This paper investigates a passivity-based hierarchical SM control (PBHSMC) approach to solve the trajectory tracking issue of a special class of UMSs using unmeasured states and in presence of both unmatched and matched perturbations. First, a passivity-based SM observer (PBSMO) is designed for quick estimation of states in the UMS. Then, we develop a nonlinear two-layer switching surface using feedback passivation. The passivation-based approach ensures global asymptotical convergence of tracking error on the switching surface with the discontinuous term. Moreover, we develop an SMC law that can satisfy reaching mode and sliding mode conditions. Finally, to illustrate the performance of theoretical results, the developed control scheme is assessed by numerical simulation of two case studies including flexible-joint manipulator (FJM) and underactuated surface vessel (USV) systems. The simulation results indicate the superiority of the PBSMO-based PBHSMC scheme over the conventional SMO-based HSMC in suppressing unwanted oscillations of link, low tracking error and overshoot, short settling time, smooth and small control efforts, and also more accurate estimation of state variables with less chattering.
AlmeidaDIRGamezCRascónR (2015) Robust regulation and tracking control of a class of uncertain 2DOF underactuated mechanical systems. Mathematical Problems in Engineering2015: 1–11.
2.
ArimotoS (1996) Control Theory of Nonlinear Mechanical Systems. Oxford, UK: Oxford University Press.
3.
AshrafiuonHErwinRS (2008) Sliding mode control of underactuated multibody systems and its application to shape change control. International Journal of Control81(12): 1849–1858.
4.
BrockettRW (1983) Asymptotic stability and feedback stabilization. Differential Geometric Control Theory27(1): 181–191.
5.
BrogliatoBLozanoRMaschkeB, et al. (2020) Dissipative Systems Analysis and Control: Theory and Applications. Berlin, Heidelberg: Springer-Verlag.
6.
ChalhoubNKfouryGBazziB (2006) Design of robust controllers and a nonlinear observer for the control of a single-link flexible robotic manipulator. Journal of Sound and Vibration291(1–2): 437–461.
7.
ChangJL (2019) Passivity‐based sliding mode controller/observer for second‐order nonlinear systems. International Journal of Robust and Nonlinear Control29(6): 1976–1989.
8.
ChangX-HJinX (2022) Observer-based fuzzy feedback control for nonlinear systems subject to transmission signal quantization. Applied Mathematics and Computation414: 126657.
9.
ChangY-CYenH-M (2011) Design of a robust position feedback tracking controller for flexible-joint robots. IET Control Theory & Applications5(2): 351–363.
10.
ChangYZhouPNiuB, et al. (2021) Switched-observer-based adaptive output-feedback control design with unknown gain for pure-feedback switched nonlinear systems via average dwell time. International Journal of Systems Science2021: 1–15.
11.
ChawengkrittayanontPPukdeboonC (2019) Continuous higher order sliding mode observers for a class of uncertain nonlinear systems. Transactions of the Institute of Measurement and Control41(3): 717–728.
12.
ChenLWangHHuangY, et al. (2020) Robust hierarchical sliding mode control of a two-wheeled self-balancing vehicle using perturbation estimation. Mechanical Systems and Signal Processing139: 106584.
13.
Choukchou-BrahamACherkiBDjemaïM, et al. (2013) Analysis and Control of Underactuated Mechanical Systems. Berlin, Germany: Springer Science & Business Media.
14.
DaiSLHeSWangM, et al. (2018) Adaptive neural control of underactuated surface vessels with prescribed performance guarantees. IEEE Transactions on Neural Networks and Learning Systems30(12): 3686–3698.
15.
DaiSLHeSXuY (2017) Transverse function approach to practical stabilisation of underactuated surface vessels with modelling uncertainties and unknown disturbances. IET Control Theory & Applications11(15): 2573–2584.
16.
DoKDJiangZPPanJ (2004) Robust adaptive path following of underactuated ships. Automatica40(6): 929–944.
17.
FantoniILozanoRSinhaS (2002) Non-linear control for underactuated mechanical systems. Applied Mechanics Reviews55(4): B67–B68.
18.
FossenT (1994) Guidance and Control of Ocean Vehicles. New York, NY: John Willey & Sons. Inc.
19.
FradkovA (2003) Passification of non-square linear systems and feedback Yakubovich-Kalman-Popov lemma. European Journal of Control9(6): 577–586.
20.
HippeP (2006) Windup in Control: Its Effects and Their Prevention. Berlin, Germany: Springer Science & Business Media, 1–20.Undesired Effects of Input Saturation
21.
HuangHGongMZhuangY, et al. (2019) A new guidance law for trajectory tracking of an underactuated unmanned surface vehicle with parameter perturbations. Ocean Engineering175: 217–222.
22.
JahangiriFTalebiHAMenhajMB, et al. (2018) A novel scheme for output definition in feedback passivation of nonlinear systems. International Journal of Systems Science49(15): 3196–3201.
23.
KhalilHK (2002) Nonlinear Systems. Upper Saddle River, NJ: Prentice-Hall.
24.
KikuuweRYasukouchiSFujimotoH, et al. (2010) Proxy-based sliding mode control: a safer extension of PID position control. IEEE Transactions on Robotics26(4): 670–683.
25.
KrafesSChalhZSakaA (2018) A review on the control of second order underactuated mechanical systems. Complexity2018: 1–17.
26.
KurodeSSpurgeonSKBandyopadhyayB, et al. (2012) Sliding mode control for slosh-free motion using a nonlinear sliding surface. IEEE/ASME Transactions on Mechatronics18(2): 714–724.
27.
LiuWChenS-YHuangH-X (2020) Double closed-loop integral terminal sliding mode for a class of underactuated systems based on sliding mode observer. International Journal of Control, Automation and Systems18(2): 339–350.
28.
LiuYYuH (2013) A survey of underactuated mechanical systems. IET Control Theory & Applications7(7): 921–935.
29.
Moghanni-Bavil-OlyaeiM-RGhanbariAKeighobadiJ (2019) Trajectory tracking control of a class of underactuated mechanical systems with nontriangular normal form based on block backstepping approach. Journal of Intelligent & Robotic Systems96(2): 209–221.
30.
Olfati-SaberR (2001) Nonlinear Control of Underactuated Mechanical Systems with Application to Robotics and Aerospace Vehicles. PhD Thesis, Massachusetts Institute of Technology, Cambridge, MA.
31.
OrtegaRSpongMWGomez-EsternF, et al. (2002) Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Transactions on Automatic Control47(8): 1218–1233.
32.
PettersenKYMazencFNijmeijerH (2004) Global uniform asymptotic stabilization of an underactuated surface vessel: Experimental results. IEEE Transactions on Control Systems Technology12(6): 891–903.
33.
QianDWLiuXJYiJQ (2009) Robust sliding mode control for a class of underactuated systems with mismatched uncertainties. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering223(6): 785–795.
34.
ReyhanogluM (1997) Exponential stabilization of an underactuated autonomous surface vessel. Automatica33(12): 2249–2254.
35.
RomeroJGDonaireAOrtegaR, et al. (2018) Global stabilisation of underactuated mechanical systems via PID passivity-based control. Automatica96: 178–185.
36.
SeronMMHillDJFradkovAL (1994) Adaptive passification of nonlinear systems. In: Proceedings of 1994 33rd IEEE Conference on Decision and Control, Lake Buena Vista, FL, 14–16 December 1994, pp. 190–195. IEEE.
37.
ShiJWangJFuF (2017) Chatter alleviation for a class of second-order under-actuated mechanical systems with matched and mismatched disturbances. Journal of Vibration and Control23(3): 458–468.
38.
SinghAMHaQP (2019) Fast terminal sliding control application for second-order underactuated systems. International Journal of Control, Automation and Systems17(8): 1884–1898.
39.
SpongMW (1987) Modeling and control of elastic joint robots. Journal of Dynamic Systems, Measurement and Control109(4): 310–318.
40.
SpongMW (1998) Underactuated mechanical systems. In: Control Problems in Robotics and Automation. Berlin, Germany: Springer, 135–150.
41.
TaoGIoannouPA (1988) Strictly positive real matrices and the Lefschetz-Kalman-Yakubovich lemma. IEEE Transactions on Automatic Control33(12): 1183–1185.
42.
TokatSFadaliMSErayO (2015) A classification and overview of sliding mode controller sliding surface design methods. In: Recent Advances in Sliding Modes: From Control to Intelligent Mechatronics. Berlin, Germany: Springer, 417–439.
43.
UtkinVGuldnerJShijunM (1999) Sliding Mode Control in Electro-Mechanical Systems. Boca Raton, FL: CRC Press.
44.
WangWYiJZhaoD, et al. (2004) Design of a stable sliding-mode controller for a class of second-order underactuated systems. IEE Proceedings - Control Theory and Applications151(6): 683–690.
45.
WeiXMottersheadJE (2017) Robust passivity-based continuous sliding-mode control for under-actuated nonlinear wing sections. Aerospace Science and Technology60: 9–19.
46.
XuJ-XGuoZ-QLeeTH (2013) Design and implementation of integral sliding-mode control on an underactuated two-wheeled mobile robot. IEEE Transactions on Industrial Electronics61(7): 3671–3681.
47.
XuRÖzgünerÜ (2008) Sliding mode control of a class of underactuated systems. Automatica44(1): 233–241.
48.
XuZRahmanMF (2012) Comparison of a sliding observer and a Kalman filter for direct-torque-controlled IPM synchronous motor drives. IEEE Transactions on Industrial Electronics59(11): 4179–4188.
49.
YanZLaiXMengQ, et al. (2021) Tracking control of single‐link flexible‐joint manipulator with unmodeled dynamics and dead zone. International Journal of Robust and Nonlinear Control31(4): 1270–1287.
50.
ZaareSSoltanpourMR (2020) Continuous fuzzy nonsingular terminal sliding mode control of flexible joints robot manipulators based on nonlinear finite time observer in the presence of matched and mismatched uncertainties. Journal of the Franklin Institute357(11): 6539–6570.
51.
ZeharDBenmahammedKBehihK (2018) Control for underactuated systems using sliding mode observer. International Journal of Control, Automation and Systems16(2): 739–748.
52.
ZhangHWangHNiuB, et al. (2021a) Sliding-mode surface-based adaptive actor-critic optimal control for switched nonlinear systems with average dwell time. Information Sciences580: 756–774.
53.
ZhangHXuNZongG, et al. (2021b) Adaptive fuzzy hierarchical sliding mode control of uncertain under-actuated switched nonlinear systems with actuator faults. International Journal of Systems Science2021: 1–16.
