# Integration of a Model Predictive Control with a Fast Energy Management Strategy for a Hybrid Powertrain of a Connected and Automated Vehicle

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## Abstract

**:**

## 1. Introduction

- Vehicle to Vehicle (V2V);
- Vehicle to Infrastructure (V2I);
- Infrastructure to Vehicle (I2V).

## 2. Related Work

#### 2.1. MPC for CAVs

- Intelligent Speed Adaptation (ISA) from Smart Road Infrastructure (e.g., point-to-point speed);
- ADAS Maps (e.g., TomTom) and systems to determine steering maneuvers;
- Environmental and road data (e.g., wind speed and road friction) provided by Infrastructure to Vehicle (I2V) communication;
- Parameters and measurements from vehicles located ahead (e.g., its acceleration, speed and mass) provided by Vehicle to Vehicle (V2V) communication;
- ADAS functionalities to maintain a certain safety distance from the vehicle located ahead.

#### 2.2. EMS for Hybrid Powertrains

#### 2.3. Integration of MPC with EMS

## 3. Methodology

#### 3.1. Vehicle Model

#### 3.1.1. Single-Track Model

- 1.
- Only the front wheels are considered to be driving, so the overall wheels torque ${\tau}_{w}$ is the sum of the torque at front wheels during accelerations. Furthermore, ${\tau}_{w}$ is assumed as the sum of the torque at all the wheels during braking;
- 2.
- The steering angles of the front wheels are equal to $\delta $ and the small angle approximation is used [34], considering that the control range on the steering angle at the wheels is [−5, 5]°; thus, $sin\delta \approx \delta $ and $cos\delta \approx 1$;
- 3.
- The longitudinal slip ratio ${\sigma}_{ij}$ (the subscripts ${}_{ij}$ indicate the positioning of the wheel on the vehicle, i.e., front right ${}_{fr}$, front left ${}_{fl}$, rear left ${}_{rl}$ and rear right ${}_{rr}$) is considered negligible and defined as follows$${\sigma}_{ij}=\left\{\begin{array}{cc}\frac{{R}_{eff}{\omega}_{ij}-{v}_{x}}{{v}_{x}},\hfill & \mathrm{during}\phantom{\rule{4.pt}{0ex}}\mathrm{acceleration}\hfill \\ \frac{{R}_{eff}{\omega}_{ij}-{v}_{x}}{{R}_{eff}{\omega}_{ij}},\hfill & \mathrm{during}\phantom{\rule{4.pt}{0ex}}\mathrm{braking}\hfill \end{array}\right.$$

#### 3.1.2. Equations of Errors with Respect to the Road

#### 3.1.3. Car-Following Model

#### 3.1.4. Complete Nonlinear Ego-Vehicle Model

#### 3.1.5. Linearization of the Complete Ego-Vehicle Model

#### 3.2. Model Predictive Control

- 1.
- 2.
- 3.
- Augmenting the model, by concatenating states and outputs of the linearized and discretized model [38].
- 4.
- Defining a cost function.
- 5.
- Setting the constraints on input and/or output variables.

#### 3.3. Powertrain and Driveline Model

#### 3.4. Efficient Thermal Electric Skipping Strategy

## 4. Results

#### 4.1. Comparative Assessment between ETESS and ECMS

#### 4.2. PIL Test for CAVs Equipped with EMS

- 1.
**ISA, EEB, and ACC in the longitudinal direction**: The simulated Smart Road provides the ego and ahead vehicles with a speed reference equal to 50 km/h (initial condition). After 20 s, the vehicle located ahead breaks hard for five seconds (the speed quickly drops from 50 to 5 km/h) and the ego-vehicle executes an EEB. The new limit is kept at 5 km/h for 5 seconds by the Smart Road (ISA). Then, being no collision, the Smart Road provides a new speed profile to allow the ahead vehicle to reach a new speed limit of 30 km/h (ISA) in 30 s, while ACC acts on the ego vehicle. Later, after further 30 s, the Smart Road resets the speed limit at 50 km/h (ISA) and the ahead vehicle reaches the limit in 30 s, while the ACC continues acting on the ego vehicle. The results are shown in Figure 9:- At first, $EM$ is working; after around 100 s, the $ICE$ driving starts, when the battery $SoC$ falls below 57% (Figure 9c,d).

- 2.
**LKS, ACC in both longitudinal and lateral directions**: ADAS Maps and C-ITS are supposed to provide the road curvature (${R}_{c}$) profile in Figure 10d. ACC and LKS act simultaneously on the ego vehicle. The speed limit is 50 km/h and the ahead vehicle applies slow braking from 50 to 40 km/h in 30 s (until the end of the road curvature). The ahead vehicle remains at that speed for 20 s and then it reaches the speed limit of 50 km/h in 30 s. The results are shown in Figure 10 and Figure 11:- Lateral displacement and yaw angle errors are shown in Figure 10a,b and go to zero when curvature ends (Figure 10d); ${e}_{1}$ has peaks in absolute value below 1 cm, ${e}_{2}$ has a minimum at about −0.05°. The steering angle at the wheels (Figure 10c) follows the trend of road curvature with a maximum at 0.37°;
- The tracking of ${v}_{ref}$ from vehicle speed ${v}_{x}$ (Figure 11a) has a similar behavior of test case 1, with a small overshoot around 140 s in order to allow the achievement of the desired relative distance ${d}_{safe}$ (Figure 11b) in the steady state. The relative distance never falls below the safe distance;
- At first, $EM$ is working; then a pure $ICE$ driving activates when the $SoC$ falls below 57% (Figure 11c,d).

#### 4.3. Robustness Test of MPC against Model Parameter Uncertainties

#### 4.4. Sensitivity Tests of MPC against Model Parameters Uncertainties

## 5. Discussion

- Awareness driving;
- Intersection management;
- Rear-end collisions;
- Long distance travels for HEVs and EVs by using benefit of Smart Road and C-ITS services.

## 6. Conclusions

- The average execution time of MPC + ETESS on the same MCU (STM32H743ZI2) was about 3.22 ms and therefore well below the typical CAN cycle time for torque request and steering angle, which is 10 ms.
- ETESS was 15 times faster than ECMS; thus, this encourages the implementation of further control strategies on the same MCU, in order to reach additional real-time features, such as path planning and eco-driving.
- Along representative maneuvers, MPC showed good tracking properties of reference speed (with an error below the 0.1% in the steady state) and lane keeping (error below 1 cm for the lateral displacement and 0.025° for the yaw angle). MPC allowed us to keep a relative distance greater than the minimum safety distance during braking phases and follows the theoretical safety distance in the steady state (with an error below 0.1%).
- The robustness of MPC against ego-vehicle model parameters uncertainties (drag coefficient, cornering stiffness and vehicle mass) showed good tracking performance of the vehicle speed ${v}_{x}$ and a slight deviation (−5 mm; the maximum allowed is equal to 35 cm) of the lateral displacement ${e}_{1}$ at the maximum parameters variations ($m={m}_{max}$, ${C}_{d}={C}_{{d}_{max}}$, ${C}_{\alpha}={C}_{{\alpha}_{max}}$). The ICE activation occurred, respectively, 14 s earlier (maximum parameters variations) and 9 s later (minimum parameter variations), depending on the battery discharge rate during the early stage of the maneuver.
- The sensitivity tests of MPC against the individual variation of single parameter of the ego-vehicle model showed a relevant influence of the maximum vehicle load ($m={m}_{max}$) towards all variables: lateral displacement ${e}_{1}$ ($MAE=1.57,RMSE=0.55\phantom{\rule{0.166667em}{0ex}}$ cm), vehicle speed ${v}_{x}$ ($MAE=0.52\phantom{\rule{0.277778em}{0ex}}RMSE=0.15\phantom{\rule{0.166667em}{0ex}}$ km/h), relative distance ${d}_{r}$ ($MAE=2.98,\phantom{\rule{0.277778em}{0ex}}RMSE=1.0\phantom{\rule{0.166667em}{0ex}}$ m) and wheels power ($MAE=0.98,RMSE=0.51\phantom{\rule{0.166667em}{0ex}}$ kW). With the minimum cornering stiffness ${C}_{{d}_{min}}$, the highest impact occurred for the lateral displacement ($MAE=1.89,\phantom{\rule{0.277778em}{0ex}}RMSE=0.6\phantom{\rule{0.166667em}{0ex}}$ cm), while with the maximum one ${C}_{{d}_{max}}$, the highest influence was on the wheels power ($MAE=0.73,\phantom{\rule{0.277778em}{0ex}}RMSE=0.03\phantom{\rule{0.166667em}{0ex}}$ kW). The wheels power was also significantly influenced by the drag coefficient, showing a $MAE=0.53\phantom{\rule{0.166667em}{0ex}}$ kW and a $RMSE=0.4\phantom{\rule{0.166667em}{0ex}}$ kW. Considering the RMSE indices, the variations were quite contained, except for the wheels power, which, as expected, was higher if the vehicle load and drag coefficient were greater.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**(

**a**) Target speed (km/h). (

**b**) Battery SoC (%) between ETESS and ECMS. (

**c**) Power split between ETESS and ECMS.

**Figure 9.**Test case 1: (

**a**) speed (km/h); (

**b**) relative distance (m); (

**c**) ICE/EM/Wheels power (kW); (

**d**) battery SoC (%).

**Figure 10.**Test case 2: (

**a**) lateral displacement (m); (

**b**) yaw angle error (deg); (

**c**) steering angle at the wheels (deg); (

**d**) road curvature (m

^{−1}).

**Figure 11.**Test case 2: (

**a**) speed (km/h); (

**b**) relative distance (m); (

**c**) ICE/EM/Wheels power (kW); (

**d**) battery SoC (%).

**Figure 12.**Robustness test (blue: nominal values, dashed red: maximum values, dashed black: minimum values)—(

**a**) lateral displacement (m); (

**b**) yaw angle error (deg); (

**c**) steering angle at the wheels (deg); (

**d**) road curvature (m

^{−1}).

**Figure 13.**Robustness test (blue: nominal values, dashed red: maximum values, dashed black: minimum values)—(

**a**) speed (km/h); (

**b**) relative distance (m); (

**c**) wheel power (kW); (

**d**) battery SoC (%); (

**e**) EM power (kW); (

**f**) ICE power (kW).

**Figure 14.**Sensitivity test (blue: nominal case (m), dashed red: maximum case (${m}_{max}$), dashed black: minimum case (${m}_{min}$)) with parametric variations on vehicle mass—(

**a**) speed (km/h); (

**b**) relative distance (m); (

**c**) wheels power (kW); (

**d**) battery SoC (%); (

**e**) EM power (kW); (

**f**) ICE power (kW).

Parameter | Description | Description |
---|---|---|

m | Vehicle mass | 1055 kg |

${R}_{eff}$ | Effective wheel radius | 0.29 m |

$0.5\rho A{C}_{d}$ | Aerodynamic force coefficient | 0.503 kg/m |

L | Vehicle length | 3.571 m |

${T}_{h}$ | Reaction time for safety distance evaluation | 2 s |

${I}_{w}$ | Moment of inertia of the wheels | 1.85 kgm^{2} |

${I}_{z}$ | Yaw moment of inertia | 1338.2 kgm^{2} |

${L}_{f}$ | Dist. vehicle’s CoG to front wheel axis | 1 m |

${L}_{r}$ | Dist. vehicle’s CoG to rear wheel axis | 1.3 m |

${C}_{\alpha}$ | Longitudinal tire stiffness | 67,689 N/rad |

${\tau}_{max}$ | Maximum wheel torque | 664 Nm |

${\tau}_{min}$ | Maximum braking torque at the wheel | −850 Nm |

${\delta}_{max}$ | Maximum steering angle at the wheel | 3° |

${\delta}_{min}$ | Minimum steering angle at the wheel | −3° |

${\tau}_{bs}$ | Braking phase time constant | 0.2 s |

${K}_{b}$ | Gain for braking system | 14 |

${K}_{c}$ | Gain for pressure of brake | 1 |

${v}_{w}$ | Wind velocity | 0.55 m/s |

$\theta $ | Slope angle | 0 rad |

${t}_{s}$ | Simulation time | 1 ms |

${\Delta}t$ | Sampling time | 10 ms |

Driving Mode | Clutch 1 | Clutch 2 | Clutch 3 |
---|---|---|---|

Braking | x | ✓ | x |

Pure electric driving | x | ✓ | x |

Pure thermal engine driving | ✓ | x | x |

Hybrid parallel driving | ✓ | ✓ | x |

Battery charging in series mode | x | ✓ | ✓ |

Battery charging in parallel mode | ✓ | ✓ | ✓ |

Parameter | Description | Value |
---|---|---|

V (cm${}^{3}$) | Engine displacement | 999 |

${\rho}_{o}$ | Geometric compression ratio | 10.5:1 |

B (mm) | Cylinder bore | 70 |

s (mm) | Cylinder stroke | 80.5 |

n | Number of cylinders | 3 |

v | Number of valves | 6 |

${P}_{max\_ICE}$ (kW) | Maximum engine power | 51 |

${T}_{max\_ICE}$ (Nm) | Maximum engine torque | 92 |

${N}_{G{B}_{1}}$ | Number of gear ratios of $G{B}_{1}$ | 6 |

${\eta}_{G{B}_{1}}$ | ICE gear efficiency | 0.97 |

${\eta}_{Diff}$ | Final-drive ratio efficiency | 1 |

${P}_{max\_EM}$ (kW) | Maximum electric motor power | 67.35 |

${T}_{max\_EM}$ (Nm) | Maximum electric motor torque | 165 |

${N}_{G{B}_{2}}$ | Number of gear ratios of $G{B}_{2}$ | 2 |

${\eta}_{G{B}_{2}}$ | EM gear efficiency | 0.99 |

${P}_{max\_EG}$ (kW) | Maximum electric generator power | 59.01 |

${T}_{max\_EG}$ (Nm) | Maximum electric generator torque | 240 |

${N}_{G{B}_{3}}$ | Number of gear ratios of $G{B}_{3}$ | 1 |

${\eta}_{G{B}_{3}}$ | EG gear efficiency | 1 |

${R}_{bat}\phantom{\rule{0.222222em}{0ex}}\left({\Omega}\right)$ | Battery internal resistance | 0.375 |

${V}_{bat}$ (V) | Battery voltage | 400 |

${Q}_{max}$ (Ah) | Battery capacity | 1.78 |

$So{C}_{range}$ (%) | Battery SoC limits | $20\xf790$ |

${\eta}_{PC}$ | Efficiency of the power converter | 0.92 |

**Table 4.**Comparison between the fuel consumption by ETESS and ECMS along three type-approval driving cycles.

Fuel Consumption (l/100 km) | WLTC | NEDC | FTP-75 |
---|---|---|---|

ECMS | 4.18 | 3.69 | 3.24 |

ETESS | 4.18 | 3.71 | 3.24 |

Difference (%) | +0.0 | +0.5 | +0.0 |

**Table 5.**Comparison between the computational time (in MIL testing) of ETESS and ECMS along three type-approval driving cycles.

Computational Time $\left(\mathit{s}\right)$ | WLTC | NEDC | FTP-75 |
---|---|---|---|

ECMS | 678.09 | 440.22 | 710.18 |

ETESS | 52.46 | 35.05 | 52.87 |

Difference (%) | −92.26 | −92.04 | −92.55 |

Task | MPC | ETESS | ECMS |
---|---|---|---|

Maximum CPU Utilization (%) | 31.90 | 0.40 | 7.93 |

Average CPU Utilization (%) | 30.30 | 0.36 | 5.36 |

Maximum Execution Time (ms) | 3.186 | 0.04 | 0.79 |

Average Execution Time (ms) | 3.031 | 0.035 | 0.530 |

Parameter | Min. Value | Nominal Value | Max. Value |
---|---|---|---|

Drag coefficient | 0.224 (${C}_{{d}_{min}}$) | 0.320 (${C}_{d}$) | 0.416 (${C}_{{d}_{max}}$) |

Vehicle mass (kg) | 1023 (${m}_{min}$) | 1050 (m) | 1371 (${m}_{max}$) |

Cornering Stiffness (N/rad) | 34,878.9 ${C}_{{\alpha}_{min}}$ | 49,827.0 (${C}_{\alpha}$) | 64,775.1 (${C}_{{\alpha}_{max}}$) |

Test Case | MAE (cm) | RMSE (cm) |
---|---|---|

$m={m}_{max}$ | 1.5730 | 0.5498 |

$m={m}_{min}$ | 0.2681 | 0.0771 |

${C}_{d}={C}_{{d}_{max}}$ | 0.1000 | 0.0977 |

${C}_{d}={C}_{{d}_{min}}$ | 0.1005 | 0.0981 |

${C}_{\alpha}={C}_{{\alpha}_{max}}$ | 1.1073 | 0.2007 |

${C}_{\alpha}={C}_{{\alpha}_{min}}$ | 1.8863 | 0.6208 |

Test Case | MAE (deg) | RMSE (deg) |
---|---|---|

$m={m}_{max}$ | 0.0148 | 0.0010 |

$m={m}_{min}$ | 0.0027 | 0.0002 |

${C}_{d}={C}_{{d}_{max}}$ | 0.0007 | 0.0001 |

${C}_{d}={C}_{{d}_{min}}$ | 0.0007 | 0.0001 |

${C}_{\alpha}={C}_{{\alpha}_{max}}$ | 0.0116 | 0.0008 |

${C}_{\alpha}={C}_{{\alpha}_{min}}$ | 0.0169 | 0.0011 |

Test Case | MAE (km/h) | RMSE (km/h) |
---|---|---|

$m={m}_{max}$ | 0.5203 | 0.1476 |

$m={m}_{min}$ | 0.1152 | 0.0261 |

${C}_{d}={C}_{{d}_{max}}$ | 0.1534 | 0.0407 |

${C}_{d}={C}_{{d}_{min}}$ | 0.1430 | 0.0364 |

${C}_{\alpha}={C}_{{\alpha}_{max}}$ | 0.0343 | 0.0040 |

${C}_{\alpha}={C}_{{\alpha}_{min}}$ | 0.0374 | 0.0060 |

Test Case | MAE (m) | RMSE (m) |
---|---|---|

$m={m}_{max}$ | 2.98 | 1.03 |

$m={m}_{min}$ | 0.46 | 0.15 |

${C}_{d}={C}_{{d}_{max}}$ | 0.47 | 0.28 |

${C}_{d}={C}_{{d}_{min}}$ | 0.47 | 0.26 |

${C}_{\alpha}={C}_{{\alpha}_{max}}$ | 0.06 | 0.04 |

${C}_{\alpha}={C}_{{\alpha}_{min}}$ | 0.11 | 0.07 |

Test Case | MAE (kW) | RMSE (kW) |
---|---|---|

$m={m}_{max}$ | 0.98 | 0.51 |

$m={m}_{min}$ | 0.58 | 0.09 |

${C}_{d}={C}_{{d}_{max}}$ | 0.53 | 0.40 |

${C}_{d}={C}_{{d}_{min}}$ | 0.53 | 0.41 |

${C}_{\alpha}={C}_{{\alpha}_{max}}$ | 0.73 | 0.03 |

${C}_{\alpha}={C}_{{\alpha}_{min}}$ | 0.55 | 0.02 |

Test Case | MAE (deg) | RMSE (deg) |
---|---|---|

$m={m}_{max}$ | 0.0105 | 0.0019 |

$m={m}_{min}$ | 0.0018 | 0.003 |

${C}_{d}={C}_{{d}_{max}}$ | 0.0002 | 0.0000 |

${C}_{d}={C}_{{d}_{min}}$ | 0.0002 | 0.0000 |

${C}_{\alpha}={C}_{{\alpha}_{max}}$ | 0.0075 | 0.0014 |

${C}_{\alpha}={C}_{{\alpha}_{min}}$ | 0.0139 | 0.0025 |

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## Share and Cite

**MDPI and ACS Style**

Landolfi, E.; Minervini, F.J.; Minervini, N.; De Bellis, V.; Malfi, E.; Natale, C.
Integration of a Model Predictive Control with a Fast Energy Management Strategy for a Hybrid Powertrain of a Connected and Automated Vehicle. *World Electr. Veh. J.* **2021**, *12*, 159.
https://doi.org/10.3390/wevj12030159

**AMA Style**

Landolfi E, Minervini FJ, Minervini N, De Bellis V, Malfi E, Natale C.
Integration of a Model Predictive Control with a Fast Energy Management Strategy for a Hybrid Powertrain of a Connected and Automated Vehicle. *World Electric Vehicle Journal*. 2021; 12(3):159.
https://doi.org/10.3390/wevj12030159

**Chicago/Turabian Style**

Landolfi, Enrico, Francesco Junior Minervini, Nicola Minervini, Vincenzo De Bellis, Enrica Malfi, and Ciro Natale.
2021. "Integration of a Model Predictive Control with a Fast Energy Management Strategy for a Hybrid Powertrain of a Connected and Automated Vehicle" *World Electric Vehicle Journal* 12, no. 3: 159.
https://doi.org/10.3390/wevj12030159