main-content

This book introduces the application of nonlinear dynamics theory for driving system of electric vehicle and hybrid electric vehicle respectively. It establishes the dynamic models for driving system of electric vehicle and hybrid electric vehicle under various working conditions. And the nonlinear dynamics theory is applied to the qualitative analysis and quantitative calculation for the models. The theoretical analysis results are applied to guide the optimization of control strategies. In the end of each chapter, corresponding simulations or experiments are provided to verify the corresponding instances which are carefully selected. This book will give some guidance to readers when they deal with nonlinear dynamics problems of vehicles in the future and provide theoretical bases for the further study of the nonlinear dynamics for driving system of electric vehicle and hybrid electric vehicle.
The book is written for engineer of electric vehicle and hybrid vehicle, teachers and students majoring in automobile and automation.

### Chapter 1. Stability Analysis for EV Powertrain

Abstract
Due to the influence of road excitation, damping and inertia resistance, the electric vehicle powertrain produces nonlinear torsional vibration, which leads to the instability of the powertrain. A nonlinear torsional vibration model considering the effect of rotor eccentricity is established. The equilibrium point of the undisturbed Hamiltonian system is solved. The effects of road excitation, damping and inertia resistance on the nonlinear vibration of the electric vehicle transmission system are studied. The way from periodic motion to chaotic motion is analyzed.
Donghai Hu, Bifeng Yin

### Chapter 2. Control Methodology of Stability Optimization for EV Powertrain

Abstract
This section looked at various nonlinear dynamics of an electric powertrain with a variable control parameter of a PI regulator in torque control mode and predicted the instability domain in order to refine the PI regulator’s control parameter. It proposed a nonlinear control model for an electric vehicle’s drive mechanism and a control technique for stability domain expansion in the mode of both rotation speed and torque control.
Donghai Hu, Bifeng Yin

### Chapter 3. Stability Analysis for HEV Powertrain

Abstract
Slow variables are added to account for the order difference between the excitation frequency and the natural frequency in order to turn this model into a fast-slow model. Under various excitation frequencies and amplitudes, the dynamic equations are obtained. When the equilibrium point is unstable, bifurcation theory is used to analyze bifurcation action, and the conditions for creating a folding bifurcation are extracted. The effect of excitation frequency and amplitude on dynamic behavior is investigated numerically using the curve of the equilibrium point, transformed phase portrait, and time course.
Donghai Hu, Bifeng Yin

### Chapter 4. Control Strategy of Stability Optimization for HEV Powertrain

Abstract
In recent years, the deterioration of energy and environmental issues has accelerated the growth of electric and hybrid vehicles. Because of their versatile driving mode, long range, and low emissions, hybrid electric vehicles (HEVs) are becoming increasingly popular. However, current research on the torsional vibration of HEV powertrains focuses primarily on the effect of engine excitation, as well as natural frequency and modal analysis. The aim of this chapter is to improve the control strategy of a HEV powertrain while taking torsional stability into account in three common driving modes.
Donghai Hu, Bifeng Yin

### Chapter 5. Control Methodology of Stability Optimization for HEV Powertrain

Abstract
Mode switching plays an important role in the operation of HEV. Clutch is the key actuator to realize mode conversion, but it is difficult to realize seamless mode conversion due to the friction caused by the use of clutch. In addition, as is usual in an electromechanical coupling system, the hybrid powertrain may exhibit complex dynamic behaviors as the operating parameters change. In this chapter, we introduce, analyze and optimize the hybrid system mathematical model of parallel series hybrid electric vehicle (PSHEV) during mode transition.
Donghai Hu, Bifeng Yin