# Getting Started with PEAs-Based Flapping-Wing Mechanisms for Micro Aerial Systems

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## Abstract

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## 1. Introduction

## 2. Piezoelectric Actuators Description

#### 2.1. PEA Principle

#### 2.2. PEA Linear Modeling

#### 2.3. PEA Nonlinear Modeling

#### 2.4. PEA Control

## 3. Aerodynamics of Basic Flapping-Wing Systems

## 4. Current PEA-Based for Flapping-Wing MAVs

## 5. Concluding Remarks and Open Questions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**A piezoelecric cantilevered actuator. (

**a**) Isometric scheme depicting the PEA’s piezolayers; (

**b**) Side view of a PEA; (

**c**) bending displacement resulting as a result of the application of an input voltage u.

**Figure 3.**Displacement control of a PEA actuator. (

**a**) Charge control considering that relationship of the PEA’s carge and displacement are linear; (

**b**) Feedfoward control structure via an hysteresis/creep compensator; (

**c**) Feedback control structure based on the displacement error.

**Figure 6.**(

**a**) Current Micromechanical Flying Insect (MFI) design (4DOF); (

**b**) Flying Insect Thorax [57].

**Figure 7.**Conceptual design of the Penn State flapping system (

**left**), four winged piezoelectric flapping system device (

**right**) [2].

**Figure 10.**Perspective Piezowing: the PEA actuates directly to flap microrobot’s wing. The flapping angle and wing’s lift attitude respectively stand for ${\gamma}_{f}$ and ${\gamma}_{r}$. The latter angle is generated by a PEA-based joint located at Piezowing’s base.

**Table 1.**List of main characteristics between the different prototypes of Micro Aerial Vehicles (MAVs) and Nano Air Vehicles (NAVs).

Model | Size | Actuator | Control | Beat Frequency | Lift/Thrust Generated | Other Features |
---|---|---|---|---|---|---|

[57] | 25 mm (wingtip to wingtip) | Unimorph piezoelectric bending actuators | Feedback Control | 275 Hz | L: 1400 µN | Piezoelectric actuator stiffness 400 N/m. |

[58] | 30 mm wingspan | Bimorph piezoelectric clamped-free bending cantilever | Adaptive Control | 120 Hz | T > 1.3 mN | 80 mg FW using Smart Composite Microstructures (SCM) process |

[2] | 37.5 mm wingspan | Piezoelectric T-beams | - | 25.5 Hz | T: 1.34 mN | - |

[60] | 90 mm wingspan | Piezoelectric THUNDER TH-8R | - | 125 Hz | L: 5.35 mN | - |

[61] | - | Bimorph Piezoelectric and a Functionally Modified Bimorph (FMB) | - | 21 Hz | L: 10 mN | Flapping angle of 45 |

[62,63,64] | - | Unimorph Piezoceramic, Lightweight Piezocomposite actuator (LIPCA) | - | 17 Hz | - | Flapping angle of 92 |

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**MDPI and ACS Style**

Durán, J.C.; Escareno, J.A.; Etcheverry, G.; Rakotondrabe, M.
Getting Started with PEAs-Based Flapping-Wing Mechanisms for Micro Aerial Systems. *Actuators* **2016**, *5*, 14.
https://doi.org/10.3390/act5020014

**AMA Style**

Durán JC, Escareno JA, Etcheverry G, Rakotondrabe M.
Getting Started with PEAs-Based Flapping-Wing Mechanisms for Micro Aerial Systems. *Actuators*. 2016; 5(2):14.
https://doi.org/10.3390/act5020014

**Chicago/Turabian Style**

Durán, J. Carlos, Juan Antonio Escareno, Gibran Etcheverry, and Micky Rakotondrabe.
2016. "Getting Started with PEAs-Based Flapping-Wing Mechanisms for Micro Aerial Systems" *Actuators* 5, no. 2: 14.
https://doi.org/10.3390/act5020014