Adaptive Front and Rear Braking Force Distribution Strategy for Electric Commercial Vehicles: Modeling, Control, and Experimental Validation

Abstract

The dynamic distribution of braking forces between front and rear axles in electric commercial vehicles represents a critical multi-objective optimization challenge requiring simultaneous satisfaction of regulatory safety compliance, regenerative energy recovery, thermal stability, and actuator coordination under varying load and road conditions. This paper addresses this challenge through the development and experimental validation of an integrated adaptive brake force distribution strategy combining model predictive control (MPC) with Particle Swarm Optimization (PSO) within a unified framework that ensures compliance with ECE Regulation No. 13. A comprehensive experimental test bench was designed and instrumented, integrating three independent braking mechanisms: magnetic brakes with front and rear torque coefficients of 4.73 N·m/A and 3.65 N·m/A, respectively; an eddy current retarder with coefficient k0= 2.220 × 10−4 N·m·s/(A2·rad), producing braking torque that is quadratic in excitation current and linear in rotor speed; a regenerative braking system with 82–90% efficiency; and a switchable magnetic clutch for FWD/4WD operation. The MPC controller was formulated with a prediction horizon Np = 20, control horizon Nc = 5, and sampling time Ts = 20 ms. PSO was employed for systematic tuning of MPC weights using 30 particles over 50 iterations with cognitive and social coefficients c1 = c2 = 2.0 and linearly decreasing inertia from 0.8 to 0.4. A vehicle state estimation module using Kalman Filtering was developed for real-time estimation of vehicle mass (<3% error), road slope (<0.3% error), and road friction coefficient (<5% error). Experimental validation across eight comprehensive test scenarios demonstrates that the PSO-optimized MPC controller achieves 43% reduction in front RMSE (from 2.65 Nm to 1.52 Nm), 44% reduction in rear RMSE (from 0.78 Nm to 0.44 Nm), 100% ECE R13 compliance (improved from 67.5%), 57% settling time improvement (from 4.2 s to 1.8 s), 92% overshoot reduction (from 67% to 5%), and average recovered energy improvement from 3.51 kJ to 4.04 kJ. The proposed framework provides a comprehensive solution for next-generation electric commercial vehicle brake management systems.