# Automated Longitudinal Control Based on Nonlinear Recursive B-Spline Approximation for Battery Electric Vehicles

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## Abstract

**:**

## 1. Introduction

#### 1.1. Driver Assistance Systems for Automated Longitudinal Control

#### 1.2. Research Gap

#### 1.3. Contribution

#### 1.4. Outline

## 2. Energy Consumption of Battery Electric Research Vehicles

#### 2.1. Research Vehicle

#### 2.2. Driving Resistances

#### 2.3. Power Train

#### 2.4. Energy Consumption and Optimization Approach

## 3. Automated Longitudinal Control System

#### 3.1. System Architecture

#### 3.2. Parameter Adaption Module

#### 3.3. Adaptive Traction Force Model

#### 3.4. Adaptive Electrical Power Model

#### 3.5. Route Data Module

#### 3.6. Trajectory Module

#### 3.6.1. Generation of Upper Speed Limit

#### 3.6.2. Representation of Velocity Trajectory

#### 3.6.3. Trajectory Optimization

#### 3.6.4. Trajectory Optimization with Consideration of Electrical Traction Power

#### 3.6.5. Consideration of Additional Trajectory Constraints

#### 3.7. Controller Module

## 4. Testing and Evaluation of the Automated Longitudinal Control

#### 4.1. Reference Route

#### 4.2. Test Drives and Acceptance Test

#### 4.3. Energy-Saving Potential of Automated Longitudinal Control and Effects of Parameters

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Power loss between HV battery and wheels ${P}_{\mathrm{Loss}}$ versus electrical traction power ${P}_{\mathrm{trac},\mathrm{elec}}$ for various combinations of vehicle velocity ${v}_{\mathrm{vhcl}}$ and vehicle longitudinal acceleration ${\dot{v}}_{\mathrm{vhcl},\mathrm{x}}$.

**Figure 3.**Electrical traction power ${P}_{\mathrm{AEPM}}$ according to the adaptive electrical power model (AEPM) depending on longitudinal specific acceleration ${a}_{\mathrm{x}}$ for various vehicle velocities ${v}_{\mathrm{vhcl}}$. The gray shaded area is the operating area of the ALC, $max{P}_{\mathrm{trac},\mathrm{elec}}$ the maximum traction power and $min{P}_{\mathrm{trac},\mathrm{elec}}$ the maximum recuperation power.

**Figure 4.**Influence of temporal safety margin to upper speed limit $\Delta {t}_{\mathrm{Lim},\mathrm{TJY}}$ on speed limit for trajectory optimization ${v}_{\mathrm{Lim},\mathrm{TJY}}$ and trajectory velocity ${v}_{\mathrm{TJY}}$. Only a subset of ${v}_{\mathrm{Lim},\mathrm{TJY}}$ is shown. Upper diagram: The speed limit from map data with desired acceleration ${v}_{\mathrm{Lim},\mathrm{Map},\dot{v}}$ is identical for both trajectories. Lower diagram: ${v}_{\mathrm{Lim},\mathrm{Map},\dot{v}}$ differs with the trajectories.

**Figure 5.**Velocity v, electrical traction power ${P}_{\mathrm{AEPM}}$ according to adaptive electrical power model (AEPM), road slope $\alpha $, energy loss between HV battery and wheels ${E}_{\mathrm{Loss}}$ and HV battery energy ${E}_{\mathrm{Batt}}$ for trajectories determined by nonlinear recursive B-spline approximation (NRBA) and Levenberg-Marquardt (LM) algorithm that differ in the weight of power error square ${R}_{P}^{-1}$.

**Figure 6.**Architecture of controller module and control loop. The trajectory velocity ${v}_{\mathrm{TJY}}$ and trajectory acceleration ${a}_{\mathrm{TJY}}$ are derived from the trajectory function. The pilot control based on the adaptive traction force model (ATFM) generates an open-loop motor torque demand ${T}_{\mathrm{des},\mathrm{PC}}$ using ${v}_{\mathrm{TJY}}$, ${a}_{\mathrm{TJY}}$ and the road slope angle $\alpha $. The model predictive control (MPC) computes a closed-loop torque demand ${T}_{\mathrm{des},\mathrm{MPC}}$ in order to minimize the remaining deviation of vehicle velocity ${v}_{\mathrm{vhcl}}$ and vehicle longitudinal acceleration ${\dot{v}}_{\mathrm{vhcl},\mathrm{x}}$ from the desired values.

**Figure 7.**Energy consumption versus average velocity on the reference route Weissach round with automated longitudinal control (ALC) under different parameter settings in comparison to adapted and resimulated real drives with manual longitudinal control (MLC).

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**MDPI and ACS Style**

Jauch, J.; Bleimund, F.; Frey, M.; Gauterin, F.
Automated Longitudinal Control Based on Nonlinear Recursive B-Spline Approximation for Battery Electric Vehicles. *World Electr. Veh. J.* **2019**, *10*, 52.
https://doi.org/10.3390/wevj10030052

**AMA Style**

Jauch J, Bleimund F, Frey M, Gauterin F.
Automated Longitudinal Control Based on Nonlinear Recursive B-Spline Approximation for Battery Electric Vehicles. *World Electric Vehicle Journal*. 2019; 10(3):52.
https://doi.org/10.3390/wevj10030052

**Chicago/Turabian Style**

Jauch, Jens, Felix Bleimund, Michael Frey, and Frank Gauterin.
2019. "Automated Longitudinal Control Based on Nonlinear Recursive B-Spline Approximation for Battery Electric Vehicles" *World Electric Vehicle Journal* 10, no. 3: 52.
https://doi.org/10.3390/wevj10030052