Observer-based fixed-time continuous nonsingular terminal sliding mode control of quadrotor aircraft under uncertainties and disturbances for robust trajectory tracking: theory and experiment

Omar Mecali, Limei Xu*, Ya Huang, Mengji Shi, Xiaomei Xie

*Corresponding author for this work

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This paper solves an accurate fixed-time attitude and position control problems of a quadrotor UAV system. The aircraft system is subject to nonlinearities, parameter uncertainties, unmodeled dynamics, and external time-varying disturbances. To deal with the under-actuation problem of the quadrotor’s dynamics, a hierarchical control structure with an inner–outer loop framework is adopted for the flight control system design. Robust nonlinear control strategies for attitude and position control are innovatively proposed based on a new continuous nonsingular terminal sliding mode control (CNTSMC) scheme. A full-order homogeneous terminal sliding surface is designed for the attitude and position states in such a way that the sliding motion is fixed-time stable independently of the system’s initial condition. Hence, this contributes to enhancing the control system robustness. A disturbance observer-based control (DOBC) approach is developed to stabilize the inner rotational subsystem (attitude-loop). This compounded control structure integrates a finite-time observer (FTO) and the CNTSMC scheme. The FTO observer is incorporated into the control framework to cope with the strong perturbations. An output-feedback control approach is adopted for the outer translational subsystem (position-loop) to ensure a velocity-free control. In this context, the CNTSMC scheme is combined with a fixed-time extended state observer (FXESO) to achieve an active disturbance rejection control (ADRC) by estimating and canceling the lumped disturbances. Therefore, within the developed control approach including the robust CNTSMC scheme, DOBC, and ADRC strategies, robust and accurate trajectory tracking control can be achieved despite uncertainties and disturbances. Stability analysis of the closed-loop system is rigorously investigated by using the Lyapunov theorem, bi-limit homogeneous theory, and the notion of input-to-state stability (ISS). Extensive experimental tests under the influence of various disturbances are conducted to corroborate the theoretical findings. To this end, an effective model-based design (MBD) framework is established to implement the developed control algorithms in real autopilot hardware. Furthermore, processor-in-the-loop (PIL) experiments are also carried out within the MBD framework. A comparative study is made involving our control algorithms and other control strategies. Overall, the obtained results show that the synthesized control system yields performance improvement regarding fixed-time tracking stability featuring fast transient, strong robustness, and high steady-state precision. Besides, the chattering effect of regular linear sliding mode control (LSMC) is significantly alleviated. Moreover, unlike conventional TSMC, the control input shows no singularity.
Original languageEnglish
Article number104806
JournalControl Engineering Practice
Early online date12 Apr 2021
Publication statusPublished - 1 Jun 2021


  • Quadrotor UAV
  • Fixed-time stability
  • Trajectory tracking control
  • continuous nonsingular terminal sliding mode control
  • Disturbance observer-based control
  • Active disturbance rejection control
  • Output-feedback control


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