# Experimental Validation of Total Energy Control System for UAVs

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{®}model is then used with a hardware-in-the-loop (HIL) simulation interface that replaces the plane and the environment with a simulator. Meanwhile, the hardware was configured exactly for flight tests connected to GCS with the simulator, rather than the aircraft. This was performed to validate flight test results and compare them to theoretical and simulated estimates.

## 2. Total Energy Control System (TECS)

#### Aircraft Energy Equations

## 3. Extended Kalman Filter Description

#### 3.1. Quaternion-Based EKF

#### 3.2. Euler-Angles-Based EKF

**Initial computation (algorithm):**

- Navigation EKF controller using a local (north, east, down (NED)) Earth frame;
- XYZ body fixed frame;
- Sequential position and velocity measurements;
- True airspeed;
- Magnetic flux measurement;
- 18-state architecture;
- IMU data;
- IMU angles and velocities are recorded with specified sample time.

**State vector:**

- Quaternions ($q0$, $q1$, $q2$, $q3$);
- Velocity—m/s (NED);
- Position—m (NED);
- Delta Angles bias—rad;
- Delta Velocities bias—m/s);
- Wind Vector—m/s (NE);
- Earth Magnetic Field—milligauss (NED)
- Body Magnetic Field —milligauss (X,Y,Z).

**Observations:**

- Velocity—m/s;
- Position—m;
- TAS—m/s;
- XYZ magnetic flux—milligauss;
- XY line of sight angular rate measurements from a downwards-looking optical flow sensor range to terrain measurements.

**Time-varying parameters:**

- Delta angle measurements in body axes—rad;
- Delta velocity measurements in body axes—m/s.

## 4. Airplane Dynamic Model

## 5. Experimental Arrangement

^{2}of wing area with an average wing load of 65 g/dm

^{2}. The power systems consisted of one brushless DC electric motor driving a $14\times 7$ in propeller, delivering about 1.4 kg of thrust. Stall speed was 9 m/s and maximum airspeed was 35 m/s.

^{®}electric servos providing a maximum ailerons deflection of 35 deg, maximum rudder deflection of 25 deg, and maximum elevator deflection of 20 deg. The properties of the airframe are shown in Table 2, and the moments of inertia were calculated using XFLR5, as shown in Figure 5 [32].

## 6. Flight Experiment and Initial Tuning

#### Flight Test

^{®}was calibrated because it only works for full control movements of pilot sticks. Manual tuning can result in better performance, but it takes more time and effort. Figure 9 shows an example of a 2-min session.

- ATRP.P is the controller P gain.
- ATRP.Achieved is what the aircraft achieved in attitude change rate.
- ATRP.Demanded is the demanded rate of attitude changes (roll rate or pitch rate) deg/s.

## 7. Telemetry Analysis and Results

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Chadli, M.; Maquin, D.; Ragot, J. Vertical Static output feedback for Takagi-Sugeno systems: An LMI approach. In Proceedings of the 10th Mediterranean Conference on Control and Automation, Lisbon, Portugal, 9–13 July 2002. [Google Scholar]
- Chadli, M.; Borne, P. Multiple Models Approach in Automation- Takagi-Sugeno Fuzzy Systems; John Wiley & Sons: London, UK, 2013; ISBN 978-1-848-21412-5. [Google Scholar]
- Mohamed, K.; Chadli, M.; Chaabane, M. Unknown Inputs Observer for a Class of Nonlinear Uncertain Systems: An LMI Approach. Int. J. Autom. Comput.
**2012**, 9, 331–336. [Google Scholar] [CrossRef] - Hassani, H.; Zarei, J.; Chadli, M.; Qiu, J. Unknown Input Observer Design for Interval Type-2 T–S Fuzzy Systems with Immeasurable Premise Variables. IEEE Trans. Cybern.
**2016**, 47, 2639–2650. [Google Scholar] [CrossRef] [PubMed] - Eure, K.; Quach, C.; Vazquez, S.; Hogge, E.; Hill, B. An Application of UAV Attitude Estimation Using a Low Cost Inertial Navigation System. NASA Tech. Rep.
**2013**, 1, 5–7. [Google Scholar] - Huang, S. Understanding Extended Kalman Filter. One Dimens. Kalman Filter
**2010**, 1, 1–9. [Google Scholar] - Chao, H.; Coopmans, C.; Di, L.; Chen, Y.U. A Comparative Evaluation of Low-Cost IMUs for Unmanned Autonomous Systems. In Proceedings of the IEEE Conference on Multisensor Fusion and Integration, Salt Lake City, UT, USA, 5–7 September 2010; Volume 1, pp. 2–4. [Google Scholar]
- Kandath, H.; Pushpangathan, J.V.; Bera, T.; Dhall, S.; Bhat, M.S. Modeling and Closed Loop Flight Testing of a Fixed Wing Micro Air Vehicle. Micromachines
**2018**, 9, 111. [Google Scholar] [CrossRef] [PubMed][Green Version] - ArduPilot Dev Team. Extended Kalman Filter Navigation Overview and Tuning. Available online: http://ardupilot.org/dev/docs/extended-kalman-filter.html (accessed on 20 December 2019).
- Qiping, C.; Mulder, B.; Choukroun, D.; Kampen, E.-J.; Visser, C.; Looye, G. Advances in Aerospace Guidance, Navigation and Control; Springer: Berlin/Heidelberg, Germany, 2013; pp. 29–40. ISBN 978-3-642-19817-5. [Google Scholar]
- Lambregts, A.A. Vertical Flight Path and Speed Control Autopilot Design Using Total Energy Principles. Aiaa Guid. Control. Conf.
**1983**, 1, 1–5. [Google Scholar] - Lambregts, A.A. Total Energy Based Flight Control System. Patent WO 1984001345, 20 August 1984. [Google Scholar]
- Faleiro, L.F.; Lambregts, A.A. Analysis and tuning of a ’Total Energy Control System’ control law using eigenstructure assignment. Aerosp. Sci. Technol.
**1999**, 3, 5–9. [Google Scholar] [CrossRef] - Kelly, J.; Person, L.; Bruce, K. Flight Testing TECS—The Total Energy Control System. In Proceedings of the SAE Aerospace Technology Conference and Exposition, Long Beach, CA, USA, 13–16 October 1986. [Google Scholar]
- Brigido-González, J.D.; Rodríguez-Cortés, H. Experimental Validation of an Adaptive Total Energy Control System Strategy for the Longitudinal Dynamics of a Fixed-Wing Aircraft. J. Aerosp. Eng.
**2015**, 29, 3–8. [Google Scholar] [CrossRef] - Jimenez, P.; Agudelo, D.; Cerpa, R.; Zuluaga, E.; Tellez, A. Diseño, análisis y validación de aeronaves no tripuladas multipropósito; Editorial Bonaventuriana: Bogota, Colombia, 2017; pp. 45–75. ISBN 978-958-8928-34-0. [Google Scholar]
- Balmer, G. Modelling and Control of a Fixed-wing UAV for Landings on Mobile Landing Platforms. Master’s Thesis, KTH Royal Institute of Technology, Stockholm, Sweden, 2015; pp. 60–71. [Google Scholar]
- Rehan, M.; Tufail, M.; Ahn, C.K.; Chadli, M. Stabilisation of locally Lipschitz non-linear systems under input saturation and quantisation. IET Control. Theory Appl.
**2017**, 11, 1459–1466. [Google Scholar] [CrossRef] - Aouaouda, S.; Chadli, M. Robust fault tolerant controller design for Takagi-Sugeno systems under input saturation. Int. J. Syst. Sci.
**2019**, 50, 1163–1178. [Google Scholar] [CrossRef] - Ferré, J. El diseño factorial completo 2
^{k}. Técnicas de Laboratorio**2004**, 292, 430–434. [Google Scholar] - Jimenez, P.; Agudelo, D. Validation and Calibration of a High-Resolution Sensor in Unmanned Aerial Vehicles for Producing Images in the IR Range Utilizable in Precision Agriculture. In Proceedings of the AIAA SciTech Forum (Infotech @ Aerospace SciTech), Kissimmee, FL, USA, 5–9 January 2015; pp. 734–749. [Google Scholar]
- Lai, Y.C.; Ting, W. Design and Implementation of an Optimal Energy Control System for Fixed-Wing Unmanned Aerial Vehicles. Appl. Sci.
**2016**, 6, 369. [Google Scholar] [CrossRef][Green Version] - Cook, M. Flight Dynamics Principles, 3rd ed.; Butterworth-Heinemann: Oxford, UK, 2013. [Google Scholar]
- Pawełek, A.; Lichota, P.; Dalmau, R.; Prats, X. Fuel-Efficient Trajectories Traffic Synchronization. J. Aircr.
**2019**, 56, 481–492. [Google Scholar] [CrossRef] - Bruce, K.R. NASA B737 Flight Test Results of the Total Energy Control System. In Proceedings of the Astrodynamics Conference, Williamsburg, VA, USA, 18–20 August 1986. [Google Scholar]
- Welch, G.; Bishop, G. An Introduction to the Kalman Filter; University of North Carolina at Chapel Hill: Chapel Hill, NC, USA, 2006. [Google Scholar]
- Jang, J.S.; Liccardo, C. Small UAV automation using MEMS. IEEE Aerosp. Electron. Syst. Mag.
**2007**, 22, 30–34. [Google Scholar] [CrossRef] - Bryan, G.; Hartley, G. Stability in aviation: An introduction to dynamical stability as applied to the motions of aeroplanes. Nature
**1912**, 88, 406–407. [Google Scholar] [CrossRef] - Lichota, P. Inclusion of the D-optimality in multisine manoeuvre design for aircraft parameter estimation. J. Theor. Appl. Mech.
**2016**, 54, 87–98. [Google Scholar] [CrossRef][Green Version] - Agudelo, D.; Lichota, P. A Priori Model Inclusion in the Multisine Maneuver Design. In Proceedings of the 17th IEEE International Carpathian Control Conference (ICCC), Tatranska Lomnica, Slovakia, 29 May–1 June 2016; pp. 440–445. [Google Scholar]
- Pamadi, B.N. Performance, Stability, Dynamics, and Control of Airplanes; American Institute of Aeronautics and Astronautics: Hampton, VA, USA, 2004; ISBN 978-156-3475-83-2. [Google Scholar]
- Segui, M.; Kuitche, M.; Botez, R. Longitudinal Aerodynamic Coefficients of Hydra Technologies UAS-S4 from Geometrical Data. In Proceedings of the AIAA Modeling and Simulation Technologies Conference, Grapevine, TX, USA, 9–13 January 2017; pp. 2–4. [Google Scholar] [CrossRef]
- Dorobantu, A.; Murch, A.; Mettler, B.; Balas, G. System Identification for Small, Low-Cost, Fixed-Wing Unmanned Aircraft. J. Aircr.
**2013**, 50, 1117–1130. [Google Scholar] [CrossRef] - Tucker, A.; Balas, G. Safety, Efficacy, and Efficiency: Design of Experiments in Flight Test. In 56th Annual Society of Experimental Test Pilots Symposium; The Society of Experimental Test Pilots: Lancaster, CA, USA, 2012; pp. 2–10. [Google Scholar]
- Hartley, R.; Hugon, F.; Anderson, R.; Moncayo, H. Development and Flight Testing of a Model Based Autopilot Library for a Low Cost Unmanned Aerial System. In Proceedings of the AIAA Guidance, Navigation, and Control (GNC) Conference, Boston, MA, USA, 19–22 August 2013; pp. 2–8. [Google Scholar]

Mode | Natural Frequency, rad/s or Time Constant, s | Damping Ratio |
---|---|---|

Phugoid | 0.3671 rad/s | 0.6142 |

Short period subsidence mode 1 | 0.0297 s | - |

Short period subsidence mode 2 | 0.0963 s | - |

Spiral | 20.8768 s | - |

Dutch roll | 4.0796 rad/s | 0.9796 |

Roll | 0.0913 s | - |

Property | Value | Unit |
---|---|---|

Mass m | 4.95 | kg |

Wing span b | 2.045 | m |

Mean aerodynamic chord $\overline{c}$ | 0.38 | m |

Wing area S | 0.76 | m^{2} |

Moment of inertia ${I}_{xx}$ | 0.3175 | kg m^{2} |

Moment of inertia ${I}_{yy}$ | 0.3493 | kg m^{2} |

Moment of inertia ${I}_{zz}$ | 0.5931 | kg m^{2} |

Moment of inertia ${I}_{xz}$ | 0.002593 | kg m^{2} |

Parameter | Value |
---|---|

Airfield location | Bogota, Colombia |

Runway altitude | 2570 m a.s.l |

Runway length | 300 m |

Runway width | 30 m |

Latitude/Longitude | 4.8240903 deg/−74.1560519 deg |

Runway heading | 314°–134° |

Parameter | Symbol | Unit |
---|---|---|

Time | t | s |

Relative altitude | h | m |

Airspeed | ${V}_{a}$ | m/s |

Ground speed | ${V}_{g}$ | m/s |

Wind speed | ${V}_{w}$ | m/s |

Wind direction | B | deg |

Vertical speed | ${V}_{\nu}$ | m/s |

Battery remaining | ${B}_{R}$ | % |

Battery voltage | ${V}_{B}$ | V |

Roll angle | $\varphi $ | deg |

Yaw angle | $psi$ | deg |

Pitch angle | $\theta $ | deg |

Roll rate | p | deg/s |

Yaw rate | r | deg/s |

Pitch rate | q | deg/s |

Throttle position | ${T}_{P}$ | % |

Elevator servo | $PWM$ | ms |

© 2019 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jimenez, P.; Lichota, P.; Agudelo, D.; Rogowski, K. Experimental Validation of Total Energy Control System for UAVs. *Energies* **2020**, *13*, 14.
https://doi.org/10.3390/en13010014

**AMA Style**

Jimenez P, Lichota P, Agudelo D, Rogowski K. Experimental Validation of Total Energy Control System for UAVs. *Energies*. 2020; 13(1):14.
https://doi.org/10.3390/en13010014

**Chicago/Turabian Style**

Jimenez, Pedro, Piotr Lichota, Daniel Agudelo, and Krzysztof Rogowski. 2020. "Experimental Validation of Total Energy Control System for UAVs" *Energies* 13, no. 1: 14.
https://doi.org/10.3390/en13010014