# Research on Active Anti-Slip Control of High-Speed Trains Based on High-Order Sliding Mode
## 4 Experiment Results
Figure 8: Comparison of displacement tracking effect. Figure 9: Comparison chart of creep and slide speed. Figures 7 and 8 compare the speed and displacement tracking effects under different control strategies. When the train encounters icy or oily road conditions, the wheelsets tend to slip because the output of the train's conventional sliding mode controller and the adaptive sliding mode controller based on perturbation compensation exceeds the maximum traction force that can be generated between the wheels and rails. This slip leads to a rapid and significant reduction in adhesion, causing the train to lose traction. As a result, the displacement tracking errors and speed tracking errors of the train increase significantly, as shown in Figures 7 and 8 (plots a and b). After 320 s, when the train transitions into wet road conditions, the braking force exerted by the motor on the wheels becomes smaller than the adhesion force, thereby restoring adhesion between the wheels and rails. As a result, the conventional sliding mode control reduces the tracking errors in both speed and displacement. However, the adaptive sliding mode control based on perturbation compensation fails to maintain accurate tracking of the target curve once adhesion is restored, due to the cumulative error of its internal integral term, which ultimately leads to controller failure. In contrast, Figures 7c and 8c demonstrate that the higher-order sliding mode-based active anti-slip control designed in this study achieves the smallest tracking errors in both speed and displacement. This effectiveness is attributed to the controller's strategy of selecting a typical road condition with slightly worse adhesion than the current conditions. By utilizing the active anti-slip strategy, the controller calculates the maximum traction force available and employs [PERSON]'s iterative method to appropriately limit the controller's output. Consequently, the wheel-rail system consistently operates within the adhesion state, avoiding wheelset slip and preventing significant traction loss. Figure 9 presents the creep-slip velocity graphs during the process of controlling the train to track the target velocity-displacement curve using different controllers. As shown in plots (a) and (b) of Figure 9, under conventional sliding mode control and adaptive  
Figure 10: Controller output comparison chart. sliding mode control based on perturbation compensation, the lack of an anti-slip strategy results in the creep speed exceeding 200 km/h after the train enters icy road conditions at 115 s, leading to noticeable wheelset slip. The variation in the vertical axis of Figure 9c demonstrates that with the designed controller, the creep-slip speed remains between \(-0.72\) and 2.88 km/h, effectively preventing slip. The observed variation in creep speed in plot (c) is attributed to the switching of road conditions or the controller output adjustments, ensuring that the wheel-rail system operates within a stable range and preventing significant traction loss. Figure 10 illustrates the output of each controller. In this study, we communicate with the real-time simulator via analog signals, converting the controller outputs to single-axis braking forces, which are then adjusted to the DA output range by a specific scale factor. To prevent DA saturation, upper and lower limits for the controller outputs are set separately. Therefore, when wheel slip occurs in the train, the control output is constrained after 115 s in Figure 10a,b. Figure 10c demonstrates that when the train encounters icy, snowy, and oily low-viscosity road conditions between 115 and 170 s, the designed active anti-slip strategy effectively limits the controller output, ensuring that it does not exceed the maximum traction force that the current rail surface can provide, thereby preventing wheel slip. It is important to note that the proposed controller output limitation incorporates both the anti-slip strategy and the traction characteristics, resulting in a more reasonable controller output.