# Off-Line Optimization Based Active Control of Torsional Oscillation for Electric Vehicle Drivetrain
## 1 Introduction
The core principles of the above concepts are similar, by controlling engine torque according to drivetrain motion state, a controller will compensate for the speed oscillations. Such a compensator will act as a feedback unit so that a close-loop system is composed to improve drivetrain system performance. However, because the inherent defects of engines (such as variability of output torque) have limited success in terms of accuracy of control and rapid response, it is difficult to apply the above methods to control engine torque to compensate motion oscillation of drivetrain in a certain frequency band. The ongoing development of electric motors and associated power electronics produces a system that can be easily and precisely controlled. [PERSON] et al. have proposed two approaches for the implementation of finite-control-set model predictive control (FCS-MPC) methods to control a permanent-magnet synchronous motor torque fed by a matrix converter; these methods were presented and their results were evaluated experimentally. Neither method needs a current PI controller and modulator, which leads to a fast dynamic [15]. [PERSON] et al. have improved MPC by proposing an alternative strategy of finite-control-set model-predictive torque control (MPTC), so that the computational burden and the torque ripple can decouple the switching frequency from the controller sampling time, which is then reduced [16]. Furthermore, motors installed in electric vehicles have shown an excellent performance with higher efficiency, lower response times, higher power density [17]; some scholars investigated the problem of automatic speed tracking control of an electric vehicle based on higher order sliding mode (HOSM) observer for the events of sensor faults/failures to maintain a good control performance [18]. More adaptable than conventional engines, electric motors can overcome large resisting moment of inertia during vehicle launch, with the motor connected rigidly and directly to the wheels. As the motor does not stall, the clutch and torque converter are no longer required. The structure of the electric vehicle drivetrain is consequently much simpler and more compact. Based on the advantages of electric motors, many researchers are determined to realize the active control for EV drivetrain oscillation. In 2015 [PERSON] et al. [19] applied fuzzy logic to control motor torque to actively reduce oscillations. [PERSON] et al. [20] presented a novel filter using wheel speeds to eliminate oscillations and improve the robustness of EV control. In 2008 [PERSON] et al. [21] proposed an adaptive sliding neuro-fuzzy speed controller for the drive system to improve robustness of control system. Similarly, in 2015 [PERSON] et al. [22] applied mode-switching-based active control of drivetrain for EV during regenerative braking. However, some of these algorithms are too complicate to be applied practically, or too time-consuming to meet the requirements of torsional oscillation frequency up to several dozens of Hertz. Furthermore, the limitations of motor external characteristics are also not considered. Aimed at a kind of motor-transmission integrated drive system, [PERSON] et al. [23] proposed an adaptive method by using the linear quadratic regulator (LQR) and dimensionality reduction observer joint algorithm. At present, the linear quadratic regulator control algorithm has been found to be one of the most effective methods in vibration control under the premise of appropriate weighting matrices, which gives optimal control gain by minimizing the performance index [24; 25; 26]. The weighting matrices Q and R will influence the optimal result directly. However, they are selected based on designer's subjective preference currently and generally; also, such optimal results may not be the real optimal value and even may cause side-effects. Many researchers are looking for methods to choose appropriate weighting matrices to bring a better control performance [27; 28; 29].