To simultaneously track the ideal slip rate and realize ideal energy recovery efficiency under different complex road conditions, an electro-hydraulic compound anti-lock braking system based on interval type-2 fuzzy logic control strategy and its corresponding braking torque allocation strategy have been developed for electric vehicles. The proposed interval type-2 fuzzy logic controller aims to calculate the ideal total braking torque by four steps, namely, fuzzification, fuzzy inference, type reduction, and defuzzification. The slip rate error and the change rate of slip rate error are utilized as inputs in the fuzzification, and then, the membership degree interval of fuzzy variables determined by the upper and lower membership functions is used to calculate the activation degree interval of different fuzzy rules in the fuzzy inference process, which enhances the anti-interference ability to external uncertainties and internal uncertainties. The braking torque allocation strategy is proposed to maintain the maximum energy recovery efficiency on the premise of safe braking. The software of MATLAB/Simulink is applied to simulate the process of anti-lock braking control under two complex road conditions. Simulation results corroborate the proposed interval type-2 fuzzy logic anti-lock braking control system can not only obtain better slip rate control effect and outstanding robustness but also achieve ideal regenerative braking energy recovery efficiency under both joint-μ and split-μ road surfaces.

Control precision and robustness can be regarded as essential challenges of slip ratio control because of the external uncertainties of road conditions and the internal delay response of braking actuators. In addition, it is difficult to obtain a trade-off between braking energy recovery efficiency and braking safety under some extreme braking conditions. To synchronously improve both slip ratio control and braking energy recovery efficiency for different road conditions, an anti-lock braking system (ABS) using a novel interval type-2 fuzzy neural network (IT2FNN) control scheme is proposed for electrohydraulic braking systems. The novel IT2FNN control scheme with five layers is designed to calculate the commanded braking torque. The membership function layer utilizes type-2 fuzzy sets to describe the slip ratio error degree, which enhances the scheme’s anti-interference ability, and the enhanced Karnik-Mendel (EKM) algorithm is used in the type-reduction layer to accelerate computation. Additionally, the network adjusts the parameters of the membership function and rules by decreasing the performance function value corresponding to the braking torque error to improve slip ratio control and enhance the self-adaptation capacity. Simulations showed that IT2FNN control can not only improve slip ratio control performance and decrease the braking torque error but also enhance the energy recovery efficiency of regenerative braking on different road surfaces.

The electro-mechanical braking (EMB) system, known for its integration and intelligence, is considered an ideal actuator for vehicles. However, accurate slip ratio tracking is hindered by uncertainties in the road adhesion coefficient and communication delays, which adversely affect anti-lock braking performance. This study proposes an interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy robust $H_{\mathrm{\infty }}$ anti-lock braking control strategy to address these challenges. An IT2 T-S fuzzy anti-lock braking system (ABS) model is designed to enhance ABS linearization accuracy under uncertainties in the road adhesion coefficient. The vehicle speed is observed using an IT2 T-S fuzzy observer. A delay-product-type Lyapunov-Krasovskii (L-K) functional robust $H_{\mathrm{\infty }}$ anti-lock braking controller is designed. The delay-product-type L-K functional effectively utilizes delay information to reduce the conservatism of the controller, improving the slip ratio tracking performance of the EMB system under input delay conditions. Additionally, a motor torque compensation strategy is introduced to optimize slip ratio control on different roads. Simulations verify that the proposed strategy improves the EMB system’s slip ratio control performance under conditions of uncertainty and input delay.