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Quadcopter nonsingular finite-time adaptive robust saturated command-filtered control system under the presence of uncertainties and input saturation

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Abstract

The nonsingular finite-time adaptive robust saturated command-filtered control problem for quadcopter unmanned aerial vehicles is investigated in this paper. Firstly, an adaptive robust command-filtered control, based on backstepping command-filtered and nonsingular fast terminal sliding mode control, is developed. Secondly, the parametric and nonparametric uncertainties are estimated by using a small number of adaptive laws. Also, a projector function is used to ensure the estimation of quadcopter parameters within an admissible set. Thirdly, error compensating signals are employed to tackle the undesirable effect of command filters. Finally, saturation compensator signals are developed to deal with the adverse effect of saturation in the system. The proposed control strategy can cope with the “explosion of complexity” and “singularity” problems. In addition, it can alleviate the chattering phenomenon and satisfy practical finite-time stability. The numerical simulation results and comparison display the effectiveness of the proposed technique over the other control methods.

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Abbreviations

\(\phi ,\theta ,\psi \) :

Angles of roll, pitch, and heading in earth-fixed frame (EFF), respectively (rad)

p, q, r :

Rotational velocities of roll, pitch, and heading in body-fixed frame (BFF), respectively (\(\hbox {rad}\,\hbox {s}^{-1}\))

\(I_{x},I_{y},I_{z}\) :

Inertia moments of roll, pitch, and yaw, respectively (\(\hbox {kg}\,\hbox {m}^{2}\))

\(u_{\phi }, u_{\theta },u_{\psi }\) :

Aerodynamic moments of roll, pitch, and heading, respectively (\(\hbox {N} \,\hbox {m}\))

\(C_\mathrm{D}\) :

Drag coefficient (\(\hbox {kg}\,\hbox {m}^{2}\))

l :

Distance between the axis of the propeller and quadcopter center mass (m)

x, y, z :

Positions of longitudinal, lateral, and vertical in EFF, respectively (m)

\(u_{z}\) :

Lift force (N)

\(C_\mathrm{L}\) :

Lift coefficient (\(\hbox {kg}\,\hbox {m}\))

m :

Mass (kg)

g :

Gravity acceleration (\(\hbox {m}\,\hbox {s}^{-2}\))

\(\omega _{\underline{j}}\) :

Rotor speed, \(\underline{j} = \left\{ 1,2,3,4 \right\} \) (\(\hbox {rad}\,\hbox {s}^{-1}\))

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Acknowledgements

This paper is partly supported by the National Science Foundation of China (61473183, U1509211, 61627810) and National Key R&D Program of China (2017YFE0128500). We would like to express our gratitude to ELIKER Bahij, OUELDKHERROUBI Zahia, and ZOUAD Nafissa for their support, comments, and helpful feedbacks for drafting this paper.

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Authors and Affiliations

  1. Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, China

    Karam Eliker & Weidong Zhang

  2. Electrical Engineering Department, University M’Hamed Bougara of Boumerdes, 35000, Boumerdes, Algeria

    Said Grouni

  3. Control Engineering Department, Ecole Nationale Polytechnique, 16200, El-Harrach, Algeria

    Karam Eliker & Mohamed Tadjine

  4. Peng Cheng Laboratory, Shenzhen, China

    Weidong Zhang

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  1. Karam Eliker
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Eliker, K., Grouni, S., Tadjine, M. et al. Quadcopter nonsingular finite-time adaptive robust saturated command-filtered control system under the presence of uncertainties and input saturation. Nonlinear Dyn 104, 1363–1387 (2021). https://doi.org/10.1007/s11071-021-06332-3

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