## 1 Introduction  
With the development of automobile electrification and intelligence, the brake-by-wire (BBW) system has received more and more attention. This system can be divided into two kinds: electro-hydraulic brake (EHB) and electro-mechanical brake (EMB).The EHB system adopts electronic control to replace part of the mechanical control, retaining part of the hydraulic components, and exists as a transitional technology with slow braking response and complex piping arrangement [1, 2, 3]. The EMB system provides a more advanced braking program compared with the former; the EMB system does not require a hydraulic system, and is driven directly by the motor to generate braking force, with a faster braking response, a small system size, a simple structure, ease of installing and maintenance, ease of integration of the parking brake, and so on. The flexibility and modular design of distributed drive systems provide ideal conditions for the integration of electro-mechanical brakes (EMBs), and their combination offers significant advantages [4, 5, 6]. The anti-lock braking system (ABS) uses the slip rate of the wheels as the controlled object, keeps the slip rate near the optimal slip rate, avoids the tire locking phenomenon when the wheels have a large braking torque, and improves the braking performance of the vehicle [7, 8, 9]. The use of the EMB system in combination with the traditional ABS can more accurately control the braking force of the wheels, maintain the optimal slip rate of the wheels, improve the performance of the ABS, and ensure that the vehicle always maintains the ability to steer, which is an important safeguard for the safety of driving the vehicle [10]. However, vehicle braking effectiveness is affected by the tire-road friction coefficient and controller robustness, which provide challenges to improving braking effectiveness. Numerous scholars have conducted extensive research on the above problems. In terms of pavement identification, [PERSON] [11] used a combination of strong tracking traceless Kalman filtering and interactive multi-model traceless Kalman filtering to estimate the road friction coefficient, which has good identification accuracy. In the literature [12], an identification method using machine learning and a bi-radial basis function neural network to build a pavement adhesion coefficient estimator using the Extended Kalman Filter is proposed, but there are significant fluctuations in the simulated pavement adhesion coefficients. [PERSON] proposed a fusion algorithm based on improved singular-value decomposition trace-free Kalman filtering for estimating the tire-road friction coefficient [13]. At the same time, ABS controller robustness and tire slip rate control are also important factors in braking effectiveness; the current automotive ABS mainly involves PID control and integral sliding-mode control (SMC) [14]. An optimized fuzzy adaptive PID algorithm is proposed in the literature [15] to improve the braking stability of the ABS. [PERSON] [16] proposed a global sliding-mode controller and utilized the Lyapunov method to establish system stability, aiming to minimize the error between the actual slip rate and the optimal slip rate. However, both of these have problems, such as poor adaptability and jitter. In the literature [17], an Hoo gain-scheduling controller is proposed, which can maintain the slip ratio within the optimal range according to road conditions, thereby achieving optimal braking performance. Auto-Disturbance Control (ADRC), with the advantages of fast response, strong decoupling, model-independence, high control accuracy, estimation of internal and external disturbances, and compensation [18], is widely used in motor control [19], trajectory tracking [20] and other fields. In the literature [21], ADRC is applied to a line-controlled braking system to analyze its effect on ABS control, but the effects of the optimal slip rate and EMB on braking performance are not studied in depth.