# Energy Management Optimization of a Dual Motor Lithium Ion Capacitors-Based Hybrid Super Sport Car
## 1 Introduction  
### Research Motivation  
The current work aims to deepen the analysis of the longitudinal dynamics of a dual motor Lithium-Ion Capacitor (LiC)-based hybrid super sport car. The study of vehicle dynamics has acquired strong importance throughout the years since it allows us to understand and optimize the vehicle characteristics fully. Moreover, the possibility to analyze the vehicle behavior through simulation and modeling activities shifts the focus on virtual or software environments instead of experimental testing. This method allows saving money and time during the vehicle development process.  
One of the great advantages of computer simulation techniques is in fact represented by the possibility to analyze various design proposals with easiness and without the need for a prototype as it would be required for experimental testing. It must be considered that computer simulations are useful only if the software is reliable, meaning that it is able to reproduce faithfully the behavior of the actual vehicle. In that case, considerable savings in time and costs are expected. The main experimental activities that are run on the entire vehicle are represented by chassis dynamometer testing through emission cycles or road experimental testing. Experimental data from the chassis dynamometer can be used toguarantee the validation of the computer simulations, along with experimental results from tests on specific components, when present.  
The vehicle model we are referring to in this document represents a Lamborghini Aventador and it has already been validated in a previous work [1]. Since the validation process has already been carried out, this document can focus on deepening the analysis of the hybrid powertrain and its control strategies.  
The longitudinal vehicle model consists of physics-based modeled and validated components as well as black box models, exclusively based on experimental data. This is the solution that has been adopted to guarantee the trade-off between simulation accuracy and simulation speed, delivering a powerful tool capable of exploring hybrid architectures and support the control strategy development.  
In particular, the longitudinal dynamics model (Figure 1) is composed of a driving cycle input, a Proportional-Integral (PI) controller that acts as the accelerator and braking pedal, an engine model subsystem, a gearbox model, a tire model, the longitudinal dynamics equations, and the hybrid electric powertrain.  
The input is given by a speed cycle, function of time, and it can be chosen between the main emission cycles and some real experimental driving cycles. The actual speed is subtracted from the target speed, and the error enters the PI controller, which simulates the driver's behavior. The PI controller output, acting as the requested pedal position, is the input of the vehicle model and determines the vehicle performance.  
The vehicle performance directly depends on the hybrid powertrain. The Electric Motors' (EMs) parallel configurations that are analyzed are represented by the P3-P4 and P2-P4 positions, as shown in Figure 2. The P4 EM is placed at the front axle, while the rear EM (P2 or P3) is directly coupled with the gearbox. In both cases, the hybrid system can directly power the wheels if requested.  
Figure 2 shows the EMs that are mechanically connected to the shafts. The gear ratios will be dimensioned to keep the motors connected until certain target speeds.  
The P4 front EM will be disengaged at 190 km/h, while the rear EMs will disengage at the vehicle's maximum speed, approximately equal to 350 km/h. Thus, they will be able to cover the complete speed range of the vehicle.  
As shown in Figure 2, the resulting Lamborghini Aventador will be a 4 WD vehicle where the front wheels are powered exclusively through the P4 EM that is mechanically connected to the front axle.  
Figure 1: Longitudinal dynamics model structure. The input is the target speed coming from the chosen cycle. The loop is closed thanks to the comparison with the actual speed.