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

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 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

- Benchaita, H.; Ladaci, S. Fractional adaptive SMC fault tolerant control against actuator failures for wing rock supervision. Aerosp. Sci. Technol.
**2021**, 114, 106745. [Google Scholar] [CrossRef] - Ynineb, A.R.; Ladaci, S. MRAC adaptive control design for an F15 aircraft pitch angular motion using Dynamics Inversion and fractional-order filtering. Int. J. Robot. Control Syst.
**2022**, 2, 240–252. [Google Scholar] [CrossRef] - Karpenko, M. Landing gear failures connected with high-pressure hoses and analysis of trends in aircraft technical problems. Aviation
**2022**, 26, 145–152. [Google Scholar] [CrossRef] - Haitao, Q.; Yongling, F.; Xiaoye, Q.; Yan, L. Architecture optimization of more electric aircraft actuation system. Chin. J. Aeronaut.
**2011**, 24, 506–513. [Google Scholar] - Goupil, P. AIRBUS state of the art and practices on FDI and FTC in flight control system. Control Eng. Pract.
**2011**, 19, 524–539. [Google Scholar] [CrossRef] - Van Den Bossche, D. The A380 flight control electrohydrostatic actuators, achievements and lessons learnt. In Proceedings of the 25th International Congress of the Aeronautical Sciences, Hamburg, Germany, 3–8 September 2006; pp. 1–8. [Google Scholar]
- Shi, C.; Wang, X.; Wang, S.; Wang, J.; Tomovic, M.M. Adaptive decoupling synchronous control of dissimilar redundant actuation system for large civil aircraft. Aerosp. Sci. Technol.
**2015**, 47, 114–124. [Google Scholar] [CrossRef] - Cochoy, O.; Hanke, S.; Carl, U.B. Concepts for position and load control for hybrid actuation in primary flight controls. Aerosp. Sci. Technol.
**2007**, 11, 194–201. [Google Scholar] [CrossRef] - Fu, J.; Maré, J.-C.; Fu, Y. Modelling and simulation of flight control electromechanical actuators with special focus on model architecting, multidisciplinary effects and power flows. Chin. J. Aeronaut.
**2017**, 30, 47–65. [Google Scholar] [CrossRef][Green Version] - Cochoy, O.; Carl, U.B.; Thielecke, F. Integration and control of electromechanical and electrohydraulic actuators in a hybrid primary flight control architecture. In Proceedings of the International Conference on Recent Advances in Aerospace Actuation Systems and Components, Insa Toulouse, France, 13–15 June 2007; pp. 1–8. [Google Scholar]
- Emadi, K.; Ehsani, M. Aircraft power systems: Technology, state of the art, and future trends. IEEE Aerosp. Electron. Syst. Mag.
**2000**, 15, 28–32. [Google Scholar] [CrossRef] - Naayagi, R. A review of more electric aircraft technology. In Proceedings of the 2013 International Conference on Energy Efficient Technologies for Sustainability, Nagercoil, India, 10–12 April 2013; pp. 750–753. [Google Scholar]
- Rosero, J.; Ortega, J.; Aldabas, E.; Romeral, L. Moving towards a more electric aircraft. IEEE Aerosp. Electron. Syst. Mag.
**2007**, 22, 3–9. [Google Scholar] [CrossRef][Green Version] - Wang, L.; Mare, J.-C. A force equalization controller for active/active redundant actuation system involving servo-hydraulic and electro-mechanical technologies. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng.
**2014**, 228, 1768–1787. [Google Scholar] [CrossRef] - Salman, I.; Lin, Y.; Hamayun, M.T. Fractional order modeling and control of dissimilar redundant actuating system used in large passenger aircraft. Chin. J. Aeronaut.
**2018**, 31, 1141–1152. [Google Scholar] - Ijaz, S.; Yan, L.; Hamayun, M.T.; Shi, C. Active fault tolerant control scheme for aircraft with dissimilar redundant actuation system subject to hydraulic failure. J. Frankl. Inst.
**2019**, 356, 1302–1332. [Google Scholar] [CrossRef] - Ijaz, S.; Hamayun, M.T.; Yan, L.; Ijaz, H.; Shi, C. Adaptive fault tolerant control of dissimilar redundant actuation system of civil aircraft based on integral sliding mode control strategy. Trans. Inst. Meas. Control
**2019**, 41, 3756–3768. [Google Scholar] [CrossRef] - Ijaz, S.; Hamayun, M.T.; Anwaar, H.; Yan, L.; Li, M.K. LPV modeling and tracking control of dissimilar redundant actuation system for civil aircraft. Int. J. Control Autom. Syst.
**2019**, 17, 705–715. [Google Scholar] [CrossRef] - Ijaz, S.; Yan, L.; Hamayun, M.T.; Baig, W.M.; Shi, C. An adaptive LPV integral sliding mode FTC of dissimilar redundant actuation system for civil aircraft. IEEE Access
**2018**, 6, 65960–65973. [Google Scholar] [CrossRef] - Cieplok, G.; Wójcik, K. Conditions for self-synchronization of inertial vibrators of vibratory conveyors in general motion. J. Theor. Appl. Mech.
**2020**, 58, 513–524. [Google Scholar] [CrossRef] - Fang, P.; Zou, M.; Peng, H.; Du, M.; Hu, G.; Hou, Y. Spatial synchronization of unbalanced rotors excited with paralleled and counterrotating motors in a far resonance system. J. Theor. Appl. Mech.
**2019**, 57, 723–738. [Google Scholar] [CrossRef] - Jacazio, G.; Gastaldi, L. Equalization techniques for dual redundant electro hydraulic servo actuators for flight control systems. Fluid Power Motion Control
**2008**, 2008, 543–557. [Google Scholar] - Qi, H.; Mare, J.-C.; Fu, Y. Force equalization in hybrid actuation systems. In Proceedings of the 7th International Conference on Fluid Power Transmission and Control, Hangzhou, China, 7–10 April 2009; pp. 342–347. [Google Scholar]
- Rehman, W.U.; Wang, S.; Wang, X.; Fan, L.; Shah, K.A. Motion synchronization in a dual redundant HA/EHA system by using a hybrid integrated intelligent control design. Chin. J. Aeronaut.
**2016**, 29, 789–798. [Google Scholar] [CrossRef][Green Version] - Waheed, U.R.; Wang, S.; Wang, X.; Kamran, A. A position synchronization control for HA/EHA system. In Proceedings of the 2015 International Conference on Fluid Power and Mechatronics (FPM), Harbin, China, 5–7 August 2015; pp. 473–482. [Google Scholar]
- Rehman, W.U.; Nawaz, H.; Wang, S.; Wang, X.; Luo, Y.; Yun, X.; Iqbal, M.N.; Zaheer, M.A.; Azhar, I.; Elahi, H. Trajectory based motion synchronization in a dissimilar redundant actuation system for a large civil aircraft. In Proceedings of the 2017 29th Chinese Control and Decision Conference (CCDC), Chongqing, China, 28–30 May 2017; pp. 5010–5015. [Google Scholar]
- Rehman, W.U.; Wang, X.; Wang, S.; Azhar, I. Motion synchronization of HA/EHA system for a large civil aircraft by using adaptive control. In Proceedings of the 2016 IEEE Chinese Guidance, Navigation and Control Conference (CGNCC), Nanjing, China, 12–14 August 2016; pp. 1486–1491. [Google Scholar]
- Rehman, W.U.; Wang, S.; Wang, X.; Shi, C.; Zhang, C.; Tomovic, M. Adaptive control for motion synchronization of HA/EHA system by using modified MIT rule. In Proceedings of the 2016 IEEE 11th Conference on Industrial Electronics and Applications (ICIEA), Hefei, China, 5–7 June 2016; pp. 2196–2201. [Google Scholar]
- Wang, X.; Liao, R.; Shi, C.; Wang, S. Linear extended state observer-based motion synchronization control for hybrid actuation system of more electric aircraft. Sensors
**2017**, 17, 2444. [Google Scholar] [CrossRef] [PubMed][Green Version] - Wang, X.; Shi, C.; Wang, S. Extended state observer-based motion synchronisation control for hybrid actuation system of large civil aircraft. Int. J. Syst. Sci.
**2017**, 48, 2212–2222. [Google Scholar] [CrossRef] - Ur Rehman, W.; Wang, X.; Cheng, Y.; Chai, H.; Hameed, Z.; Wang, X.; Saleem, F.; Lodhi, E. Motion synchronization for the SHA/EMA hybrid actuation system by using an optimization algorithm. Automatika
**2021**, 62, 503–512. [Google Scholar] [CrossRef] - Guo, L.L.; Yu, L.M.; Lu, Y.; Fan, D.L. Multi-mode switching control for HSA/EHA hybrid actuation system. In Applied Mechanics and Materials; Trans Tech Publications Ltd.: Bäch, Switzerland, 2014; pp. 1088–1093. [Google Scholar]
- Rehman, W.U.; Khan, W.; Ullah, N.; Chowdhury, M.S.; Techato, K.; Haneef, M. Nonlinear Control of Hydrostatic Thrust Bearing Using Multivariable Optimization. Mathematics
**2021**, 9, 903. [Google Scholar] [CrossRef] - Rehman, W.U.; Wang, X.; Cheng, Y.; Chen, Y.; Shahzad, H.; Chai, H.; Abbas, K.; Ullah, Z.; Kanwal, M. Model-based design approach to improve performance characteristics of hydrostatic bearing using multivariable optimization. Mathematics
**2021**, 9, 388. [Google Scholar] [CrossRef] - Wang, S.; Tomovic, M.; Liu, H. Commercial Aircraft Hydraulic Systems: Shanghai Jiao Tong University Press Aerospace Series; Academic Press: Cambridge, MA, USA, 2015. [Google Scholar]
- Wang, X.; Wang, S. Adaptive fuzzy robust control of PMSM with smooth inverse based dead-zone compensation. Int. J. Control Autom. Syst.
**2016**, 14, 378–388. [Google Scholar] [CrossRef] - Wang, L.; Maré, J.-C.; Fu, Y. Investigation in the dynamic force equalization of dissimilar redundant actuation systems operating in active/active mode. In Proceedings of the 28th International Congress of the Aeronautical Sciences ICAS 2012, Brisbane, Australia, 23–28 September 2012; p. session-6.8.1. [Google Scholar]
- Wang, L.; Mare, J.-C.; Fu, Y.; Qi, H. Force equalization for redundant active/active position control system involving dissimilar technology actuators. In Proceedings of the 8th JFPS International Symposium on Fluid Power, Okinawa, Japan, 25–26 October 2011; pp. 136–143. [Google Scholar]
- Elias, N.; Yahya, N. Simulation study for controlling direct current motor position utilising fuzzy logic controller. Int. J. Automot. Mech. Eng.
**2018**, 15, 5989–6000. [Google Scholar] [CrossRef] - Liu, X.; Wang, Y.; Wang, M. Speed Fluctuation Suppression Strategy of Servo System with Flexible Load Based on Pole Assignment Fuzzy Adaptive PID. Mathematics
**2022**, 10, 3962. [Google Scholar] [CrossRef] - Yin, H.; Yi, W.; Wu, J.; Wang, K.; Guan, J. Adaptive Fuzzy Neural Network PID Algorithm for BLDCM Speed Control System. Mathematics
**2021**, 10, 118. [Google Scholar] [CrossRef]

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 ${\mathrm{j}}_{\mathrm{cs}}$ | $6.0$ | $\mathrm{Kg}\xb7{\mathrm{m}}^{2}$ |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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