On the Fractional-Order Derivative Effects on the ABS Robust Control Performance

Abstract

This study conducts a comparative analysis of sliding mode control (SMC) and fractional-order sliding mode control (FOSMC) for application in antilock braking systems (ABS). Based on foundational principles of theoretical mechanics, the ABS dynamics are modeled as a single-input system to analyze wheel-slip regulation under diverse and variable road conditions. Both the conventional SMC and the proposed FOSMC are designed using a Lyapunov-based approach to ensure robust stability, with the latter incorporating fractional-order derivatives to refine the sliding surface and dynamic response. The conventional SMC method, while demonstrating strong robustness and disturbance rejection capabilities, is found to induce persistent chattering during transient phases, which can compromise system reliability and actuator longevity. By contrast, the FOSMC controller enhances transient behavior by attenuating chattering and yielding smoother, more consistent wheel-slip tracking. The inclusion of fractional-order terms contributes to faster convergence and improved adaptation to abrupt changes in road friction, though it introduces increased computational complexity. Numerical simulations validate the performance of both controllers across multiple driving scenarios, including dry, wet, and icy road conditions. Results confirm that FOSMC significantly reduces chattering, accelerates system convergence, and maintains stable braking performance with greater consistency compared to conventional SMC, establishing its potential for implementation in advanced ABS designs.