# Nonlinear Modeling and Coordinate Optimization of a Semi-Active Energy Regenerative Suspension with an Electro-Hydraulic Actuator

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## Abstract

**:**

## 1. Introduction

## 2. Structure and Principle of the Semi-Active Energy Regenerative Suspension with an EHA

## 3. Nonlinear Modeling of the Semi-Active Energy Regenerative Suspension with an EHA

#### 3.1. Dynamic Model of a Two Degrees of Freedom Suspension System for a Quarter-Vehicle

#### 3.2. Parameter Identification of Nonlinear Model

#### 3.3. Mathematical Model of the Semi-Active Energy Regenerative Suspension with an EHA

## 4. The Control Strategy of the Semi-Active Energy Regenerative Suspension with an EHA

## 5. Parameter Optimization of the Semi-Active Energy Regenerative Suspension with an EHA

#### 5.1. Parameter Sensitivity Analysis

#### 5.2. Optimization Objectives and Constraints

#### 5.3. Optimization Result Analysis

#### 5.4. Test and Analysis

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The structure of the semi-active energy regenerative suspension with an electro-hydraulic actuator (EHA). DC: direct current.

**Figure 6.**Influence of the effective area of the hydraulic cylinder piston on evaluation indicators: (

**a**) Influence of the effective area of the hydraulic cylinder piston on the damping performance; (

**b**) Influence of the effective area of the hydraulic cylinder piston on energy regenerative performance.

**Figure 7.**Influence of the displacement of the hydraulic motor on evaluation indicators: (

**a**) Influence of the displacement of the hydraulic motor on the damping performance; (

**b**) Influence of the displacement of the hydraulic motor on energy regenerative performance.

**Figure 8.**Influence of the back electromotive force constant of the generator on evaluation indicators: (

**a**) Influence of the back electromotive force constant of the generator on the damping performance; (

**b**) Influence of the back electromotive force constant of the generator on energy regenerative performance.

Optimal Parameters | Symbol | Value |
---|---|---|

The effective area of the hydraulic cylinder piston | $A$ | $7.66\times {10}^{-4}$ ${\mathrm{m}}^{2}$ |

The displacement of the hydraulic motor | $q$ | 4.25 $\mathrm{mL}/\mathrm{r}$ |

The back electromotive force constant of the generator | ${k}_{e}$ | 8.28$\times {10}^{-3}$ $\mathrm{V}\cdot \mathrm{min}/\mathrm{r}$ |

Performance Index | Symbol | Value | Control Effect/% | |
---|---|---|---|---|

Before Optimization | After Optimization | |||

Sprung mass acceleration | ${\sigma}_{a}$ | 2.1585 $\mathrm{m}/{\mathrm{s}}^{2}$ | 1.7571 $\mathrm{m}/{\mathrm{s}}^{2}$ | −18.60 |

Tire dynamic load | ${\sigma}_{Fd}$ | 802.7 $\mathrm{N}$ | 701.5 $\mathrm{N}$ | −12.61 |

Energy regenerative power | ${\sigma}_{Preg}$ | 59.82 $\mathrm{W}$ | 89.53 $\mathrm{W}$ | 49.67 |

Energy regenerative efficiency | $\eta $ | 18.68$\%$ | 27.26$\%$ | 45.93 |

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**MDPI and ACS Style**

Kou, F.; Du, J.; Wang, Z.; Li, D.; Xu, J.
Nonlinear Modeling and Coordinate Optimization of a Semi-Active Energy Regenerative Suspension with an Electro-Hydraulic Actuator. *Algorithms* **2018**, *11*, 12.
https://doi.org/10.3390/a11020012

**AMA Style**

Kou F, Du J, Wang Z, Li D, Xu J.
Nonlinear Modeling and Coordinate Optimization of a Semi-Active Energy Regenerative Suspension with an Electro-Hydraulic Actuator. *Algorithms*. 2018; 11(2):12.
https://doi.org/10.3390/a11020012

**Chicago/Turabian Style**

Kou, Farong, Jiafeng Du, Zhe Wang, Dong Li, and Jianan Xu.
2018. "Nonlinear Modeling and Coordinate Optimization of a Semi-Active Energy Regenerative Suspension with an Electro-Hydraulic Actuator" *Algorithms* 11, no. 2: 12.
https://doi.org/10.3390/a11020012