# Fuzzy Logic-Based Control for a Morphing Wing Tip Actuation System: Design, Numerical Simulation, and Wind Tunnel Experimental Testing

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## Abstract

**:**

## 1. Introduction

_{2}emission, fuel optimization, and weight reduction of the aircraft. To achieve this target, aircraft manufacturers are focusing on the development of the MEA technology [27].

## 2. Short Description of the Morphing Wing Project

## 3. Physical Architecture and Simulink Model of the Controlled Actuator

## 4. The Control System Design and Numerical Validation Results

^{4}, 5 × 10

^{4}] interval as universe of discourse its second input, six membership functions (mf) were chosen for each of the two inputs (${A}_{1}^{1}$ to ${A}_{1}^{6}$, respectively, ${A}_{2}^{1}$ to ${A}_{2}^{6}$). The linguistic terms for both inputs, but also for the output, were NB (negative big), NM (negative medium), NS (negative small), PS (positive small), PM (positive medium), and PB (positive big). The considered shapes for the first input membership functions were z-functions (mf1), π-functions (mf2 to mf5, respectively), and s-functions (mf6), whereas for the second input membership functions shapes was a triangular one.

^{4}, 1.5 × 10

^{4}] interval as universe of discourse for its second input. This time, seven membership functions (mf) were chosen for each of the two inputs of the FIS, while, from the linguistic terms point of view, for both inputs, but also for the output, a new one has been added (Z (zero)) comparatively with the “PositionFIS”. The considered shapes for the both inputs membership functions were z-functions (mf1), π-functions (mf2 to mf6), respectively s-functions (mf7).

_{m}

_{1}, x

_{m}

_{2}] middle interval. x is the independent variable on the universe of discourse, x

_{left}is the left breakpoint, and x

_{right}is the right breakpoint [22]. In the other way, the triangular shape can be expressed as follows [34]

_{1}, x

_{2}) is a crisp function in the consequent, and f is a polynomial function [34,35]. If f is a constant, then the Sugeno fuzzy model is a zero-order model. Considering [−3000, 3000] interval as universe of discourse for the “PositionFIS” output and a zero-order Sugeno fuzzy model, the output mf were chosen as constants with the values: NB = −3000, NM = −2500, NS = −1000, PS = 1000, PM = 2500, and PB = 3000. Also, for the output of the “SpeedFIS”, the [−120, 120] interval was used as universe of discourse, and the mf resulted with the values NB = −120, NM = −60, NS = −30, Z = 0, PS = 30, PM = 60, and PB = 120, whereas for the “CurrentFIS” output, the [−1.5, 1.5] interval was used as universe of discourse, and the mf resulted with the values N = −1.5, Z = 0, and P = 1.5.

## 5. Wind Tunnel Experimental Testing of the Wing-Aileron Morphing System

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A, B | fuzzy sets in the antecedent |

${A}_{i}^{j}$ | inputs’ membership functions |

a, c | parameters locating the feet of the triangle in triangular membership functions |

b | parameter giving the peak of the triangle in triangular membership functions |

f | polynomial function |

K_c | change in output gain in current control loop |

K_p | change in output gain in position control loop |

K_s | change in output gain in speed control loop |

Kd_p | derivative gain in position control loop |

Kd_s | derivative gain in speed control loop |

Ki_c | integral gain in current control loop |

Ki_s | integral gain in speed control loop |

Kp_c | proportional gain in current control loop |

Kp_p | proportional gain in position control loop |

Kp_s | proportional gain in speed control loop |

M | Mach number |

s | s-function shaped membership function |

x | the independent variable on the universe of discourse |

x_{left} | the left breakpoint |

x_{mi} | parameters delimitating the middle interval for a π -function |

x_{right} | the right breakpoint |

y | crisp function in the consequent |

z | z-function shaped membership function |

BLDC | Brushless Direct Current |

FIS | Fuzzy Inference System |

FFT | Fast Fourier Transform |

GUI | Graphic User Interface |

IR | Infrared |

MEA | More Electrical Aircraft |

mf | membership function |

N | negative |

NB | negative big |

NM | negative medium |

NS | negative small |

P | positive |

PB | positive big |

PD | Proportional-Derivative |

PI | Proportional-Integral |

PID | Proportional-Integral-Derivative |

PM | positive medium |

PS | positive small |

SMA | Shape Memory Alloy |

STD | Standard Deviation |

Z | zero |

α | angle of attack |

δ | aileron deflection angle |

π | π-function shaped membership function |

## References

- NOvel Air VEhicle Configurations: From Fluttering Wings to MORphing Flight (NOVEMOR), Grant Agreement ID: 285395, Programme FP7-TRANSPORT—Specific Programme “Cooperation”: Transport (Including Aeronautics). Available online: https://cordis.europa.eu/project/rcn/99991/factsheet/en (accessed on 25 July 2019).
- Smart Intelligent Aircraft Structures (SARISTU), Grant Agreement ID: 284562, Programme FP7-TRANSPORT—Specific Programme “Cooperation”: Transport (Including Aeronautics). Available online: https://cordis.europa.eu/project/rcn/100047/factsheet/en (accessed on 25 July 2019).
- Wings of the future (FUTUREWINGS), Grant agreement ID: 335042, Programme FP7-TRANSPORT—Specific Programme “Cooperation”: Transport (Including Aeronautics). Available online: https://cordis.europa.eu/project/rcn/109751/factsheet/en (accessed on 25 July 2019).
- Leading Edge Actuation Topology Design and Demonstration (LeaTop), Grant Agreement ID: 271861, Programme FP7-JTI—Specific Programme “Cooperation”: Joint Technology Initiatives. Available online: https://cordis.europa.eu/project/rcn/102033/factsheet/en (accessed on 25 July 2019).
- Kota, S.; Osborn, R.; Ervin, G.; Maric, D.; Flick, P.; Paul, D. Mission adaptive compliant wing—Design, fabrication and flight test. In Proceedings of the RTO-MP-AVT-168, NATO AVT-168 Morphing Vehicles Symposium, Evora, Portugal, 20–23 April 2009; pp. 1–19. [Google Scholar]
- Ameduri, S.; Brindisi, A.; Tiseo, B.; Concilio, A.; Pecora, R. Optimization and integration of shape memory alloy (SMA)-based elastic actuators within a morphing flap architecture. J. Intell. Mater. Syst. Struct.
**2012**, 23, 381–396. [Google Scholar] [CrossRef] - Barbarino, S.; Pecora, R.; Lecce, L.; Concilio, A.; Ameduri, S.; De Rosa, L. Airfoil structural morphing based on S.M.A. actuator series: Numerical and experimental studies. J. Intell. Mater. Syst. Struct.
**2011**, 22, 987–1004. [Google Scholar] [CrossRef] - Peel, L.D.; Mejia, J.; Narvaez, B.; Thomson, K.; Lingala, M. Development of a simple morphing wing using elastomeric composites as skins and actuators. In Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, Ellicott City, MD, USA, 28–30 October 2008. [Google Scholar]
- Larco, C.; Constatin, L.; Demșa, M.; Mustata, S. Wing lift-drag ratio optimization. In Proceedings of the 20th Edition of the International Conference Scientific Research and Education in the Air Force (AFASES 2018), Brasov, Romania, 25–27 May 2018; pp. 191–196. [Google Scholar]
- Pahonie, R.C.; Larco, C.; Mihaila Andres, M.; Nastasescu, V.; Barbu, C.; Costuleanu, C.L. Experimental characterisation of hyperelastic materials for use in a passive-adaptive membrane on MAVs wing. Mater. Plast.
**2017**, 54, 768–772. [Google Scholar] - Pahonie, R.C.; Mihai, R.V.; Larco, C. Towards Flexible-Winged Unmanned Aircraft Systems. In Proceedings of the International Conference of Aerospace Sciences “AEROSPATIAL 2014”, Bucharest, Romania, 18–19 September 2014. [Google Scholar]
- Larco, C. Analyse des instabilités dans l’écoulement transsonique. In Proceedings of the International Symposium Research and Education in an Innovation Era—Engineering Sciences, Arad, Romania, 20–21 November 2008. [Google Scholar]
- Wereley, N.M.; Kothera, C.; Bubert, E.; Woods, B.; Gentry, M.; Vocke, R. Pneumatic artificial muscles for aerospace applications. In Proceedings of the 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Palm Springs, CA, USA, 4–7 May 2009. [Google Scholar]
- Kudva, J.N. Overview of the DARPA Smart Wing Project. J. Intell. Mater. Syst. Struct.
**2004**, 15, 261–267. [Google Scholar] [CrossRef] - Martinez, J.M.; Scopelliti, D.; Bil, C.; Carrese, R.; Marzocca, P.; Cestino, E.; Frulla, G. Design, analysis and experimental testing of a morphing wing. In Proceedings of the 25th AIAA/AHS Adaptive Structures Conference, Grapevine, TX, USA, 9–13 January 2017. [Google Scholar]
- Kumar, D.; Faruque Ali, S.; Arockiarajan, A. Structural and aerodynamics studies on various wing configurations for morphing. In Proceedings of the 5th IFAC Conference on Advances in Control and Optimization of Dynamical Systems ACODS 2018, Hyderabad, India, 18–22 February 2018. [Google Scholar]
- Yokozeki, T.; Sugiura, A.; Hirano, Y. Development of variable camber morphing airfoil using corrugated structure. J. Aircr.
**2014**, 51, 1023–1029. [Google Scholar] [CrossRef] - Liauzun, C.; Le Bihan, D.; David, J.-M.; Joly, D.; Paluch, B. Study of morphing winglet concepts aimed at improving load control and the aeroelastic behavior of civil transport aircraft. Aerosp. J.
**2018**, 14, 1–16. [Google Scholar] [CrossRef] - Popov, A.V.; Grigorie, T.L.; Botez, R.M.; Mamou, M.; Mebarki, Y. Real time morphing wing optimization validation using wind-tunnel tests. J. Aircr.
**2010**, 47, 1346–1355. [Google Scholar] [CrossRef] - Popov, A.V.; Grigorie, T.L.; Botez, R.M.; Mébarki, Y.; Mamou, M. Modeling and testing of a morphing wing in open-loop architecture. J. Aircr.
**2010**, 47, 917–923. [Google Scholar] [CrossRef] - Grigorie, T.L.; Botez, R.M.; Popov, A.V. How the Airfoil shape of a morphing wing is actuated and controlled in a smart way. J. Aerosp. Eng.
**2015**, 28, 4014043. [Google Scholar] [CrossRef] - Grigorie, T.L.; Popov, A.V.; Botez, R.M.; Mamou, M.; Mebarki, Y. A new morphing wing mechanism using smart actuators controlled by a self-tuning fuzzy logic controller. In Proceedings of the 11th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference, Virginia Beach, VA, USA, 20–22 September 2011; pp. 1–12. [Google Scholar]
- Grigorie, T.L.; Popov, A.V.; Botez, R.M. Control strategies for an experimental morphing wing model. In Proceedings of the AIAA Atmospheric Flight Mechanics Conference, Atlanta, GA, USA, 16–18 June 2014; pp. 1–12. [Google Scholar]
- Popov, A.V.; Grigorie, T.L.; Botez, R.M.; Mamou, M.; Mebarki, Y. Closed-loop control validation of a morphing wing using wind tunnel tests. J. Aircr.
**2010**, 47, 1309–1317. [Google Scholar] [CrossRef] - Wheeler, P.W.; Clare, J.C.; Trentin, A.; Bozhko, S. An overview of the more electrical aircraft. Proc. Inst. Mech. Eng. G J. Aerosp. Eng.
**2013**, 227, 578–585. [Google Scholar] [CrossRef] - Madonna, V.; Giangrande, P.; Galea, M. Electrical Power Generation in Aircraft: Review, Challenges, and Opportunities. IEEE Trans. Transp. Electrif.
**2018**, 4, 646–659. [Google Scholar] [CrossRef] - Sun, J.; Guan, Q.; Yanju, L.; Leng, J. Morphing aircraft based on smart materials and structures: A state-of-the-art review. J. Intell. Mater. Syst. Struct.
**2016**, 27, 2289–2312. [Google Scholar] [CrossRef] - Koreanschi, A.; Sugar-Gabor, O.; Botez, R.M. Drag optimization of a wing equipped with a morphing upper surface. Aeronaut. J.
**2016**, 120, 473–493. [Google Scholar] [CrossRef] - Amendola, G.; Dimino, I.; Magnifico, M.; Pecora, R. Distributed actuation concepts for a morphing aileron device. Aeronaut. J.
**2016**, 120, 1365–1385. [Google Scholar] [CrossRef] - Arena, M.; Amoroso, F.; Pecora, R.; Amendola, G.; Dimino, I.; Concilio, A. Numerical and experimental validation of a full scale servo-actuated morphing aileron model. Smart Mater. Struct.
**2018**, 27, 105034. [Google Scholar] [CrossRef] - Choosing Between Brush and Brushless DC Motors—Allied Motion Technologies Inc. Available online: https://www.alliedmotion.com/wp-content/uploads/whitepapers/Choosing-Between-Brush-Brushless-Motors-201801.pdf (accessed on 26 July 2019).
- Maxon Motor Inc. Available online: http://www.maxonmotor.com/maxon/view/content/index (accessed on 26 July 2019).
- Khan, S.; Botez, R.M.; Grigorie, T.L. A new method for tuning PI gains for position control of BLDC motor based wing morphing actuators. In Proceedings of the AIAA Modeling and Simulation Technologies Conference, Dallas, TX, USA, 22–26 June 2015. [Google Scholar]
- Grigorie, T.L.; Popov, A.V.; Botez, R.M.; Mamou, M.; Mebarki, Y. An intelligent controller based fuzzy logic techniques for a morphing wing actuation system using shape memory alloy. In Proceedings of the 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Denver, CO, USA, 4–7 April 2011. [Google Scholar]
- Mahfouf, M.; Linkens, D.A.; Kandiah, S. Fuzzy Takagi-Sugeno Kang model predictive control for process engineering. In Proceedings of the IEE Workshop on Model Predictive Control: Techniques and Applications, London, UK, 29 April 1999. [Google Scholar]

**Figure 3.**The wing on the bench test at Ecole de Technologie Supérieure (ETS) during 1g structural static test.

**Figure 5.**The morphing actuator: (

**a**) piston, (

**b**) piston housing, (

**c**) LVDT sensor, (

**d**) actuator coupling with wing skin, and (

**e**) principle of rotary to linear conversion.

**Figure 8.**Structures of the controllers used in the three loops: (

**a**) position, (

**b**) speed, and (

**c**) current.

**Figure 10.**Membership functions for the FISs inputs: (

**a**) PositionFIS, (

**b**) SpeedFIS, and (

**c**) CurrentFIS.

**Figure 12.**The fuzzy control surfaces for the three FISs: (

**a**) PositionFIS, (

**b**) SpeedFIS, and (

**c**) CurrentFIS.

**Figure 13.**The control results for a step input as desired position: (

**a**) position, (

**b**) speed, and (

**c**) current.

**Figure 14.**Control for successive steps signal as desired position: (

**a**) position, (

**b**) speed, and (

**c**) current.

**Figure 16.**Morphing wing-aileron experimental model in the Institute for Aerospace Research of the National Research Council Canada (IAR-NRC) wind tunnel testing room.

**Figure 17.**Actuators real-time monitoring for the M = 0.2, α = 2°, and δ = 4° flow case with the wing morphed.

**Figure 18.**Fast Fourier transform (FFT) results for the wing un-morphed configuration in M = 0.2, α = 2°, and δ = 4° flow conditions.

**Figure 19.**FFT results for the wing morphed configuration in M = 0.2, α = 2°, and δ = 4° flow conditions.

**Table 1.**Parameters of the mf for the “PositionFIS” first input and for the “CurrentFIS” both inputs.

PositionFIS/Input1 | CurrentFIS/Input1 | CurrentFIS/Input2 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Param. | mf1 | mf2 | mf3 | mf4 | mf5 | mf6 | mf1 | mf2 | mf1 | mf2 |

x_{left} | −4 | −4 | −3 | −1 | 0 | 2 | −3 | −2.4 | −0.01 | −0.008 |

x_{m}_{1} | −2 | −1 | 1 | 2 | ||||||

x_{m}_{2} | −2 | −1 | 1 | 2 | ||||||

x_{right} | −2 | 0 | 1 | 3 | 4 | 4 | 2.4 | 3 | 0.008 | 0.01 |

SpeedFIS/Input1 | SpeedFIS/Input2 | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Param. | mf1 | mf2 | mf3 | mf4 | mf5 | mf6 | mf7 | mf1 | mf2 | mf3 | mf4 | mf5 | mf6 | mf7 |

x_{left} | −150 | −150 | −100 | −50 | 0 | 50 | 100 | −1.5 × 10^{4} | −1.5 × 10^{4} | −1 × 10^{4} | −5 × 10^{3} | 0 | 5 × 10^{3} | 1 × 10^{4} |

x_{m}_{1} | −100 | −50 | 0 | 50 | 100 | −1 × 10^{4} | −5 × 10^{3} | 0 | 5 × 10^{3} | 1 × 10^{4} | ||||

x_{m}_{2} | −100 | −50 | 0 | 50 | 100 | −1 × 10^{4} | −5 × 10^{3} | 0 | 5 × 10^{3} | 1 × 10^{4} | ||||

x_{right} | −100 | −50 | 0 | 50 | 100 | 150 | 150 | −1 × 10^{4} | −5 × 10^{3} | 0 | 5 × 10^{3} | 1 × 10^{4} | 1.5 × 10^{4} | 1.5 × 10^{4} |

PositionFIS/Input2 | ||||||
---|---|---|---|---|---|---|

Param. | mf1 | mf2 | mf3 | mf4 | mf5 | mf6 |

a | −7 × 10^{4} | −5 × 10^{4} | −3 × 10^{4} | −1 × 10^{4} | 1 × 10^{4} | 3 × 10^{4} |

b | −5 × 10^{4} | −3 × 10^{4} | −1 × 10^{4} | 1 × 10^{4} | 3 × 10^{4} | 5 × 10^{4} |

c | −3 × 10^{4} | −1 × 10^{4} | 1 × 10^{4} | 3 × 10^{4} | 5 × 10^{4} | 7 × 10^{4} |

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**MDPI and ACS Style**

Khan, S.; Grigorie, T.L.; Botez, R.M.; Mamou, M.; Mébarki, Y. Fuzzy Logic-Based Control for a Morphing Wing Tip Actuation System: Design, Numerical Simulation, and Wind Tunnel Experimental Testing. *Biomimetics* **2019**, *4*, 65.
https://doi.org/10.3390/biomimetics4040065

**AMA Style**

Khan S, Grigorie TL, Botez RM, Mamou M, Mébarki Y. Fuzzy Logic-Based Control for a Morphing Wing Tip Actuation System: Design, Numerical Simulation, and Wind Tunnel Experimental Testing. *Biomimetics*. 2019; 4(4):65.
https://doi.org/10.3390/biomimetics4040065

**Chicago/Turabian Style**

Khan, Shehryar, Teodor Lucian Grigorie, Ruxandra Mihaela Botez, Mahmoud Mamou, and Youssef Mébarki. 2019. "Fuzzy Logic-Based Control for a Morphing Wing Tip Actuation System: Design, Numerical Simulation, and Wind Tunnel Experimental Testing" *Biomimetics* 4, no. 4: 65.
https://doi.org/10.3390/biomimetics4040065