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Since the coupling relationship of excitation sources is complicated, meantime the motor torque changes quickly under the acceleration condition, the problem of torsional vibration is prominent. This paper studies an active damping control (ADC) strategy for a parallel hybrid electric vehicle (HEV) under acceleration condition. Primarily, a full-order dynamic model is built, and the corresponding motion equations are derived. Moreover, a controller design–oriented model is established based on model reduction algorithm. Furthermore, a method that considers time delay characteristics of actuator based on model predictive control (MPC) theory is proposed to solve the torsional vibration problem. The controller handles delay characteristics of an actuator by state-space reorganization method, and the optimal control sequence is obtained by solving the objective function. Finally, the controller is tested using Simulink simulation and hardware-in-loop simulation platform, which mainly includes the verification of model reduction and vibration damping effect. The results show that simplified third-order model has a good consistency with the original full-order model in time and frequency domain. Meanwhile, the designed controller has a considerable damping effect and ensures the comfort performance of the vehicle. This study provides an important reference for vibration control of the hybrid powertrain.

To improve the ride comfort of vehicles, active suspension control strategy has received widespread attention. Although based on the finite-time and sliding mode control (SMC) technology design scheme, the convergence problem has been solved, the controller chattering and the poor control effect in the face of random interference will definitely limit its application in practice. To address such limitation, considering the variety of driving conditions, based on finite-time and SMC technology, an Adaptive Finite-time High-order SMC Active Suspension control Systems via disturbance observation (AFHASS) is proposed. Firstly, to improve the ride comfort of vehicle, a quarter dynamic model is established for vehicle active suspension; Then, given the advantages of finite-time and SMC technology, an AFHASS method is designed, and based on the Lyapunov analysis function constructed, the stability of the presented AFHASS control strategy has been proved; Finally, the effectiveness of the proposed AFHASS algorithm is validated by performing simulation, and compared with the different methods. Taking the finite-time control algorithm as a benchmark, under the C grade road roughness, the root mean square of vertical displacement has been improved by 29% and the energy consumption has been improved by 8%. The results are presented and discussed to illustrate the advantage and effectiveness of the proposed AFHASS algorithm in terms of energy consumption, vertical performance and controller chattering.