Original Manuscript Journal of Vibration and Control 2022, Vol. 0(0) 1–13 © The Author(s) 2022 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/10775463221074098 journals.sagepub.com/home/jvc Robust flight control for a quadrotor under external disturbances based on predefined-time terminal sliding mode manifold Moussa Labbadi 1 , Kamal Elyaalaoui 2 , Mohamed Amine Dabachi 3 , Soufian Lakrit 4 , Mohamed Djemai 1 , and Mohamed Cherkaoui 2 Abstract This paper investigates the terminal sliding-mode control (TSMC) with predefined-time stability (PTS) for a disturbed quadrotor system (DQS). First, for both the rotational and translational subsystems of the DQS, a novel notion of predefined-time terminal sliding-mode manifold (PTTSMM) is created. Using the proposed PTTSMM method, the DQS state variables reach their origin in a predefined-time. The influence of disturbances is taken into consideration in the design of the suggested control to show its performance. A formal analysis technique is also provided, as well as the stability of the closed-loop DQS. The performance and effectiveness of the predefined-time method proposed in this work are illustrated by numerical simulations and also comparison study with other control techniques is presented. Keywords predefined-time stability, TSMC, predefined-time terminal sliding mode, external disturbances, Lyapunov theorem 1.Introduction 1.1.Motivations and background In the last decade, the problem of tracking-trajectory of quadrotor system (QS) has been addressed by many re- searches due to various applications of this vehicle Ullah et al. (2021), including surveillance, application in aerial filming, inspection of large areas, delivery system, de- tection, agriculture, and identification of different objects. In the real flight of the QS, its dynamics involve the pa- rameters uncertainties and external disturbances, which have negatively impacted on the stabilization and the tracking performance. To solve these problems, many control methods have been developed including sliding mode control (SMC) and the advanced control approaches based on SMC and integral SMC Labbadi and Cherkaoui (2019b), nonsingular TSMC Labbadi and Cherkaoui (2020), and adaptive backstepping TSMC Labbadi and Cherkaoui (2019 (@). The SMC is robust control and has the capability of disturbance rejection. The linear sliding mode surface is used to design most of the existing SMC approaches, on which the system state variables converge to the origin asymptotic or exponentially in infinite-time Ge et al. (2020) and Liang et al. (2019). Then, to deal with this problem, the TSMC has been introduced to achieve a finite-time stability? Ghadiri et al. (2021), Su and Zheng (2020), and Eliker and Zhang (2019). The initial conditions of the state variables have a negative influence on the finite time obtained, which is increased if the value of these initial states increases. In this context, some recent works focused on fixed time stability Shao et al. (2020), Zuo (2015a, 2015b), Huang and Jia (2017). In general, fixed-time procedures outperform finite-time methods in terms of 1 University Polytechnique Hauts-de-France, INSA Hauts-de-France, LAMIH, Valenciennes, Francem 2 Engineering for Smart and Sustainable Systems Research Center, Mohammadia School of Engineers, Mohammed V University in Rabat, Rabat, Morocco 3 LMPGI, ESTC, Hassan II University of Casablanca, Casablanca, Morocco 4 AMISL, ESTof Nador, Mohammed First University Oujda, Nador, Morocco Received: 5 August 2021; revised: 23 November 2021; accepted: 26 December 2021 Corresponding author: Moussa Labbadi, University Polytechnique Hauts-de-France, INSA Hauts- de-France, LAMIH, CNRS, UMR 8201, Valenciennes 59313, Francem. Email: moussa.labbadi@uphf.fr