Abstract
In this paper, a finite-time controller is proposed for the quadrotor aircraft to achieve hovering control in a finite time. The design of controller is mainly divided into two steps. Firstly, a saturated finite-time position controller is designed such that the position of quadrotor aircraft can reach any desired position in a finite time. Secondly, a finite-time attitude tracking controller is designed, which can guarantee that the attitude of quadrotor aircraft converges to the desired attitude in a finite time. By homogenous system theory and Lyapunov theory, the finite-time stability of the closed-loop systems is given through rigorous mathematical proofs. Finally, numerical simulations are given to show that the proposed algorithm has a faster convergence performance and a stronger disturbance rejection performance by comparing to the PD control algorithm.
Similar content being viewed by others
References
Zhao, B., Xian, B., Zhang, Y., Zhang, X.: Nonlinear robust adaptive tracking control of a quadrotor UAV via immersion and invariance methodology. IEEE Trans. Ind. Electron. 62(5), 2891–2902 (2015)
Liu, M., Egan, G.K., Santoso, F.: Modeling, autopilot design, and field tuning of a UAV with minimum control surfaces. IEEE Trans. Control Syst. Technol. 23(6), 2353–2360 (2015)
Lim, H., Park, J., Lee, D., Kim, H.J.: Build your own quadrotor: open-source projects on unmanned aerial vehicles. IEEE Robot. Autom. Mag. 19(3), 33–45 (2012)
Hamel, T., Mahony, R., Lozano, R., Ostrowski, J.: Dynamic modelling and configuration stabilization for an X4 Flyer. IFAC Trienn. World Congr. 35(1), 217–222 (2002)
Yin, C., Cheng, Y., Zhong, S.: Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems. Automatica 50(12), 3173–3181 (2014)
Yin, C., Starkb, B., Chen, Y., Zhong, S., Lau, E.: Fractional-order adaptive minimum energy cognitive lighting control strategy for the hybrid lighting system. Energy Build. 87, 176–184 (2015)
Yin, C., Cheng, Y., Chen, Y., Stark, B., Zhong, S.: Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems. Nonlinear Dyn. 82(1), 39–52 (2015)
Xiong, J., Zheng, E.: Position and attitude tracking control for a quadrotor UAV. ISA Trans. 53(3), 725–731 (2014)
Khalil, H.K.: Nonlinear System, 3rd edn. Prentice hall, Upper Saddle River (2002). 303–334
Xu, R., Ozguner, U.: Sliding mode control of a class of underactuated systems. Automatica 44(1), 233–241 (2008)
Zuo, Z., Ru, P.: Augmented L1 adaptive tracking control of quad-Rotor unmanned aircrafts. IEEE Trans. Aerosp. Electron. Syst. 50(4), 3090–3100 (2014)
Liu, H., Li, D.J., Zuo, Z.Y., Zhong, Y.S.: Robust three-loop trajectory tracking control for quadrotors with multiple uncertainties. IEEE Trans. Ind. Electron. 63(4), 2263–2273 (2016)
Yu, Y., Li, B., Hu, Q.: Quaternion-based output feedback attitude control for rigid spacecraft with bounded input constraint. In: The 34th Chinese Control Conference, pp. 489–493 (2015)
Guerrero-Castellanos, J.F., Marchand, N., Hably, A., Lesecq, S., Delamare, J.: Attitude control of rigid bodies: real-time experimentation to a quadrotor mini-helicopter. Control Eng. Pract. 19(8), 790–797 (2011)
Liu, H., Wang, X., Zhong, Y.: Quaternion-based robust attitude control for uncertain robotic quadrotors. IEEE Trans. Ind. Inform. 11(2), 406–415 (2015)
Bhat, S., Bernstein, D.: Finite-time stability of homogeneous systems. Am. Control Conf. 4(4), 2513–2514 (1997)
Shen, Y., Huang, Y., Gu, J.: Global finite-time observers for Lipschitz nonlinear systems. IEEE Trans. Autom. Control 56(2), 418–424 (2011)
Shen, Y., Huang, Y.: Uniformly observable and globally Lipschitzian nonlinear systems admit global finite-time observers. IEEE Trans. Autom. Control 54(11), 2621–2625 (2009)
Shen, Y., Xia, X.: Semi global finite time observers for nonlinear systems. Automatica 44(12), 3152–3156 (2008)
Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)
Li, S., Du, H., Lin, X.: Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica 47(8), 1706–1712 (2011)
Li, S., Liu, H., Ding, S.: A speed control for a PMSM using finite-time feedback control and disturbance compensation. Trans. Inst. Meas. Control 32(2), 170–187 (2010)
Li, S., Zhou, M., Yu, X.: Design and implementation of terminal sliding mode control method for PMSM speed regulation system. IEEE Trans. Ind. Inform. 9(4), 1879–1891 (2013)
Yang, X., Wu, Z., Cao, J.: Finite-time synchronization of complex networks with nonidentical discontinuous nodes. Nonlinear Dyn. 73(4), 2313–2327 (2013)
Sun, H., Li, S., Sun, C.: Finite time integral sliding mode control of hypersonic vehicles. Nonlinear Dyn. 73(1–2), 229–244 (2013)
Frye, M.T., Ding, S., Qian, C., Li, S.: Fast convergent observer design for output feedback stabilisation of a planar vertical takeoff and landing aircraft. IET Control Theory Appl. 4(4), 690–700 (2010)
Zavala-Rio, A., Fantoni, I., Sanahuja, G.: Finite-time observer-based output-feedback control for the global stabilisation of the PVTOL aircraft with bounded inputs. Int. J. Syst. Sci. 47(7), 1543–1562 (2016)
Zhang, C., Li, S., Ding, S.: Finite-time output feedback stabilization and control for a quadrotor mini-aircraft. Kybernetika 48(2), 206–222 (2012)
Abdelhamid, T., Stephen, M.: Attitude stabilization of a VTOL quadrotor aircraft. IEEE Trans. Control Syst. Technol. 14(3), 562–571 (2006)
Shuster, M.D.: A survey of attitude representations. J. Astronaut. Sci. 41(4), 439–517 (1993)
Hughes, P.: Spacecraft Attitude Dynamics. Wiley, Hoboken (1986)
Xia, Y., Zhu, Z., Fu, M., Wang, S.: Attitude tracking of rigid spacecraft with bounded disturbances. IEEE Trans. Ind. Electron. 58(2), 647–659 (2011)
Islam, S., Liu, P., Saddik, A.E.: Robust control of four-rotor unmanned aerial vehicle with disturbance uncertainty. IEEE Trans. Ind. Electron. 62(3), 1563–1571 (2015)
Liu, H., Xi, J., Zhong, Y.: Robust motion control of quadrotors. J. Frankl. Inst. 351(12), 5494–5510 (2014)
Qian, C., Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Autom. Control 46(7), 1061–1079 (2001)
Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1952)
Liao, W., Zong, Q., Ma, Y.: Moedling and finite-time control for quadrotor mini unmanned aerial vehicles. J. Control Theory Appl. 32(10), 1343–1350 (2015)
Li, S., Ding, S., Tian, Y.: A finite-time state feedback stabilization method for a class of second order nonlinear systems. Acta Autom. Sin. 33(1), 101–104 (2007)
Zavala-Rio, A., Fantoni, I.: Global finite-time stability characterized through a local notion of homogeneity. IEEE Trans. Autom. Control 59(2), 471–477 (2014)
Hong, Y., Xu, Y., Huang, J.: Finite-time control for robot manipulators. Syst. Control Lett. 46(4), 185–200 (2002)
Bhat, S.P., Bernstein, D.S.: A topological obstruction to continuous global stabilizationof rotational motion and the unwinding phenomenon. Syst. Control Lett. 39(1), 63–70 (2000)
Jin, E., Sun, Z.: Robust controllers design with finite time convergence for rigid spacecraft attitude tracking control. Aerosp. Sci. Technol. 12(4), 324–330 (2008)
Acknowledgements
This work was supported by National Natural Science Foundation of China (61673153,61304007,) the Scientific Research and Development Funds of Hefei University of Technology (JZ2016HGXJ0023), and the Fundamental Research Funds for the Central Universities (JZ2016HGTA0700).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhu, W., Du, H., Cheng, Y. et al. Hovering control for quadrotor aircraft based on finite-time control algorithm. Nonlinear Dyn 88, 2359–2369 (2017). https://doi.org/10.1007/s11071-017-3382-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-017-3382-8