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Fixed-time nonlinear homogeneous sliding mode approach for robust tracking control of multirotor aircraft: Experimental validation

Mechali, Omar; Xu, Limei; Xie, Xiaomei; Iqbal, Jamshed


Omar Mechali

Limei Xu

Xiaomei Xie


This paper presents a robust scheme for fixed-time tracking control of a multirotor system. The aircraft is subjected to matched lumped disturbances, i.e., unmodeled dynamics, parameters uncertainties, and external perturbations besides measurement noise. Firstly, a novel Nonlinear Homogeneous Continuous Terminal Sliding Manifold (NHCTSM) based on the weighted homogeneity theory is presented. The sliding manifold is designed with prescribed dynamics featuring Global Asymptotic Stability (GAS) and fixed-time convergence. Then, a novel Fixed-time Non-switching Homogeneous Nonsingular Terminal Sliding Mode Control (FNHNTSMC) is proposed for the position and attitude loops by employing the developed NHCTSM and an appropriate reaching law. Moreover, the control framework incorporates a disturbance observer to feedforward and compensate for the disturbances. The designed control scheme can drive the states of the system to the desired references in fixed-time irrespective of the values of the Initial Conditions (ICs). Since the existing works on homogeneous controllers rely on the bi-limit homogeneity concept in the convergence proofs, the estimate of the settling-time or its upper-bound cannot be given explicitly. In contrast, this study employs Lyapunov Quadratic Function (LQF) and Algebraic Lyapunov Equation (ALE) in the stability analysis of both controller and observer. Following this method, an expression of the upper-bound of the settling-time is explicitly derived. Furthermore, to assure the Uniform Ultimate Boundedness (UUB) of all signals in the feedback system, the dynamics of the observer and controller are jointly analyzed. Simulations and experiments are conducted to quantify the control performance. The proposed approach achieves superior performance compared with recent literature on fixed-time/finite-time control and a commercially available PID controller. The comparative results witness that the developed control scheme improves the convergence-time, accuracy, and robustness while overcoming the singularity issue and mitigating the chattering effect of conventional SMC.


Mechali, O., Xu, L., Xie, X., & Iqbal, J. (2022). Fixed-time nonlinear homogeneous sliding mode approach for robust tracking control of multirotor aircraft: Experimental validation. Journal of The Franklin Institute, 359(5), 1971-2029.

Journal Article Type Article
Acceptance Date Jan 12, 2022
Online Publication Date Jan 31, 2022
Publication Date 2022-03
Deposit Date Jan 25, 2022
Publicly Available Date Feb 1, 2023
Journal Journal of the Franklin Institute
Print ISSN 0016-0032
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 359
Issue 5
Pages 1971-2029
Keywords Quadrotor aircraft; Trajectory tracking control; Fixed-time stability; Bounded settling-time; Weighted homogeneity; Nonsingular terminal sliding mode control; Real-time experiment
Public URL


Accepted manuscript (3.4 Mb)

Copyright Statement
© 2022. This manuscript version is made available under the CC-BY-NC-ND 4.0 license

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