# Motion Synchronization Control for a Large Civil Aircraft’s Hybrid Actuation System Using Fuzzy Logic-Based Control Techniques

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## Abstract

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## 1. Introduction

## 2. Problem Description

## 3. Mathematical Model of Hybrid Actuation System (HAS)

#### 3.1. Modelling of Aircraft’s Control Surface

#### 3.2. Mathematical Model of SHA

#### 3.3. Mathematical Model of EMA

## 4. Nested-Loop Intelligent Control Strategy

_{tr}is the reference position, ${\dot{X}}_{\mathrm{tr}}$ is the reference velocity, and ${\ddot{X}}_{\mathrm{tr}}$ is the reference acceleration signal. ${u}_{1}$ and ${u}_{2}$ are position controller’s output of the SHA and the EMA, respectively. ${u}_{11}$ and ${u}_{21}$ are the outputs of the force controller for the SHA and the EMA, respectively.

#### 4.1. Trajectory Generator

- ${\omega}_{tr}$ = Reference natural frequency
- ${\xi}_{tr}$ = Reference damping factor
- ${x}_{r}$ = Reference input signal

#### 4.2. Position Controller

#### 4.3. Force Controller

## 5. Result and Discussion

#### 5.1. Results with Step Signal as Input Command

#### 5.2. Results with Dynamic Signal as Input Command

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Parameters in Membership Function | Membership Function | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{e}}_{\mathbf{p}}$ | ${\dot{\mathit{e}}}_{\mathbf{p}}$ | ${\mathit{K}}_{\mathbf{p}}^{\prime}$$,{\mathit{K}}_{\mathbf{i}}^{\prime}$$,{\mathit{K}}_{\mathit{d}}^{\prime}$ | |||||||||||||

NB | NS | ZE | PS | PB | NB | NS | ZE | PS | PB | S | MS | M | MB | B | |

a_{r} | −15 | −10 | −5 | 0 | 5 | −75 | −50 | −25 | 0 | 25 | 0.1 | 0.15 | 0.30 | 0.5 | 0.7 |

b_{r} | −10 | −5 | 0 | 5 | 10 | −50 | −25 | 0 | 25 | 50 | 0.15 | 0.3 | 0.5 | 0.7 | 1 |

c_{r} | −5 | 0 | 5 | 10 | 15 | −25 | 0 | 25 | 50 | 75 | 0.3 | 0.5 | 0.7 | 1 | 1.15 |

Parameters in Membership Function | Membership Function | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{e}}_{\mathbf{f}}$ | ${\dot{\mathit{e}}}_{\mathbf{f}}$ | ${\mathit{K}}_{\mathbf{ph}}^{\prime},{\mathit{K}}_{\mathbf{ih}}^{\prime},{\mathit{K}}_{\mathbf{dh}}^{\prime},{\mathit{K}}_{\mathbf{im}}^{\prime},{\mathit{K}}_{\mathbf{dm}}^{\prime}$ | ${\mathit{K}}_{\mathbf{pm}}^{\prime}$ | |||||||||||||||||

NB | NS | ZE | PS | PB | NB | NS | ZE | PS | PB | S | MS | M | MB | B | S | MS | M | MB | B | |

a_{r} | −100 | −10 | −5 | 0 | 5 | −100 | −8 | −4 | 0 | 4 | 0.1 | 0.15 | 0.3 | 0.5 | 0.7 | 0.87 | 0.90 | 0.92 | 0.95 | 0.97 |

b_{r} | −10 | −5 | 0 | 5 | 10 | −8 | −4 | 0 | 4 | 8 | 0.15 | 0.3 | 0.5 | 0.7 | 1 | 0.90 | 0.92 | 0.95 | 0.97 | 1 |

c_{r} | −5 | 0 | 5 | 10 | 100 | −4 | 0 | 4 | 8 | 100 | 0.3 | 0.5 | 0.7 | 1 | 1.15 | 0.92 | 0.95 | 0.97 | 1 | 1.15 |

SHA/EMA Parts | Parameters | Values | Units | ||
---|---|---|---|---|---|

Servo-hydraulic Actuator (SHA) | Gain Coefficient ${\mathrm{k}}_{\mathrm{sv}}$ | $3.04\times {10}^{-4}$ | $\mathrm{m}/\mathrm{A}$ | ||

Flow /opening gain ${\mathrm{k}}_{\mathrm{sq}}$ | $2.7$ | ${\mathrm{m}}^{2}/\mathrm{s}$ | |||

Flow / pressure gain ${\mathrm{k}}_{\mathrm{sc}}$ | $1.75\times {10}^{-11}$ | $\left({\mathrm{m}}^{3}/\mathrm{s}\right)\mathrm{Pa}$ | |||

Area of Piston ${\mathrm{A}}_{\mathrm{j}}$ | $1.1\times {10}^{-3}$ | ${\mathrm{m}}^{2}$ | |||

Cylinder chamber volume ${\mathrm{v}}_{\mathrm{j}}$ | $1.1\times {10}^{-4}$ | ${\mathrm{m}}^{3}$ | |||

Mass of piston including chamber ${\mathrm{m}}_{\mathrm{j}}$ | $25$ | $\mathrm{Kg}$ | |||

Damping constant ${\mathrm{B}}_{\mathrm{j}}$ | $1\times {10}^{4}$ | $\mathrm{N}\xb7\mathrm{s}/\mathrm{m}$ | |||

Bulk modulus constant ${\mathrm{E}}_{\mathrm{j}}$ | $8\times {10}^{8}$ | $\mathrm{Pa}$ | |||

Coefficient of Leakage ${\mathrm{k}}_{\mathrm{ac}}$ | $1\times {10}^{-11}$ | $\left({\mathrm{m}}^{3}/\mathrm{s}\right)\mathrm{Pa}$ | |||

Electro-mechanical Actuator (EMA) | Bake emf constant ${\mathrm{k}}_{\mathrm{m}}$ | $0.161$ | $\mathrm{V}/\left(\mathrm{rad}/\mathrm{s}\right)$ | ||

Armature Inductance ${\mathrm{L}}_{\mathrm{m}}$ | $4.13\times {10}^{-3}$ | $\mathrm{H}$ | |||

Armature resistance ${\mathrm{R}}_{\mathrm{m}}$ | $0.54$ | $\mathsf{\Omega}$ | |||

Electro-magnetic coefficient ${\mathrm{k}}_{\mathrm{bm}}$ | $0.64$ | $\mathrm{Nm}/\mathrm{A}$ | |||

Total inertia of rotating parts ${\mathrm{j}}_{\mathrm{m}}$ | $1.136\times {10}^{-3}$ | $\mathrm{Kg}\xb7{\mathrm{m}}^{2}$ | |||

Damping coefficient ${\mathrm{B}}_{\mathrm{m}}$ | $4\times {10}^{-3}$ | $\mathrm{Nm}\xb7\mathrm{s}/\mathrm{rad}$ | |||

Transmission coefficient ${\mathrm{k}}_{\mathrm{gm}}$ | $1.256\times {10}^{3}$ | $\mathrm{rad}/\mathrm{m}$ | |||

Transmission efficiency ${\mathsf{\eta}}_{\mathrm{m}}$ | $0.9$ | ||||

Control Surface | Connection stiffness | SHA | ${\mathrm{k}}_{\mathrm{s}}$ | $1\times {10}^{8}$ | $\mathrm{N}/\mathrm{m}$ |

EMA | ${\mathrm{k}}_{\mathrm{m}}$ | ||||

Radial distance for control surface ${\mathrm{r}}_{\mathrm{cs}}$ | $0.1$ | $\mathrm{m}$ | |||

Moment of inertia for control surface ${\mathrm{j}}_{\mathrm{cs}}$ | $6.0$ | $\mathrm{Kg}\xb7{\mathrm{m}}^{2}$ |

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**MDPI and ACS Style**

Ur Rehman, W.; Wang, X.; Hameed, Z.; Gul, M.Y.
Motion Synchronization Control for a Large Civil Aircraft’s Hybrid Actuation System Using Fuzzy Logic-Based Control Techniques. *Mathematics* **2023**, *11*, 1576.
https://doi.org/10.3390/math11071576

**AMA Style**

Ur Rehman W, Wang X, Hameed Z, Gul MY.
Motion Synchronization Control for a Large Civil Aircraft’s Hybrid Actuation System Using Fuzzy Logic-Based Control Techniques. *Mathematics*. 2023; 11(7):1576.
https://doi.org/10.3390/math11071576

**Chicago/Turabian Style**

Ur Rehman, Waheed, Xingjian Wang, Zeeshan Hameed, and Muhammad Yasir Gul.
2023. "Motion Synchronization Control for a Large Civil Aircraft’s Hybrid Actuation System Using Fuzzy Logic-Based Control Techniques" *Mathematics* 11, no. 7: 1576.
https://doi.org/10.3390/math11071576