In this paper, the dynamic model is established for the two-link rigid-flexible manipulator, which is represented by nonlinear ordinary differential equations–partial differential equations (ODEs–PDEs). Based on the nonlinear ODE–PDE model, the boundary control strategy is designed to drive the manipulator to follow a given trajectory and eliminate the vibration simultaneously. Considering actuators saturation, smooth hyperbolic tangent function is introduced for dealing with control input constraints problem. It has been rigorously proved that the nonlinear closed-loop system is asymptotically stable by using LaSalle's invariance principle. Simulation results show that the proposed controller is effective.
Issue Section:
Technical Brief
References
1.
Han
, Z.-J.
, and Xu
, G.-Q.
, 2010
, “Exponential Stabilisation of a Simple Tree-Shaped Network of Timoshenko Beams System
,” Int. J. Control
, 83
(7
), pp. 1485
–1503
.2.
He
, W.
, Sun
, C.
, and Ge
, S. S.
, 2014
, “Top Tension Control of a Flexible Marine Riser by Using Integral-Barrier Lyapunov Function
,” IEEE/ASME Trans. Mechatronics
, 20
(2
), pp. 497
–505
.3.
Zhao
, Z.
, Liu
, Y.
, He
, W.
, and Luo
, F.
, 2016
, “Adaptive Boundary Control of an Axially Moving Belt System With High Acceleration/Deceleration
,” J. Franklin Inst.
, 10
(11
), pp. 1299
–1306
.4.
Li
, Z.
, Yang
, C.
, Su
, C.-Y.
, Deng
, S.
, Sun
, F.
, and Zhang
, W.
, 2015
, “Decentralized Fuzzy Control of Multiple Cooperating Robotic Manipulators With Impedance Interaction
,” IEEE Trans. Fuzzy Syst.
, 23
(4
), pp. 1044
–1056
.5.
Liu
, Y.
, Zhao
, Z.
, and He
, W.
, 2016
, “Boundary Control of an Axially Moving Accelerated/Decelerated Belt System
,” Int. J. Robust Nonlinear Control
, 26
(17
), pp. 3849
–3866
.6.
Wongratanaphisan
, T.
, and Cole
, M. O. T.
, 2009
, “Robust Impedance Control of a Flexible Structure Mounted Manipulator Performing Contact Tasks
,” IEEE Trans. Rob.
, 25
(2
), pp. 445
–451
.7.
Monje
, C. A.
, Ramos
, F.
, Feliu
, V.
, and Vinagre
, B. M.
, 2007
, “Tip Position Control of a Lightweight Flexible Manipulator Using a Fractional Order Controller
,” IET Control Theory Appl.
, 1
(5
), pp. 1451
–1460
.8.
Xu
, G. Q.
, Liu
, D. Y.
, and Liu
, Y. Q.
, 2008
, “Abstract Second Order Hyperbolic System and Applications to Controlled Network of Strings
,” Siam J. Control Optim.
, 47
(4
), pp. 1762
–1784
.9.
He
, W.
, Zhang
, S.
, and Ge
, S. S.
, 2014
, “Robust Adaptive Control of a Thruster Assisted Position Mooring System
,” Automatica
, 50
(7
), pp. 1843
–1851
.10.
Zhao
, Z. J.
, Liu
, Y.
, Guo
, F.
, and Fu
, Y.
, 2017
, “Modelling and Control for a Class of Axially Moving Nonuniform System
,” Int. J. Syst. Sci.
, 48
(4
), pp. 849
–861
.11.
He
, W.
, and Ge
, S. S.
, 2011
, “Robust Adaptive Boundary Control of a Vibrating String Under Unknown Time-Varying Disturbance
,” IEEE Trans. Control Syst. Technol.
, 20
(1
), pp. 48
–58
.12.
He
, W.
, He
, X.
, and Ge
, S. S.
, 2016
, “Vibration Control of Flexible Marine Riser Systems With Input Saturation
,” IEEE Trans. Mechatronics
, 21
(1
), pp. 254
–265
.13.
Chen
, M.
, Ge
, S. S.
, and Ren
, B.
, 2011
, “Adaptive Tracking Control of Uncertain Mimo Nonlinear Systems With Input Constraints
,” Automatica
, 47
(3
), pp. 452
–465
.14.
Wen
, C.
, Zhou
, J.
, Liu
, Z.
, and Su
, H.
, 2011
, “Robust Adaptive Control of Uncertain Nonlinear Systems in the Presence of Input Saturation and External Disturbance
,” IEEE Trans. Autom. Control
, 56
(7
), pp. 1672
–1678
.15.
Liu
, Z.
, Liu
, J.
, and He
, W.
, 2017
, “Modeling and Vibration Control of a Flexible Aerial Refueling Hose With Variable Lengths and Input Constraint
,” Automatica
, 77
, pp. 302
–310
.16.
Yang
, X.
, and Ge
, S. S.
, 2014
, “Backstepping Control and Active Vibration Control for a Free-Flying Space Robot With Rigid-Flexible Links by Singular Perturbation Approach
,” IEEE International Conference on Information and Automation
(ICIA
), Hailar, China, July 28–30, pp. 164–169.17.
Khorrami
, F.
, and Jain
, S.
, 1993
, “Nonlinear Control With End-Point Acceleration Feedback for a Two-Link Flexible Manipulator: Experimental Results
,” J. Rob. Syst.
, 10
(4
), pp. 505
–530
.18.
Zhang
, L.
, and Liu
, J.
, 2012
, “Observer-Based Partial Differential Equation Boundary Control for a Flexible Two-Link Manipulator in Task Space
,” Control Theory Appl. IET
, 6
(13
), pp. 2120
–2133
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