Nonlinear Backstepping Control of Electro-Hydraulic Brake System Based on Bond Graph Model

Zhao, Jian; Song, Dongjian; Zhu, Bing; Chen, Zhicheng; Sun, Yuhang · 2020 · DOAJ

DOI: 10.1109/ACCESS.2020.2968513

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Summary

This paper addresses the challenge of accurately and rapidly controlling brake pressure in electro-hydraulic brake (EHB) systems, which are critical for intelligent electric vehicles. EHB systems exhibit complex, highly nonlinear dynamics due to factors such as valve resistance, brake fluid compressibility, and caliper stiffness. Existing control methods often rely on simplified models or model-free approaches that ignore these nonlinearities, leading to suboptimal performance. To overcome this, the authors propose a nonlinear backstepping control algorithm based on a detailed bond graph model of the EHB system. The study begins by constructing a nonlinear, single-wheel brake system model using the bond graph method. This model accounts for the capacitive effect of the hydraulic fluid, as well as the damping and inertia effects of the calipers. The master cylinder is treated as a pressure source, while the inlet and outlet valves and wheel brake are explicitly modeled. To compensate for ignored hysteresis effects in brake pipelines, a first-order inertia-delay system is added to the model. Based on this validated nonlinear model, a backstepping controller is designed using Lyapunov stability theory. The controller divides the system into three states, defining virtual control variables for each to ensure asymptotic stability. The control signals for the inlet and outlet valves are unified into a single expression, allowing for coordinated operation during pressure building, holding, and dumping phases. The authors analyze the impact of three controller parameters ($k_1, k_2, k_3$) on system performance using phase trajectory and time-domain analyses to determine optimal values. The proposed algorithm was verified through simulations and hardware-in-the-loop tests. The results demonstrate that the backstepping controller effectively regulates the inlet and outlet valves, enabling the brake pressure to follow the desired reference value rapidly and accurately. The controller exhibits good robustness, successfully handling the nonlinear characteristics of the EHB system. The study confirms that considering the full nonlinear dynamics through the bond graph model and applying backstepping control significantly improves brake pressure regulation compared to simpler control strategies. The significance of this work lies in providing a robust, model-based control solution for EHB systems that accounts for complex physical nonlinearities. By integrating bond graph modeling with backstepping control, the approach offers a systematic method for designing controllers that ensure stability and precise pressure tracking. This contributes to the development of safer and more responsive brake-by-wire systems for future automotive platforms, particularly in electric and intelligent vehicles where active and decoupled braking is essential.

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• braking response