# Off-Line Optimization Based Active Control of Torsional Oscillation for Electric Vehicle Drivetrain
## 1 Introduction  
With the increasing emergence of environment and energy issues as factors impacting on the design of passenger transportation system, scholars all over the world are devoting themselves to finding alternative energy and clean energy solutions for industry [1]. As a major energy-consuming product, reducing fuel consumption or finding alternative energy resources are significant targets for the automotive industry [2], electric vehicles (EV) have advantages of lower transportation cost, no direct emissions, no consumption of fuel, and smoother driving experience, which has drawn attention from vehicle designers and academics around the world. In 1976, a law is passed in America to ensure the healthy development of the electric vehicle industry [3]; today, the electric vehicle is occupying a larger and larger market share. There are many differences in the drivetrain for traditional fuel-consuming vehicles and electric vehicles. The main parts of a typical a rear-wheel drive electric vehicle drivetrain are motor, transmission, shafts, and wheels as shown in Figure 1. A typical compact automobile drivetrain integrates the motor and automated manual transmission (AMT) with final drive to reduce speed and generate larger torque for driving the vehicle. The most obvious difference is that there is no clutch or hydraulic torque converter in electric vehicles. Considering the elastic and damping parts,the drivetrain should be regarded as a second order oscillatory system, because there are fewer parts to interrupt the transmission of power, and no parts to buffer or absorb torsional vibration oscillation caused by rapid torque changes. Figure 2, cited from reference [4], shows the typical oscillations of driveline when shifting. The primary dynamic response in vehicle drivetrain is referred to as shuffle, and is linked to the lowest natural frequency of the drivetrain. This is one of the most critical issues of motor-transmission directly coupled to the drive system of electric vehicles. Some of these oscillations are transmitted through the bearing mounts and transmission shafts to the gearbox housing. In some instances it may be radiated into the environment as noise as well [5]. Improving the performance of the driveline by reducing undesirable oscillations is, therefore, a critical issue in automotive development. There are two main kinds of schemes to solve such problems, one is to add torsional shock absorbers or clutch [6]. In 2009 [PERSON] et al. [7] have analyzed electric vehicle drivelines and drawn a conclusion that it is an underdamped vibration system. Oscillations can be reduced by designing a damper, but it may introduce other vibrations caused by structural change, and it also increases  
Figure 1: Structure of rear-wheel-drive electric vehicle drivetrain with motor-transmission integrated system. Figure 2: Up and down shift transients for clutchless automated manual transmission (AMT) powertrain for a 20 ms stage duration at 200 Nm motor torque (**a**) system speeds, (**b**) vehicle longitudinal acceleration, and (**c**) vehicle longitudinal jerk. complexity of the system and manufacturing cost. The other option is controlling the motor reference torque output, by adjusting motor torque output dynamically to give the driveline torque compensation against oscillation; this is an active control method. [PERSON] et al. [8] at Sweden Linkoping University has conducted research on shifting without detaching the clutch for a heavy truck with an internal combustion engine, by applying engine torque control during gear shifting to unload torque, minimize shift time and increase shift quality. Subsequent research has shown that there are still many researchers investigating active control for drivetrain vibrations by controlling engine torque output actively and dynamically with feed forward control method [9], optimal algorithm [10; 11], model predictive control [12; 13], H-infinity optimization [14] to replace the simple open-loop system to reduce oscillation when shifting or during tip in/out.