# Optimal Control Strategy for Parallel Plug-in Hybrid Electric Vehicles Based on Dynamic Programming

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## Abstract

**:**

## 1. Introduction

## 2. Parallel Hybrid System Modeling

#### 2.1. Powertrain Structure

#### 2.2. Key Component Models

#### 2.2.1. Battery Model

#### 2.2.2. Engine Model

#### 2.2.3. Motor Model

#### 2.2.4. Transmission Model

#### 2.2.5. Vehicle Model

#### 2.3. Controller Model

## 3. Control Strategy Based on the Dynamic Programming Algorithm

#### 3.1. Dynamic Programming Theory

#### 3.2. Control Strategy

#### 3.3. Control Process Command

#### 3.4. Dynamic Programming Algorithm Results Analysis

#### 3.5. Strategy Extraction Based on Dynamic Programming Algorithm Results

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

${V}_{bat\_out}$ | Battery terminal voltage |

${R}_{bat}$ | Battery equivalent internal resistance |

${V}_{bat\_oc}$ | Open circuit voltage |

C | Capacity of the electricity (A·h) |

$\alpha $ | Engine throttle |

${T}_{eng}$ | Torque output of the engine (N·m) |

$\stackrel{\u2022}{{V}_{fuel}}$ | Instantaneous fuel consumption |

${T}_{mot}$ | Actual output torque of the motor |

${n}_{mot}$ | Motor speed (r/min) |

${T}_{out}$ | Gearbox output torque (N∙m) |

${n}_{in}$ | Gearbox input shaft speed (r/min) |

F | Driving force |

$s$ | Oil-electricity equivalent factor |

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**Figure 2.**Relationship between open circuit voltage/internal resistance and the SOC of a single cell.

**Figure 3.**Engine torque and fuel consumption map. (

**a**) Engine torque map. (

**b**) Engine fuel consumption map.

**Figure 11.**Battery SOC and battery output current as a function of time. (

**a**) Battery SOC. (

**b**) Battery output current.

**Figure 12.**Comparison of torque and speed between engine and motor. (

**a**) Engine and motor torque. (

**b**) Engine and motor speed.

**Figure 15.**Relationship between the clutch’s position and the gear with time. (

**a**) Gear. (

**b**) Clutch’s position.

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**MDPI and ACS Style**

Tian, Y.; Liu, J.; Yao, Q.; Liu, K.
Optimal Control Strategy for Parallel Plug-in Hybrid Electric Vehicles Based on Dynamic Programming. *World Electr. Veh. J.* **2021**, *12*, 85.
https://doi.org/10.3390/wevj12020085

**AMA Style**

Tian Y, Liu J, Yao Q, Liu K.
Optimal Control Strategy for Parallel Plug-in Hybrid Electric Vehicles Based on Dynamic Programming. *World Electric Vehicle Journal*. 2021; 12(2):85.
https://doi.org/10.3390/wevj12020085

**Chicago/Turabian Style**

Tian, Ying, Jiaqi Liu, Qiangqiang Yao, and Kai Liu.
2021. "Optimal Control Strategy for Parallel Plug-in Hybrid Electric Vehicles Based on Dynamic Programming" *World Electric Vehicle Journal* 12, no. 2: 85.
https://doi.org/10.3390/wevj12020085