基于描述函数法的直线增程器动力学模型极限环分析

Analysis of Limit Cycle of Dynamic Model of Linear Range Extender Based on Describing Function Method

摘要:

基于一个简化的直线増程器动力学模型，运用描述函数法在频域对直线増程器的极限环进行研究.以描述函数表示直线増程器动力学模型的非线性部分，利用描述函数和线性部分频率响应函数的图像对系统极限环的存在性、数量和稳定性进行了分析，进而求出极限环的近似频率和振幅.同时研究了直线増程器关键运行参数对极限环的频率、振幅和相对稳定性的影响.最后，以一样机的试验数据对分析结果进行试验验证.研究结果表明,在适当的系统参数下，直线増程器在物理约束范围内存在唯一的稳定极限环；喷油量和电磁力负载对极限环的频率和振幅都有影响；极限环的幅值与其相对稳定性存在关联.

关键词:直线増程器; 极限环; 描述函数; 存在性; 稳定性

Abstract:

According to a simplified dynamics model of the linear range extender, the limit cycle of linear range extender was studied in frequency domain by using the describing function method. The nonlinear part of the linear range extender dynamics model was described by using the describing function, and the existence, quantity and stability of the system limit cycle were analyzed by using the image of the describing function and the frequency response function. Then the approximate frequency and approximate amplitude of the limit cycle were obtained. This method can also explore the influence of parameters of the linear range extender on the frequency, amplitude, and relative stability of limit cycles. Finally, the analysis results were verified by the experimental data of a prototype. The results show that when the system parameters are appropriate, the linear range extender has the only stable limit cycle in the physical constraint range, and the fuel injection quantity and the electromagnetic force load have influence on the frequency and amplitude of the limit cycle; the amplitude of the limit cycle is related to its relative stability.

Key words:linear range extender; limit cycle; describing function; existence; stability