In this article, the nonlinear damping characteristics of magnetorheological damper are expressed with hyperbolic tangent model to simulate its mechanical experimental results. The fitted hyperbolic tangent model can represent hysteretic behavior for magnetorheological damper exactly. Based on the hyperbolic tangent model, a quarter-car model with magnetorheological damper is established, and a new hybrid fuzzy and fuzzy proportional-integral-derivative (HFFPID) controller integrated with hybrid fuzzy control and fuzzy proportional–integral–derivative control is developed to improve the semi-active suspension performance, which can overcome the absence of precise mathematical model. Furthermore, numerical simulations for fuzzy proportional–integral–derivative (PID), hybrid fuzzy proportional–integral–derivative (HFPID), and HFFPID controllers are investigated to demonstrate the effectiveness of the proposed approaches. The simulation results show that the body acceleration, suspension deflection, and tyre displacement can be reduced more effectively using HFFPID controller under sinusoidal road excitation. It can be further concluded that the suspension performance is improved more effectively by using HFFPID controller under random road excitation, especially in the peak points.

The performance of a semi-active suspension depends on the quality of the control algorithm. Considering the limitations of conventional PID controllers within intricate nonlinear systems, such as imprecise parameter tuning and performance deterioration, we introduced a fractional-order PID (FOPID) control strategy for vehicle semi-active suspension, this approach amalgamates fractional-order theory with conventional PID control to enhance both the controllable scope and precision of the suspension system. Research on semi-active suspension control was conducted using a nonlinear dynamic model of a quarter vehicle. Simulations and analyses were performed utilizing random road excitation and impact road excitation as input signals for both FOPID control, Fuzzy-PID control, and conventional PID control strategies. The analysis findings demonstrated that in the presence of random road excitation, the semi-active suspension system controlled by FOPID reduced vehicle body acceleration by 18.9%, in contrast to a 14.7% reduction by the Fuzzy-PID-controlled suspension, and a 12% reduction achieved by the PID-controlled suspension when compared to the passive suspension. In response to impact road excitation, the suspension system under FOPID control effectively mitigated the peak value of vehicle body acceleration by 29.4%, surpassing the 25.2% reduction achieved by Fuzzy-PID-controlled suspension, and the 24.6% reduction achieved by the PID-controlled suspension. The simulation outcomes substantiated that ride comfort and handling stability of the semi-active suspension system were effectively improved by the implementation of FOPID control.

Aiming at the problem of system controller performance failure caused by improperly setting the value of each weighting coefficient of the model predictive control (MPC), a fractional-order MPC strategy with Takagi–Sugeno fuzzy optimization (T–SFO MPC) is proposed for a vehicle active suspension system. Firstly, the fractional-order model predictive control framework for active suspension systems is designed based on a 1/4 vehicle model. Then, we analyze the influence of different weighting coefficients on the suspension performance and introduce the Takagi–Sugeno fuzzy optimization theory to adaptively adjust the weighting coefficients of the fractional-order MPC controller. Finally, the system responses of the T–SFO MPC, traditional MPC, linear quadratic regulator (LQR), and passive suspension control are numerically analyzed under various road conditions. Simulation results show that suspension response with the T–SFO MPC is significantly improved compared with passive suspension control, traditional MPC control, and LQR control, and the weight coefficients of the T–SFO MPC can be adaptively adjusted according to the dynamic changes of suspension response. Compared with passive suspension, the root mean square (RMS) value of the vertical acceleration of the T–SFO MPC under various roads decreased by a maximum of 37.97%, and the RMS value of suspension dynamic deflection and tire dynamic load decreased by a maximum of 32.94% and 37.8%, respectively. These results validate that the proposed control method can achieve coordinated optimization of vehicle comfort and handling stability.

Autonomous driving technology is constantly developing to a higher level of complex scenes, and there is a growing demand for the utilization of end-to-end data-driven control. However, the end-to-end path tracking process often encounters challenges in learning efficiency and generalization. To address this issue, this paper designs a deep deterministic policy gradient (DDPG)-based reinforcement learning strategy that integrates imitation learning and feedforward exploration in the path following process. In imitation learning, the path tracking control data generated by the model predictive control (MPC) method is used to train an end-to-end steering control model of a deep neural network. Another feedforward exploration behavior is predicted by road curvature and vehicle speed, and adds it and imitation learning to the DDPG reinforcement learning to obtain decision-making experience and action prediction behavior of the path tracking process. In the reinforcement learning process, imitation learning is used to update the pre-training parameters of the actor network, and a feedforward steering technique with random noise is adopted for strategy exploration. In the reward function, a hierarchical progressive reward form and a constrained objective reward function referring to MPC are designed, and the actor-critic network architecture is determined. Finally, the path tracking performance of the designed method is verified by comparing various training results, simulations, and HIL tests. The results show that the designed method can effectively utilize pre-training and feedforward prior experience to obtain optimal path tracking performance of an autonomous vehicle, and has better generalization ability than other methods. This study provides an efficient control scheme for improving the end-to-end control performance of autonomous vehicles.

To improve the characteristics of traditional model predictive control (MPC) semi-active suspension that cannot achieve the optimal suspension control effect under different conditions, a variable horizon model predictive control (VHMPC) method is devised for magnetorheological semi-active suspension with air springs. Mathematical models are established for the magnetorheological dampers and air springs. Based on the improved hyperbolic tangent model, a forward model is established for the magnetorheological damper. The adaptive fuzzy neural network method is used to establish the inverse model of the magnetorheological damper. The relationship between different road excitation frequencies and the control effect of magnetorheological semi-active suspension with air springs is simulated, and the optimal prediction horizons under different conditions are obtained. The VHMPC method is designed to automatically switch the predictive horizon according to the road surface excitation frequency. The results demonstrate that under mixed conditions, compared with the traditional MPC, the VHMPC can improve the smoothness of the suspension by 2.614% and reduce the positive and negative peaks of the vertical vibration acceleration by 11.849% and 6.938%, respectively. Under variable speed road conditions, VHMPC improved the sprung mass acceleration, dynamic tire deformation, and suspension deflection by 7.191%, 7.936%, and 22.222%, respectively, compared to MPC.

The performance of the suspension is a crucial criterion for evaluating both vehicle handling and passenger comfort. To enhance suspension performance, this study proposes the design of a Quantum Genetic Fuzzy Sliding Mode Controller (S-QFSMC) based on the Smith predictor estimator, building upon the foundation of the vehicle magneto-rheological semi-active air suspension. According to the physical model of the vehicle suspension, a mechanical model of a quarter-vehicle magneto-rheological semi-active air suspension with time delay is established. On this basis, a conventional sliding mode controller is designed, and quantum genetic algorithm and fuzzy control principles are employed to optimize the chattering issue associated with sliding mode control. The Smith predictor estimator is utilized to effectively compensate for the time delay in the suspension system. Subsequently, a simulation analysis of the vehicle suspension performance is conducted. The results indicate that, compared to passive suspension control, both the QFSMC controller and the S-QFSMC controller improve the suspension performance, with the S-QFSMC controller exhibiting superior comprehensive improvement. This validates the effectiveness of the designed controllers.