Abstract
Hovercraft is commonly used for military operations, transportation, and scientific research. Therefore, considering the use of hovercraft, it is very important to design a controller that ensures its stabilization to enhance its performance. Since a hovercraft has only two control inputs with three degrees of freedom, designing a stabilization controller is a very difficult task. The hovercraft model is derived from a simple ship equation that is nonlinear and underactuated. In this work, the controller design is conducted for the full-state stabilization problem to stabilize the underactuated hovercraft. Using the inputs and state transformations, the dynamic model of the hovercraft is transformed into an equivalent system consisting of two cascaded connected subsystems. Dynamic input terms are introduced due to the modified dynamic cascaded system, and an adaptive sliding mode control (SMC) scheme is employed to handle these terms and to clutch the stabilization problem. To eliminate the high-frequency switching effect in SMC and enhance the speed of reaching phase, an atan-based strong exponential reaching law is employed. To construct the stabilizing controller, an appropriate Hurwitz sliding surface and a Lyapunov function are selected, and the adaptive laws are derived such that the derivative of the Lyapunov function is strictly negative, so as to guarantee the stability of the closed-loop system. To demonstrate the efficacy of the proposed control, numerical simulations are run to stabilize the planar position and orientation, revealing that all states and control inputs are asymptotically convergent to the origin since a quantitative comparison is also made between the classical switching law and the suggested switching law for energy consumption.
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References
Pettersen KY, Nijmeijer H (2001) Semi-global practical stabilization and disturbance adaptation for an underactuated ship. Model Identif Control Nor Res Bull 22(2):89–101
Do KD, Jiang ZP, Pan J (2002) Universal controllers for stabilization and tracking of underactuated ships. Syst Control Lett 47(4):299–317
Kim T-H, Basar T, Ha I-J (2002) Asymptotic stabilization of an underactuated surface vessel via logic-based control. In: Proceedings of the 2002 American control conference (IEEE Cat. No. CH37301)
Mazenc F, Pettersen K, Nijmeijer H (2002) Global uniform asymptotic stabilization of an underactuated surface vessel. IEEE Trans Autom Control 47(10):1759–1762
Do KD, Jiang ZP, Pan J (2003) Robust global stabilization of underactuated ships on a linear course. In: Proceedings of the 2002 American control conference (IEEE Cat. No. CH37301)
Dong W, Guo Y (2005) Global time-varying stabilization of underactuated surface vessel. IEEE Trans Autom Control 50(6):859–864
Ghommam J, Mnif F, Benali A, Derbel N (2006) Asymptotic backstepping stabilization of an underactuated surface vessel. IEEE Trans Control Syst Technol 14(6):1150–1157
Cheng J, Yi J, Zhao D (2007) Stabilization of an underactuated surface vessel via discontinuous control. In: 2007 American control conference
Ma B-L (2009) Global k-exponential asymptotic stabilization of underactuated surface vessels. Syst Control Lett 58(3):194–201
Zheng X, Wu Y (2009) Adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts. Nonlinear Anal Theory Methods Appl 70(2):904–920
Ghommam J, Mnif F, Derbel N (2010) Global stabilisation and tracking control of underactuated surface vessels. IET Control Theory Appl 4(1):71–88
Zhang B, Ma B (2010) Robust stabilization of underactuated surface vessels with parameter uncertainties. In: Proceedings of the 29th Chinese control conference, pp 547–552
Liu Z, Yu R, Zhu Q (2011) Stabilization control and simulation of an unmanned surface vessel. In: Proceedings of the 30th Chinese control conference, pp 3606–3609
Xie W, Ma B (2015) Robust global uniform asymptotic stabilization of underactuated surface vessels with unknown model parameters. Int J Robust Nonlinear Control 25(7):1037–1050
Gao S, Xie W, Ma B (2013) Robust position stabilization of underactuated hovercrafts with modeling parameter uncertainties. In: Proceedings of the 32nd Chinese control conference, pp 535–540
Liu L, Liu Z, Zhang J (2014) LMI-based model predictive control for underactuated surface vessels with input constraints. Abstr Appl Anal 2014:1–9
Wen-Jing X, Bao-Li M (2015) Robust position stabilization of underactuated surface vessels with unknown modeling parameters via simple P/D-like feedback: the center manifold approach: robust position stabilization of USVs via simple P/D-like feedback. Asian J Control 17(4):1222–1232
He G, Zhang C, Sun W, Geng Z (2016) Stabilizing the second-order nonholonomic systems with chained form by finite-time stabilizing controllers. Robotica 34(10):2344–2367
Zhang Z, Wu Y (2015) Further results on global stabilisation and tracking control for underactuated surface vessels with non-diagonal inertia and damping matrices. Int J Control 88(9):1679–1692
Zhang P, Guo G, Yue W (2016) Stabilization of underactuated surface vessel with the roll. In: 2016 Sixth international conference on information science and technology (ICIST)
Lin X, Nie J, Jiao Y, Liang K, Li H (2018) Adaptive fuzzy output feedback stabilization control for the underactuated surface vessel. Appl Ocean Res 74:40–48
Lixia Y, Baoli M (2019) Full-state stabilization of hovercraft based on discrete constant control. In: Proceedings of 2018 Chinese intelligent systems conference. Springer Singapore, Singapore, pp 725–734
Zhang J, Yu S, Yan Y (2019) Fixed-time extended state observer-based trajectory tracking and point stabilization control for marine surface vessels with uncertainties and disturbances. Ocean Eng 186(106109):106109
Abro GEM, Jabeen B, Manan A (2019) Stabilization of non-holonomic 03 DOF hovercraft using robust RST control design. Sukkur IBA J Emerg Technol 2(1):45–50
Mustafa Abro GE, Zulkifli SA, Asirvadam VS, Ali ZA, Mathur N, Kumar R (2021) Modeling, controlling and stabilization of an underactuated air-cushion vehicle (ACV). In: 2021 IEEE international conference on signal and image processing applications (ICSIPA)
Karami H, Ghasemi R (2021) Adaptive neural observer-based nonsingular super-twisting terminal sliding-mode controller design for a class of hovercraft nonlinear systems. J Mar Sci Appl 20(2):325–332
Zhang P, Guo G (2020) Fixed-time switching control of underactuated surface vessels with dead-zones: global exponential stabilization. J Frankl Inst 357(16):11217–11241
Hu X, Zhu G, Ma Y, Li Z, Malekian R, Sotelo MA (2022) Event-triggered adaptive fuzzy setpoint regulation of surface vessels with unmeasured velocities under thruster saturation constraints. IEEE Trans Intell Transp Syst 23(8):13463–13472
Rigatos Gerasimos G (2015) Nonlinear control and filtering using differential flatness approaches: applications to electromechanical systems, vol 25. Springer, Berlin
Mahmood A, Bhatti AI, Siddique BA (2019) Landing of aircraft using integral state feedback sliding mode control. In: 2019 International conference on electrical, communication, and computer engineering (ICECCE)
Mahmood A, ur Rehman F, Bhatti AI (2023) Range guidance for subsonic unpowered gliding vehicle using integral action-based sliding mode control. Int J Dyn Control. https://doi.org/10.1007/s40435-023-01229-y
Acknowledgements
The authors would like to acknowledge the Control and Signal Processing Research (CASPR) group of Capital University of Science and Technology, Islamabad, Pakistan. Special thanks go to the editor and reviewers for their valuable suggestions which resulted in substantial improvement of the paper.
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ur Rehman, F., Mahmood, A. Adaptive sliding mode-based full-state stabilization control of an underactuated hovercraft. Int. J. Dynam. Control 12, 1512–1521 (2024). https://doi.org/10.1007/s40435-023-01270-x
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DOI: https://doi.org/10.1007/s40435-023-01270-x