# Study on Adaptive Cruise Control Strategy for Battery Electric Vehicle Considering Weight Adjustment

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## Abstract

**:**

## 1. Introduction

## 2. Model for BEV

_{oc}and R

_{int}are the open circuit voltage and battery internal resistance, respectively, and the U

_{c}and I

_{c}are the voltage and current of external load. The efficiency of the battery related to the internal resistance of the battery is considered in the battery model. The efficiency of the motor related to the speed and torque of the motor is considered in the motor model [24,25]. The maximum torque and speed characteristics for the motor are shown in Figure 3. The maximum torque and speed characteristics are defined as follows:

_{M_max}is the maximum driving torque, P

_{M_max}is the peak power of the motor, f

_{m}(ω

_{m}) is the correction for the motor torque related to the motor efficiency, ω

_{m}is the angular velocity of the motor, ω

_{ini}is the minimum speed for constant torque control, ω

_{b}is the base speed, and ω

_{end}is the highest speed. The main parameters for the BEV model are listed in Table 1.

## 3. Proposed ACC System

## 4. Car-Following Model

_{rel}at moment k are defined as follows:

_{f}and s are the distance of the front vehicle and the own vehicle, respectively, and v

_{f}and v are the speeds of the front vehicle and the own vehicle, respectively.

_{f}and a are the acceleration of the front vehicle and the own vehicle, respectively, and T

_{s}is the sampling time.

## 5. Multi-Objective Optimization Algorithm

_{des}is the expected spacing obtained from the constant time headway (CTH) spacing policy, δ is the difference between the real spacing and the expected spacing, and ∆s

_{des}and δ at moment k can be defined as follows:

_{0}is the fixed distance between the two vehicles when the vehicle speed is low and zero, t

_{h}is the time headway.

_{r}is the reference trajectory for the error of spacing, and α is the time constant of the reference trajectory for the spacing error.

_{δ}, ρ

_{vrel}, ρ

_{a}and ρ

_{j}are the coefficients in the reference trajectory, and ρ

_{δ}is the coefficient of the spacing error, and ρ

_{vrel}is the coefficient of relative velocity, ρ

_{a}is the coefficient for the acceleration of the own vehicle, and ρ

_{j}is the coefficient for the jerk of the own vehicle. The reference trajectory matrix is in symmetrical form along the diagonal of the matrix in order to reduce the complexity of the calculation.

_{c}is the minimum safe spacing between two vehicles.

_{p}(k + i|k) is the prediction of the performance vector for the moment k + i at the moment k, p is the predictive horizon, m is the control horizon, Q and R are the weight matrices, and u(k + i) is the control command at moment k + i.

## 6. Strategy for Weight Adjustment

_{δ}(k), w

_{vrel}(k), w

_{a}(k) and w

_{j}(k) in the Q matrix are the weights corresponding to the spacing error, relative velocity, and acceleration and jerk of the own vehicle at moment k, w

_{u}(k) in the R matrix is the weight corresponding to the control command of the acceleration at moment k.

_{δ}, w

_{vrel}, w

_{a}, w

_{j}and w

_{u}) in the objective function, but only four weights (w

_{δ}, w

_{vrel}, w

_{a}and w

_{j}) are considered in the strategy for weight adjustment. The reason for this is that a constant value for w

_{u}can ensure good performances for the controller in a series of trial and error operations, and there is no need to adjust the weight w

_{u}in real time.

_{δ}(0), w

_{vrel}(0), w

_{a}(0), w

_{j}(0) and w

_{u}(0), corresponding to w

_{δ}(k), w

_{vrel}(k), w

_{a}(k), w

_{j}(k) and w

_{u}(k) obtained from a series of trial-and-error operations, are 1, 10, 1, 1 and 1, respectively. Moreover, the safety, tracking, comfort and energy economy are also considered in the selection of the initial weights.

_{rel}< 0, the spacing between the two vehicles decreases gradually. The greater the absolute value of relative velocity, the faster the spacing between the two vehicles decreases. If the own vehicle is in this state for a long time, there will be a collision between the own vehicle and the front vehicle. Therefore, the velocity of the own vehicle should be adjusted as soon as possible to be close to the velocity of the front vehicle. The weight for the relative velocity should be bigger, and the weights of spacing error, acceleration and jerk should be smaller, so as to regulate the velocity of the own vehicle at close to the velocity of the front vehicle. The corresponding ratio is greater (>10). The greater the absolute value of the relative velocity, the bigger the change in weights relative to the initial weights and the bigger the change in ratio relative to the initial ratio.

_{rel}> 0, the spacing between the two vehicles increases gradually. In addition, the greater the absolute value of the relative velocity, the faster the spacing between the two vehicles increases. If the vehicle is in this state for a long time, the spacing between the two vehicles will increase, and greater spacing will result in worse tracking for the expected spacing. Therefore, the spacing between the two vehicles should be adjusted as soon as possible to be close to the expected spacing. The weights of error of spacing, acceleration and jerk should be bigger, the weight for the relative velocity should be smaller, in order to regulate the spacing to be close to the expected spacing. The corresponding ratio is smaller (<10). The greater the absolute value of the relative velocity, the bigger the change in weight relative to the initial weight, and the bigger the change in ratio relative to the initial ratio.

_{rel}(k) < 0, w

_{vrel}(k) is adjusted to increase, and w

_{δ}(k), w

_{a}(k) and wj(k) are adjusted to decrease; when v

_{rel}(k) > 0, w

_{vrel}(k) is adjusted to decrease, and w

_{δ}(k), w

_{a}(k) and w

_{j}(k) are adjusted to increase. In the definition of weights, the n

_{vrel}(k − 1) is the normalization function changing the range for v

_{rel}(k) from (−∞, +∞) to (−1,1), and r(k) is used to make the sum of all adjustable weight coefficients equal to 1. The driving condition of v

_{rel}= 0 is also considered in Equation (33), and the ratio in this driving condition is 10, and the weights in this driving condition are 1/13, 10/13, 1/13 and 1/13, respectively.

## 7. Simulation Experiment and Discussion

#### 7.1. Method

_{rel}(i) are the spacing error and relative velocity at moment i.

_{rel}_ini is the initial relative velocity, v_ini and v

_{f}_ini are the initial speed for the own vehicle and the front vehicle, respectively, and a_amp is the amplitude of acceleration for the front vehicle. The parameters of the optimization algorithm are shown in Table 4. The control strategies were designed in the Matlab/Simulink, and verified through co-simulation in Carsim.

#### 7.2. Scenario 1

_{rel}> 0, greater weights are applied for spacing errors, and the own vehicle adjusts in response to speed, acceleration and jerk in order to reduce spacing error.

^{3}, which is the maximum value accepted by passengers. Therefore, comfort is ensured in both MPC_ADJ and MPC_CON. From Figure 5e, the peak values of battery power are greater in the MPC_ADJ before 10 s, and after 10 s, the peak values of battery power are smaller in MPC_ADJ. From Figure 5f, the change of SOC in MPC_ADJ is smaller than MPC_CON. In addition, the rate of SOC change and the distance for MPC_ADJ and MPC_CON are 0.0049 km

^{−1}and 0.0061 km

^{−1}, the improvement of the index of the energy economy is 19.66%. The reasons for the improvement in energy economy include the facts that the weight adjustment strategy is adopted in MPC_ADJ, and a good compromise between fast response and the reduction of system response fluctuation is achieved in MPC_ADJ. From Figure 5g,h, the peak values for the brake pressure and driving torque in MPC_ADJ are smaller throughout most of the simulation time. The smaller peak values of brake pressure correspond to less kinetic waste, and the smaller peak values of driving torque for the motor correspond to lower energy consumption. Therefore, the energy economy is improved.

#### 7.3. Scenario 2

_{rel}> 0, the greater weight is applied for spacing error, acceleration and jerk, and the vehicle adjusts in response to the speed, acceleration and jerk in orer to reduce the spacing error.

^{3}, which is the maximum jerk for ordinary passengers. Therefore, comfort is ensured in both ACC systems. From Figure 6e, the peak values of the battery power are smaller for MPC_ADJ throughout the entire simulation period. However, in MPC_CON, the maximal peak values of the battery power are 53.69 KW. From Figure 6f, the change in SOC is smaller in MPC_ADJ. In addition, the rates of the SOC change and distance for the MPC_ADJ and MPC_CON are 0.0028 km

^{−1}and 0.0039 km

^{−1}, respectively, and the improvement of the energy economy index is 28.84%. The reason for the improvement in energy economy in the cut in scenario is that the weight adjustment strategy is adopted in order to improve the tracking performance in MPC_ ADJ. In addition, a good compromise between fast response and reduction of system response fluctuation is achieved. In Figure 6g,h, the peak values of the brake pressure and driving torque are smaller in MPC_ADJ compared to the MPC_CON. For the entire simulation time, smaller peak values of the brake pressure are able to reduce loss of kinetic energy during the braking process, and smaller driving torque is able to reduce energy consumption during the driving process.

#### 7.4. Scenario 3

_{rel}< 0, the greater weight is applied to relative velocity in MPC_ ADJ. The vehicle adjusts the speed, acceleration and jerk responses in order to obtain better tracking for the velocity of the front vehicle.

^{3}. Therefore, comfort is ensured in both ACC systems. From Figure 7e, the peak values of the battery power are smaller in MPC_ADJ throughout the entire simulation process. From Figure 7f, the change of the SOC is smaller in MPC_ADJ. The rates of the SOC change and distance in MPC_ADJ and MPC_CON are 0.0024 km

^{−1}and 0.0026 km

^{−1}, respectively, and the improvement of the energy economy index is 8.65%. This is because the weight adjustment strategy is adopted in MPC_ADJ, a good compromise is made betwen fast response and reduction of the fluctuation range for the various responses. In Figure 7g,h, the peak values of the brake pressure and driving torque are smaller in MPC_ ADJ compared to the MPC_CON. Throughout the entire simulation time, the smaller peak values of the brake pressure are able to reduce the loss of kinetic energy during the braking process, and smaller peak values of driving torque can reduce the energy consumption during the driving process. The improvement of the index for energy economy in hard braking is less than in the first two scenarios. This is because the safety is the most important performance metric in the hard brake scenario; other performance metrics are temporarily ignored.

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Symbol | Description | Values |
---|---|---|

M_{v} | vehicle weight | 1550 kg |

A | front area | 2.28 m^{2} |

C_{w} | drag coefficient | 0.36 |

f_{r} | rolling resistance coefficient | 0.015 |

ρ_{air} | air density | 1.206 kg/m^{3} |

P_{M_max} | Maximum power of the motor | 87 KW |

SOC_{ini} | Initial SOC | 0.6 |

Q_{bat} | Total battery capacity | 93 Ah |

Driving Conditions | v_{rel} < 0 | v_{rel} > 0 |
---|---|---|

Expected ratio | bigger ratio | Smaller ratio |

w_{δ} | small | large |

w_{v} | large | small |

w_{a} | small | large |

w_{j} | small | large |

Scenario | v_{rel}_{_}ini | ∆s_ini | v_ini | v_{f}_ini | a_amp |
---|---|---|---|---|---|

Scenario 1 | >0 | 50 m | 10 m/s | 15 m/s | 2 m/s^{2} |

Scenario 2 | <0 | 30 m | 15 m/s | 10 m/s | 2 m/s^{2} |

Scenario 3 | =0 | 50 m | 20 m/s | 20 m/s | −4 m/s^{2} |

Symbol | Values | Symbol | Values |
---|---|---|---|

T_{s} | 0.2 s | u_{min} | −5.5 m/s^{2} |

t_{h} | 1.5 s | u_{max} | 2.5 m/s^{2} |

τ | 0.15 s | j_{min} | −3 m/s^{3} |

d_{0} | 7 m | j_{max} | 3 m/s^{3} |

d_{c} | 5 m | ρ | 0.94 |

v_{min} | 0 m/s | Q | diag{1,10,1,1} |

v_{max} | 36 m/s | R | 1 |

a_{min} | −5.5 m/s^{2} | T | 50 s |

a_{max} | 2.5 m/s^{2} | - | - |

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**MDPI and ACS Style**

Zhang, S.; Zhuan, X.
Study on Adaptive Cruise Control Strategy for Battery Electric Vehicle Considering Weight Adjustment. *Symmetry* **2019**, *11*, 1516.
https://doi.org/10.3390/sym11121516

**AMA Style**

Zhang S, Zhuan X.
Study on Adaptive Cruise Control Strategy for Battery Electric Vehicle Considering Weight Adjustment. *Symmetry*. 2019; 11(12):1516.
https://doi.org/10.3390/sym11121516

**Chicago/Turabian Style**

Zhang, Sheng, and Xiangtao Zhuan.
2019. "Study on Adaptive Cruise Control Strategy for Battery Electric Vehicle Considering Weight Adjustment" *Symmetry* 11, no. 12: 1516.
https://doi.org/10.3390/sym11121516