This paper presents a fixed-time observer-based sliding mode control strategy for trajectory tracking of magnetic levitation systems. The strategy utilizes a novel fixed-time observer to estimate unmeasurable states and compensate for uncertainties and external disturbances. An adaptive mechanism is introduced, eliminating the need for prior knowledge of the lumped disturbances. To ensure rapid convergence of the sliding mode surface, a fixed-time variable exponent reaching law based on the arctan function is proposed. Building on the observer and reaching law, a fixed-time sliding mode controller is designed to guarantee fast convergence and avoid singularity issues. Lyapunov theory is used to rigorously prove the stability of the closed-loop system. Simulation results confirm the effectiveness and robustness of the proposed method.
ElbukenCKhameseeMBYavuzM.Design and implementation of a micromanipulation system using a magnetically levitated mems robot. IEEE/ASME Trans Mechatron2009; 14(4): 434–445.
2.
ZhouHDengHDuanJ.Hybrid fuzzy decoupling control for a precision maglev motion system. IEEE/ASME Trans Mechatron2018; 23(1): 389–401.
3.
ZhuQWangSMNiYQ.A review of levitation control methods for low- and medium-speed maglev systems. Buildings2024; 14(3): 837.
4.
WangJJiangQWangH.Generalized disturbance estimation based continuous integral terminal sliding mode control for magnetic levitation systems. IEEE Trans Autom Sci Eng2025; 22: 1725–1737.
5.
AVSSS. Design of sliding mode controller for magnetic levitation system. Comput Electr Eng2019; 78: 184–203.
6.
VoATTruongTNKangH, et al. A fixed-time sliding mode control for uncertain magnetic levitation systems with prescribed performance and anti-saturation input. Eng Appl Artif Intell2024; 133: 108373.
7.
ZongGXieHYangD, et al. Adaptive fuzzy tracking control for switched nonlinear systems under fdi attacks and input saturation: a flexible transient performance approach. IEEE Trans Cybern2024; 54(12): 7479–7488.
8.
QiWWangYZongG, et al. Adaptive protocol-based control for nonhomogeneous stochastic jump systems with dos attacks and applications. IEEE Trans Circuits Syst I Regul Pap2024; 71(9): 4274–4283.
9.
ChangZZongGSongS, et al. Fast finite-time bipartite formation with obstacle avoidance for time-delay multiagent systems: application in mobile robot swarm. IEEE Trans Ind Inform2025; 21: 4586–4594.
10.
SuXXuYYangX.Neural network adaptive sliding mode control without overestimation for a maglev system. Mech Syst Signal Process2022; 168: 108661.
11.
ZongGWangYNiuB, et al. Event-triggered adaptive NN tracking control for nonlinear systems with asymmetric time-varying output constraints and application to an AUVs. IEEE Trans Vehicular Technol2025; 74(1): 413–424.
12.
ZhuPZhangTZhouD, et al. Research on magnetic levitation control method under elastic track conditions based on backstepping method. Mathematics2024; 12(13): 2134.
13.
FridmanLMorenoJIriarteR, et al. Sliding modes after the first decade of the 21st century. Springer, New York, NY, 2011. Vol. 412.
14.
ZouQChangS.A new fixed-time terminal sliding mode control for second-order nonlinear systems. J Franklin Inst2024; 361(3): 1255–1267.
15.
WangJZhaoLYuL.Adaptive terminal sliding mode control for magnetic levitation systems with enhanced disturbance compensation. IEEE Trans Ind Electron2021; 68(1): 756–766.
16.
MoulayELechappeVBernuauE, et al. Robust fixed-time stability: application to sliding-mode control. IEEE Trans Automat Contr2022; 67(2): 1061–1066.
17.
YangJYangCZhangX, et al. Fixed-time sliding mode control with varying exponent coefficient for modular reconfigurable flight arrays. IEEE/CAA J Automat Sin2024; 11(2): 514–528.
18.
WangYZongG.Dynamic event-triggered adaptive fixed-time practical tracking control for nonlinear systems through funnel function. IEEE Trans Autom Sci Eng2025; 22: 7008–7017.
19.
WangYZongGZhaoX, et al. Adaptive practical fixed-time synchronized tracking control of ASV with prescribed performance. Automatica2024; 166: 111716.
20.
LuYSBerkelmanP.Design and evaluation of state and disturbance observers for a multivariable magnetic levitation system. IETE J Res2023; 69(1): 420–437.
21.
WangJRongJYangJ.Adaptive fixed-time position precision control for magnetic levitation systems. IEEE Trans Autom Sci Eng2023; 20(1): 458–469.
22.
DongardiveAMManeHRChileRH, et al. Design of super twisting disturbance observer-based controller for magnetic levitation system. Int J Dyn Control2023; 11(3): 1190–1202.
23.
TruongTNVoATKangHJ. Real-time implementation of the prescribed performance tracking control for magnetic levitation systems. Sensors2022; 22(23): Article no. 9132.
24.
BidikliB.An observer-based adaptive control design for the maglev system. Trans Inst Meas Contr2020; 42(14): 2771–2786.
25.
TanCPYuXManZ.Terminal sliding mode observers for a class of nonlinear systems. Automatica2010; 46(8): 1401–1404.
26.
DongardiveAMChileRHHamdeST.Advanced control strategy for magnetic levitation system: a higher order sliding mode observer approach. Int J Dyn Control2024; 12(7): 2498–2510.
27.
PolyakovA.Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Automat Contr2012; 57(8): 2106–2110.
28.
PolycarpouMM.Stable adaptive neural control scheme for nonlinear systems. IEEE Trans Automat Contr1996; 41(3): 447–451.
29.
GuoGZhangQ.Adaptive prescribed-time sliding mode control of nonlinear systems with unknown dynamics. Int J Syst Sci2024; 55(13): 2771–2779.
30.
ZuoZ.Non-singular fixed-time terminal sliding mode control of non-linear systems. IET Control Theory Appl2015; 9(4): 545–552.
31.
LiuZZhangOGaoY, et al. Adaptive neural network-based fixed-time control for trajectory tracking of robotic systems. IEEE Trans Circuits Syst II Express Briefs2023; 70(1): 241–245.
32.
ChuZMengFZhuD, et al. Fault reconstruction using a terminal sliding mode observer for a class of second-order mimo uncertain nonlinear systems. ISA Trans2020; 97: 67–75.
