In this work, we present a robust dynamic sliding mode controller (DSMC) for the position tracking and attitude stabilization of a quadrotor. The proposed controller overcomes the problem of chattering in classical sliding mode control while preserving the advantages of conventional sliding surfaces. The mathematical model of the quadrotor is decomposed into a fully actuated, and an under-actuated subsystem, and DSMC is designed for each of them. The proposed controller is observed to give a high precision robust tracking performance for up to 80% inertial uncertainties present in the plant model. The stability of the overall non-linear system is proved using Lyapunov theory. Finally, simulation results are presented to test the efficacy of the control allocation in the presence of external disturbances.
TayebiAMcGilvrayS. Attitude stabilization of a VTOL quadrotor aircraft. IEEE Trans Control Syst Technol2006; 14(3): 562–571.
2.
BouabdallahSMurrieriPSiegwartR. Design and control of an indoor micro quadrotor. In: IEEE International Conference on Robotics and Automation, 2004 Proceedings ICRA’04 2004. Piscataway: IEEE, 2004, pp. 4393–4398.
3.
NicolCMacnabCJBRamirez-SerranoA. Robust adaptive control of a quadrotor helicopter. Mechatronics2011; 21(6): 927–938.
4.
HuiLLiJ. Terminal sliding mode control for spacecraft formation flying. IEEE Trans Aero Electron Syst2009; 45(3): 835–846.
5.
CutlerMUreNKMichiniB, et al. Comparison of fixed and variable pitch actuators for agile quadrotors. AIAA guidance, navigation, and control conference. Portland, Oregon: AIAA, 2011, p. 6406.
6.
SinghPGiriDKGhoshAK. Robust sliding mode augmenting integral backstepping for lateral-directional control of a highly maneuverable aircraft. Proc Inst Mech Eng G J Aerosp Eng2023; 237(10): 2428–2441.
7.
SinghPSalahuddenGDKGhoshAK. Attitude control of hansa-3 aircraft with perturbation using sliding-mode controller. In: IEEE Aerospace Conference Proceedings. Washington, D.C.: IEEE Computer Society, 2022.
8.
UtkinV. Sliding modes in control and optimization. Berlin: Springer Science & Business Media, 2013.
EbrahimiNOzgoliSRamezaniA. Model-free sliding mode control, theory and application. Proc IME J Syst Control Eng2018; 232(10): 1292–1301.
11.
XuRÖzgünerÜ. Sliding mode control of a class of underactuated systems. Automatica2008; 44(1): 233–241.
12.
WangNSuSFHanM, et al.Backpropagating constraints-based trajectory tracking control of a quadrotor with constrained actuator dynamics and complex unknowns. IEEE Trans Syst Man Cybern Syst2019; 49(7): 1322–1337.
13.
WangNDengQXieG, et al.Hybrid finite-time trajectory tracking control of a quadrotor. ISA Trans2019; 90: 278–286.
14.
ZhengEHXiongJJLuoJL. Second order sliding mode control for a quadrotor UAV. ISA Trans2014; 53(4): 1350–1356.
15.
BartoliniGFerraraAUsaiE. Chattering avoidance by second-order sliding mode control. IEEE Trans Automat Control1998; 43(2): 241–246.
16.
KoshkoueiAJBurnhamKJZinoberASI. Dynamic sliding mode control design. IEE Proc Control Theor Appl2005; 152(4): 392–396.
17.
VenkataramanSTGulatiS. Terminal sliding modes: a new approach to nonlinear control synthesis. In: Fifth International Conference on Advanced Robotics’ Robots in Unstructured Environments. Piscataway: IEEE, 1991, pp. 443–448.
18.
KamalSMorenoJAChalangaA, et al.Continuous terminal sliding-mode controller. Automatica2016; 69: 308–314.
19.
ParkKBTsujiT. Terminal sliding mode control of second-order nonlinear uncertain systems. Int J Robust Nonlinear Control1999; 9(11): 769–780.
20.
YuXManZ. Model reference adaptive control systems with terminal sliding modes. Int J Control1996; 64(6): 1165–1176.
21.
ZhihongMYuXH. Terminal sliding mode control of MIMO linear systems. IEEE Trans Circ Syst I1997; 44(11): 1065–1070.
22.
ZouAMKumarKDHouZG, et al.Finite-time attitude tracking control for spacecraft using terminal sliding mode and Chebyshev neural network. IEEE Trans Syst Man Cybern B2011; 41(4): 950–963.
23.
WuYYuXManZ. Terminal sliding mode control design for uncertain dynamic systems. Syst Control Lett1998; 34(5): 281–287.
24.
FengYYuXManZ. Non-singular terminal sliding mode control of rigid manipulators. Automatica2002; 38(12): 2159–2167.
25.
TranMDKangHJ. Nonsingular terminal sliding mode control of uncertain second-order nonlinear systems. Math Probl Eng2015; 2015: 1–8.
26.
YuXZhihongM. Fast terminal sliding-mode control design for nonlinear dynamical systems. IEEE Trans Circ Syst I2002; 49(2): 261–264.
27.
BesnardLShtesselYBLandrumB. Quadrotor vehicle control via sliding mode controller driven by sliding mode disturbance observer. J Franklin Inst2012; 349(2): 658–684.
28.
HuaCCWangKChenJN, et al.Tracking differentiator and extended state observer-based nonsingular fast terminal sliding mode attitude control for a quadrotor. Nonlinear Dyn2018; 94(1): 343–354.
29.
XiongJJZhengEH. Position and attitude tracking control for a quadrotor UAV. ISA Trans2014; 53(3): 725–731.
30.
XiongJJZhangGB. Global fast dynamic terminal sliding mode control for a quadrotor UAV. ISA Trans2017; 66: 233–240.
31.
BeardRW. Quadrotor dynamics and control. Brigham Young University2008; 19(3): 46–56.
32.
BrescianiT. Modelling, identification and control of a quadrotor helicopter. Sweden: Lund University, 2008.
33.
ZhangXLiXWangK, et al.A survey of modelling and identification of quadrotor robot. In: Abstract and Applied Analysis. London: Hindawi, 2014.
34.
SmetanaFOSummeryDCJohnsonWD. Riding and handling qualities of light aircraft. A review and analysis. NASA, 1972.
35.
LatosińskiP. Sliding mode control based on the reaching law approach—a brief survey. In: 2017 22nd International Conference on Methods and Models in Automation and Robotics (MMAR). Piscataway: IEEE, 2017, pp. 519–524.
36.
LeeJMukherjeeRKhalilHK. Output feedback stabilization of inverted pendulum on a cart in the presence of uncertainties. Automatica2015; 54: 146–157.
37.
BhargavapuriMSahooSRKothariM. Robust attitude tracking in the presence of parameter uncertainty for a variable-pitch quadrotor. In: 2018 Annual American Control Conference (ACC). Piscataway: IEEE, 2018, pp. 3454–3459.
38.
KhalilHK. Nonlinear systems. New Jersey: Prentice-Hall; 1996.
