Mode transition plays an important role in the operation of hybrid electric vehicles. The clutch is a key actuator for mode transition, but friction resulting from its use makes it difficult to achieve seamless mode transition. Moreover, as is usual in an electromechanical coupling system, the hybrid powertrain may exhibit complex dynamic behaviours as operating parameters change during mode transition. This paper considered changes in the clutch friction coefficient, and established a mathematical model of the hybrid powertrain in a parallel-series hybrid electric vehicle (PSHEV) during mode transition. The Routh-Hurwitz criterion and bifurcation theory are introduced to analyse the influence of speed difference on the dynamic characteristics of the hybrid powertrain, and the corresponding instability threshold were given. Furthermore, an optimised adaptive control methodology was proposed to control the dynamic behaviours, and tests on PSHEV were carried out. The results show that the variations of speed difference may lead to the occurrence of Fold and Hopf bifurcations, and that once the speed difference reaches the instability threshold, it may cause the system to enter a chaotic state and exhibit random oscillation. The proposed control methodology can effectively expand the security domain and suppress the oscillation to improve smoothness of mode transition.

模式转换在混合动力电动汽车的运行中起着重要作用。离合器是模式转换的关键执行器，但其使用产生的摩擦使得难以实现无缝模式转换。此外，正如在机电耦合系统中常见的那样，混合动力系统可能会随着模式转换期间运行参数的变化而表现出复杂的动态行为。本文考虑了离合器摩擦系数的变化，建立了并联串联混合动力电动汽车（PSHEV）模式转换过程中混合动力系统的数学模型。引入 Routh-Hurwitz 判据和分岔理论，分析了速度差对混合动力系统动态特性的影响，并给出了相应的失稳阈值。此外，提出了一种优化的自适应控制方法来控制动态行为，并对 PSHEV 进行了测试。结果表明，速度差的变化可能导致Fold和Hopf分岔的发生，一旦速度差达到不稳定阈值，可能会导致系统进入混沌状态并表现出随机振荡。所提出的控制方法可以有效地扩展安全域并抑制振荡以提高模式转换的平滑度。它可能导致系统进入混沌状态并表现出随机振荡。所提出的控制方法可以有效地扩展安全域并抑制振荡以提高模式转换的平滑度。它可能导致系统进入混沌状态并表现出随机振荡。所提出的控制方法可以有效地扩展安全域并抑制振荡以提高模式转换的平滑度。