# Torque Allocation of Hybrid Electric Trucks for Drivability and Transient Emissions Reduction
## 1 Introduction  
In recent years, an ever-increasing number of researchers have focused their efforts on the substantial challenge of powertrain electrification in an attempt to deal with new government requirements that aim at reducing pollutant emissions and fuel consumption [1]. In this context, the Research and Development (R&D) departments of several automobile companies are engaged in the development of innovative powertrain solutions to replace vehicles with fuel motorization. A slow and progressive transition from internal combustion engine vehicles (ICEVs) to zero emissions vehicles (ZEVs), battery electric vehicles (BEVs), and fuel cell electric vehicles (FCEVs) is occurring, along with the development of hybrid electric vehicles (HEVs) and plug-in hybrid electric vehicles (HEVs). As proposed in [2], several possible topological architectures can be implemented in HEVs, where two or more sources of power/energy are combined to achieve the required power necessary to propel the vehicle. HEV vehicles combine the ICE power with an electric traction motor, which is powered by an energy storage device generally known as battery pack. The most common configurations adopted to couple different power sources can be summarized as parallel hybrid [3], series hybrid [4] or combined series-parallel architectures, with a mechanical power-split [5; 6; 7; 8] or innovative magnetic split [9]. Different control strategies have been investigated and proposed to achieve optimal energy management [10] between different power sources. HEVs combine the advantages of electric motor drives--having quick acceleration--with good ICE performance at constant speeds. On the other hand, vehicle drivability [11] is highly affected, as during rapid torque transients--due to drivers' abrupt accelerations--noise and vibrations [12] can occur during engine start/stop conditions [13] in mild hybrid electric vehicles. Besides this aspect, sudden driver torque requests can generate an increase in NOx emissions, as investigated in [14] during tip-in/tip-out manoeuvres. Hence, control strategies should act in a multiphysics way, also considering--besides optimal energy management--NOx and CO2 emissions [15] and, more generally, the reduction of pollutant emissions into the environment [16]. The aim of this paper is to address the topics of both drivability enhancement and the reduction of pollutant emissions; thus, the development of a vehicle model that is able to predict and highlight all these aspects is required--as carried out in [17], where Gear Shift Patterns were optimized to fulfil multiple constraints in terms of customer requirements such as drivability, NVH performance, emissions, and fuel consumption. These last two aspects were considered in [18] to evaluate fuel savings and NOx benefits when predictive control is applied to a mild hybrid truck, using dynamic programming with backtracking. Conversely, [19] proposed a novel real-time Energy Management Strategy (EMS) that was integrated with a model to use physical considerations to estimate energy consumption during gearshifts in Dual-Clutch Transmissions (DCT). The development of a transmission model with a high level of accuracy is necessary to describe the dynamic behaviour of the whole system well, although its complexity can be reduced with appropriate simplifications--as carried out in [20] with a hybrid model of a vehicle driveline that was partially lumped and partially distributed to investigate vibrational phenomena inside the transmissions known as \"shuffle\" and \"clonk\". A methodology for the evaluation of clunking noises during gearshifts was also proposed in [21] using a nonlinear lumped parameter model of DCT, developed in an Amesim environment, while a Matlab/Simulink environment was adopted in [22] for the evaluation of NVH performance in the DCT transmission of a C-segment passenger car.