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

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

Abstract

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.

Citation

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. https://doi.org/10.1016/j.jfranklin.2022.01.010

• 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
• DOI: https://doi.org/10.1016/j.jfranklin.2022.01.010
• Keywords: Quadrotor aircraft; Trajectory tracking control; Fixed-time stability; Bounded settling-time; Weighted homogeneity; Nonsingular terminal sliding mode control; Real-time experiment
• Public URL: https://hull-repository.worktribe.com/output/3916764