# Port-Hamiltonian Modeling and IDA-PBC Control of an IPMC-Actuated Flexible Beam

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## Abstract

**:**

## 1. Introduction

## 2. Port-Hamiltonian Formulation for IPMC Actuated Flexible Beam

#### 2.1. Flexible Beam with Distributed Control

#### 2.2. The IPMC Actuator Model

**Remark**

**1.**

## 3. Control Design via IDA-PBC

#### 3.1. Ida-Pbc Control Method

#### 3.2. Control Design

**Remark**

**2.**

**Remark**

**3.**

## 4. Control Validation by Experimentation and Simulation

#### 4.1. Control of a Single IPMC-Actuated Flexible Beam

#### 4.2. Multi-Actuation of a Flexible Beam

## 5. Conclusion and Perspectives

## Author Contributions

## Funding

## Conflicts of Interest

## References

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L | Length | $1.6\times {10}^{-1}$ m |
---|---|---|

W | Width | $7\times {10}^{-3}$ m |

T | Thickness | $2.2\times {10}^{-4}$ m |

$\rho $ | Mass density | 936 kg$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m${}^{3}$ |

I | Inertia moment of area | $4.7\times {10}^{-15}$ m${}^{4}$ |

${I}_{\rho}$ | Angular moment of inertia | $4.34\times {10}^{-12}$ kg$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{2}$ |

E | Young’s modulus | $4.14\times {10}^{9}$ Pa |

K | shear modulus | $1.418\times {10}^{9}$ Pa |

${R}_{t}$ | Traversal viscous fraction | $2\times {10}^{5}$ kg$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m${}^{3}$/s |

${R}_{r}$ | Angular viscous fraction | $1\times {10}^{5}$ kg$\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}$m/s |

C | Capacitance | $5.8\times {10}^{-2}$ F |

${r}_{1}$ | Resistance ${r}_{1}$ | 29.75 $\mathsf{\Omega}$ |

${r}_{2}$ | Resistance ${r}_{2}$ | 700 $\mathsf{\Omega}$ |

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**MDPI and ACS Style**

Zhou, W.; Wu, Y.; Hu, H.; Li, Y.; Wang, Y. Port-Hamiltonian Modeling and IDA-PBC Control of an IPMC-Actuated Flexible Beam. *Actuators* **2021**, *10*, 236.
https://doi.org/10.3390/act10090236

**AMA Style**

Zhou W, Wu Y, Hu H, Li Y, Wang Y. Port-Hamiltonian Modeling and IDA-PBC Control of an IPMC-Actuated Flexible Beam. *Actuators*. 2021; 10(9):236.
https://doi.org/10.3390/act10090236

**Chicago/Turabian Style**

Zhou, Weijun, Yongxin Wu, Haiqiang Hu, Yanjun Li, and Yu Wang. 2021. "Port-Hamiltonian Modeling and IDA-PBC Control of an IPMC-Actuated Flexible Beam" *Actuators* 10, no. 9: 236.
https://doi.org/10.3390/act10090236