltage applied in the armature windings of the DC motor [21]. The authors of [21] addressed a PID control for controlling the wheel's angular velocity using the voltage of the DC motor. Inspired by [21], we control the voltage on the DC motor, in order to stop the vehicle smoothly and safely. This distinguishes our article from ABS-based papers which use a brake unit, such as electro-mechanical brake units or hydraulic brake units, for abrupt vehicle stop. In our article, the vehicle's motor voltage is controlled such that the wheel's angular velocity, say \(w\), converges to an optimal angular velocity. Once the optimal angular velocity, say \(w^{o}\), is set, PID controls can be used to control the armature voltage, so that the angular velocity \(w\) converges to the optimal angular velocity \(w^{o}\). As far as we know, our article is unique, since our automatic stop strategy does not require any brake units. Moreover, our article is unique in presenting automatic braking controls for the smooth stop of electric vehicles with DC motors, while considering both weather condition and road slope. The effectiveness of the proposed braking system is demonstrated via MATLAB simulations. The simulations show that increasing the voltage limit in the motor can decrease the braking distance. This article is organized as follows. Section 2 addresses definitions and assumptions used in the article. Section 3 presents the proposed braking system in this article. Section 4 presents MATLAB simulations to verify the effectiveness of the proposed braking system.