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**Characteristic analyzes, experimental testing and control for attitude system of QUAV under disturbance.**
*(English)*
Zbl 1481.70097

Summary: The disturbance influences the dynamic characteristics of the quadrotor unmanned aerial vehicle (QUAV), especially the stability. With the disturbance, the study of characteristics and controller design is challenging. In this paper, an attitude system of a QUAV with disturbance and gyroscopic effect is developed. The disturbed QUAV attitude system dynamics influenced by the rotor speeds are analyzed via multi-parameter bifurcation diagrams. The chaotic parameter area in which the QUAV is in an abnormal vibration state is plotted, guiding the design of the fuselage structure and controller of the QUAV. The transient chaos characterizing chaos within a long period but eventually becoming periodic is found in the system. The chaotic phenomenon of the angular velocity trajectory of the QUAV is verified by obtaining the positive Lyapunov exponent using the experimental data. A back-stepping sliding mode controller is designed, and the stability of the closed system is proved via the Lyapunov method. Numerical simulations verify the effectiveness of controlling the QUAV. The designed controller is effective for suppressing chaos. The stability of the back-stepping sliding mode controller is superior to that of the PID controller is verified via numerical simulations.

### Keywords:

QUAV attitude system; disturbance; bifurcation; transient chaos; back-stepping sliding mode controller; chaos existence using experimental data### Software:

LYAPROSEN
Full Text:
DOI

### References:

[1] | Niemiec, R.; Gandhi, F.; Singh, R., Control and performance of a reconfigurable multicopter, J. Aircr., 55, 5, 1855-1866 (2018) |

[2] | Wang, L., Aerodynamic optimization of a micro quadrotor aircraft with different rotor spacings in hover, Appl. Sci., 10, 4, 1272 (2020), -1-12 |

[3] | Cabecinhas, D.; Cunha, R.; Silvestre, C., A nonlinear quadrotor trajectory tracking controller with disturbance rejection, Control Eng. Pract., 26, 1-10 (2014) |

[4] | Ivan, G.; Munoz, P. F.; Salazar, C. S., Real-time altitude control for a quadrotor helicopter using based on high-order sliding mode observer, Int. J. Adv. Robot Syst., 14, 1, 1-15 (2017) |

[5] | Tian, B.; Cui, J.; Lu, H., Adaptive finite-time attitude tracking of quadrotors with experiments and comparisons, IEEE Trans. Ind. Electron. (2019) |

[6] | Liu, Y.; Chen, C.; Wu, H., Structural stability analysis and optimization of the quadrotor unmanned aerial vehicles via the concept of Lyapunov exponents, Int. J. Adv. Manuf. Technol., 94, 4, 1-11 (2018) |

[7] | Bi, H.; Qi, G.; Hu, J., Modeling and analysis of chaos and bifurcations for the attitude system of a quadrotor unmanned aerial vehicle, Complexity, 2019, Article 6313925-1-17 (2019) |

[8] | Singh, J. P.; Roy, B. K.; Kuznetsov, N. V., Multistability and hidden attractors in the dynamics of permanent magnet synchronous motor, Int. J. Bifurc. Chaos, 29, 04, Article 1950056 pp. (2019), -1-17 · Zbl 1416.34043 |

[9] | Faradja, P.; Qi, G., Analysis of multistability, hidden chaos and transient chaos in brushless DC motor, Chaos Soliton. Fract., 132, Article 109606 pp. (2020), -1-10 |

[10] | Bi, H.; Qi, G.; Hu, J., Hidden and transient chaotic attractors in the attitude system of quadrotor unmanned aerial vehicle, Chaos Soliton. Frac., 138, Article 109815 pp. (2020), -1-10 |

[11] | Lin, H.; Wang, C.; Tan, Y., Hidden extreme multistability with hyperchaos and transient chaos in a hopfield neural network affected by electromagnetic radiation, Nonlinear Dynamics, 99, 2369-2386 (2020) |

[12] | Godara, P.; Dudkowski, D.; Prasad, A., New topological tool for multistable dynamical systems, Chaos, 28, 11, Article 111101 pp. (2018), -1-6 · Zbl 1403.65266 |

[13] | Liu, Y.; Li, X.; Wang, T., Quantitative stability of quadrotor unmanned aerial vehicles, Nonlinear Dyn., 87, 3, 1819-1833 (2017) |

[14] | Shapour, M., Lyaprosen: Matlab Function to Calculate Lyapunov Exponent (2009), University of Tehran: University of Tehran Iran |

[15] | Sun, Y.; Wu, C., Stability analysis via the concept of Lyapunov exponents: a case study in optimal controlled biped standing, Int. J. Control, 85, 12, 1952-1966 (2012) · Zbl 1253.93098 |

[16] | Ge, Z.; Lin, G., The complete, lag and anticipated synchronization of a BLDCM chaotic system, Chaos Soliton. Fractals, 34, 3, 740-764 (2007) |

[17] | Zribi, M.; Oteafy, A.; Smsoui, N., Controlling chaos in the permanent magnet synchronous motor, Chaos Soliton. Fractals, 41, 3, 1266-1276 (2009) |

[18] | Faramin, M., Chaotic attitude analysis of a satellite via Lyapunov exponents and its robust nonlinear control subject to disturbances and uncertainties, Nonlinear Dyn., 83, 1-2, 361-374 (2016) · Zbl 1349.34245 |

[19] | Iñarrea, M., Chaos and its control in the pitch motion of an asymmetric magnetic spacecraft in polar elliptic orbit, Chaos Soliton. Fractals, 40, 4, 1637-1652 (2009) · Zbl 1198.70016 |

[20] | Farivara, F.; Shoorehdeli, M. A., Fault tolerant synchronization of chaotic heavy symmetric gyroscope systems versus external disturbances via Lyapunov rule-based fuzzy control, ISA Trans., 51, 1, 50-64 (2012) |

[21] | Choi, J. J.; Han, S. I.; Kim, J. S., Development of a novel dynamic friction model and precise tracking control using adaptive back-stepping sliding mode controller, Mechatronics, 16, 2, 97-104 (2006) |

[22] | Xia, Y.; Zhu, Z.; Fu, M., Back-stepping sliding mode control for missile systems based on an extended state observer, IET Control Theory A, 5, 1, 93-102 (2011) |

[23] | Chen, F.; Jiang, R.; Zhang, K., Robust back-stepping sliding-mode control and observer-based fault estimation for a quadrotor UAV, IEEE Trans. Ind. Electron., 63, 8, 5044-5056 (2016) |

[24] | Ioannou, P. A.; Fidan, B., Adaptive Control Tutorial (2006), Society for Industrial and Aapplied Mathematics: Society for Industrial and Aapplied Mathematics Philadelphia · Zbl 1116.93001 |

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