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

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