Adaptive torsional vibration suppression in power-split HEVs: Integrating BPNN-based secondary path estimation and variable-step FxLMS

In recent years, power-split Hybrid Electric Vehicles (HEVs) have attracted widespread attention for their superior fuel efficiency and performance. However, the planetary gear sets that mechanically couple the engine and drivetrain often induce undesirable torsional vibrations, degrading drivability and component durability. To mitigate this, an efficient multi-channel Active Vibration Control (AVC) strategy is proposed, utilizing a notch Filtered-x Least-Mean-Square (FxLMS) algorithm to leverage motor torque for compensating engine torque fluctuations. First, the system’s torsional vibration responses are analyzed to identify the input and output shafts as critical control targets. Second, a Back Propagation Neural Network (BPNN) is employed to model the secondary paths, which improves estimation accuracy and reduces errors by 65%–95% compared to the traditional Finite Impulse Response (FIR) filtering method. Third, a multi-channel AVC strategy is developed based on a modified notch FxLMS algorithm featuring variable step sizes. The proposed AVC strategy is then incorporated into the vehicle’s energy management system, forming an integrated control framework (ICF) for coordinated vibration suppression and energy optimization. Simulation and experimental results under various operation conditions verify that the proposed strategy effectively reduces torsional vibration amplitudes and improves powertrain smoothness, thereby enhancing overall drivability and comfort.