## 1 Introduction
Some studies have designed path tracking controllers based on the linear quadratic regulator (LQR) method [24; 25]. However, the robustness of the control system is difficult to guarantee when the system needs to handle model uncertainty and external disturbance. Model predictive control (MPC) has the capability of handling system constraints and future prediction in the design process. It minimizes the gap between the reference path and the actual path by the vehicle dynamics model in a prediction horizon, and it has become a popular method in the  
Figure 1: Ackerman’s steering geometry method. Figure 2: Vehicle kinematics model. control of autonomous vehicles [26; 27; 28; 29; 30]. A differential evolution algorithm was introduced into the MPC path tracking controller in order to improve the computational efficiency [31]. The influences caused by the parameters such as prediction horizon, control horizon, and sampling time on tracking accuracy and computational efficiency were analyzed, and a parameter adjustment method for an MPC controller was proposed in [32]. Ref. [33] studied the control incremental modeling method based on Laguerre function to simplify parameter complexity in prediction horizon. [PERSON]. [34; 35] proposed a hierarchical control framework based on the combination of MPC control and other methods. In existing research on path tracking in MPC control frames, it is assumed that the vehicle longitudinal speed in the prediction horizon is constant, aiming to ensure the optimization problem is a convex optimization problem. Most of the previous literature has only considered the dynamics on the lateral and yaw directions, and generally neglected the longitudinal dynamics in the prediction horizon. However, the speed fluctuates under actual driving conditions in the prediction horizon, which causes the prediction error of the vehicle states in the prediction horizon, thus affecting the control accuracy. In particular, it will cause greater prediction errors and change the stability constraint of the closed-loop control system, when the vehicle is at high speed and rapid acceleration or deceleration. Then control system produces control deviation and affect path tracking accuracy. In order to minimize the control deviation caused by speed change in the predicted horizon in the MPC control frame, an MPC path tracking controller, with longitudinal speed compensation in the prediction horizon to reduce the prediction error and tracking error, is proposed in this paper, as shown in Figure 3. The main contributions of this paper include: (1) the mechanism of action of longitudinal speed changes upon the state vector variation and the stability of the path tracking closed-loop control system in prediction horizon is analyzed; (2) a longitudinal speed compensation strategy is proposed to reduce tracking error; and (3) the MPC controller with longitudinal speed compensation is designed and tested on the platform of CarSim-Simulink. The structure of this paper is as follows. The vehicle dynamics model, tire model and path tracking model are presented in Section 2. The MPC path tracking controller is presented and longitudinal speed compensation strategy is proposed in Section 3. The simulation is conducted in Section 4. In Section 5, the paper concludes with a brief discussion of the results.