# Torque Allocation of Hybrid Electric Trucks for Drivability and Transient Emissions Reduction

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions [15] and, more generally, the reduction of pollutant emissions into the environment [16].

- propose a nonlinear dynamic model that considers the main vehicle nonlinearities, e.g., the elastic and damping behaviour of the torsional damper and the transient model of the tyres’ dynamics—thus representing a reference model for vehicle performance assessment and torque controller validation;
- show the benefits introduced by the proposed controller in terms of dynamic performance, driveline oscillations, and NOx emissions;
- test the controller’s robustness against the presence of unpredictable external inputs, e.g., a sudden road slope.

## 2. Hybrid Vehicle Powertrain Layout

#### 2.1. Matlab/Simulink Nonlinear Truck Model

#### 2.2. Dynamic Equations

#### 2.2.1. Power Source: ICE and EM

#### 2.2.2. Transmission: From Clutch Damper to Differential

#### 2.2.3. Vehicle and Wheels

#### 2.2.4. NOx Modelling

## 3. Closed Loop Control System

#### 3.1. High-Level Control Strategy

#### 3.2. Control Allocation

## 4. Results

#### 4.1. Reference Tracking Performance

#### 4.2. Control Allocation Evaluation

## 5. Conclusions

- The high level of the torque control logic generated a total torque demand that satisfied the performance requirements in terms of vehicle speed and acceleration. Both the FF and FB contributions were designed based on a simplified version of the more accurate non-linear model. The FB contribution was fundamental in improving the vehicle’s transient response, damping the acceleration and jerk oscillations. Differing calibrations of the FB gains can cope with different trade-offs between state error tracking performance and the power required to minimize errors;
- The paper also showed how the FB contribution was effective in rejecting external disturbances, e.g., the road slope, by compensating for the FF contribution with an additional contribution—thus satisfying the desired reference tracking performance;
- The control allocation strategy proved to produce a satisfactory vehicle drivability performance, even in the presence of tighter constraints in the ICE torque rate. The hybrid architecture showed outstanding robustness properties against variations in the ICE torque rate when compared to the ICE-only configuration. The redundancy offered by the fast dynamics of an electric machine represents an effective way of establishing the best combination between emissions and dynamic performance.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 7.**Control effort distribution between the ICE and EM, according to the dynamic limits of the engine.

**Figure 8.**Vehicle state tracking performance during a tip-in manoeuvre with only the FF torque contribution (

**a**) and with FF + FB integration (

**b**): longitudinal acceleration (top left), front wheels, rear wheels, and primary shaft speeds (top right), rear axle deformation (down left) and torque ${T}_{t}$.

**Figure 9.**Control torque request (top), jerk (centre) and weighted states errors (down) during a tip-in manoeuvre with only the FF torque contribution (

**a**) and with FF + FB integration (

**b**).

**Figure 10.**Control torque request (

**a**), road slope (

**b**), longitudinal acceleration (

**c**) and weighted states errors (

**d**) during a tip-in manoeuvre with the FF + FB controller mode.

**Figure 11.**Vehicle acceleration (

**a**), jerk (

**b**), total power requested (

**c**) and weighted rear speed error (

**d**) during a tip-in manoeuvre with different $r$ weights.

**Figure 12.**Torque split during a tip-in manoeuvre with only the ICE (

**a**) and with a hybrid configuration (

**b**) for different constraints on the ICE torque slope saturation.

**Figure 13.**Longitudinal acceleration during a tip-in manoeuvre with only the ICE (

**a**) and with a hybrid configuration (

**b**) for different constraints on the ICE torque slope saturation.

**Figure 14.**NOx emissions during a tip-in manoeuvre with the hybrid configuration for different constraints on the ICE torque slope saturation.

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**MDPI and ACS Style**

Dimauro, L.; Tota, A.; Galvagno, E.; Velardocchia, M.
Torque Allocation of Hybrid Electric Trucks for Drivability and Transient Emissions Reduction. *Appl. Sci.* **2023**, *13*, 3704.
https://doi.org/10.3390/app13063704

**AMA Style**

Dimauro L, Tota A, Galvagno E, Velardocchia M.
Torque Allocation of Hybrid Electric Trucks for Drivability and Transient Emissions Reduction. *Applied Sciences*. 2023; 13(6):3704.
https://doi.org/10.3390/app13063704

**Chicago/Turabian Style**

Dimauro, Luca, Antonio Tota, Enrico Galvagno, and Mauro Velardocchia.
2023. "Torque Allocation of Hybrid Electric Trucks for Drivability and Transient Emissions Reduction" *Applied Sciences* 13, no. 6: 3704.
https://doi.org/10.3390/app13063704