0
Research Papers

Adaptive Boundary Control for a Flexible Manipulator With State Constraints Using a Barrier Lyapunov Function

[+] Author and Article Information
Tingting Jiang

Jiangsu Automation Research Institute of CSIC,
Lianyungang 222061, China;
School of Automation Science and
Electrical Engineering,
Beihang University (Beijing University of
Aeronautics and Astronautics),
Beijing 100191, China

Jinkun Liu

School of Automation Science
and Electrical Engineering,
Beihang University (Beijing University of
Aeronautics and Astronautics),
Beijing 100191, China
e-mail: ljk@buaa.edu.cn

Wei He

Key Laboratory of Knowledge Automation
for Industrial Processes,
Ministry of Education,
School of Automation and
Electrical Engineering,
University of Science and Technology Beijing,
Beijing 100083, China

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received March 15, 2017; final manuscript received November 16, 2017; published online March 30, 2018. Assoc. Editor: Davide Spinello.

J. Dyn. Sys., Meas., Control 140(8), 081018 (Mar 30, 2018) (7 pages) Paper No: DS-17-1152; doi: 10.1115/1.4039364 History: Received March 15, 2017; Revised November 16, 2017

In this paper, the problem of state constraints control is investigated for a class of output constrained flexible manipulator system with varying payload. The dynamic behavior of the flexible manipulator is represented by partial differential equations. To prevent states of the flexible manipulator system from violating the constraints, a barrier Lyapunov function which grows to infinity whenever its arguments approach to some limits is employed. Then, based on the barrier Lyapunov function, boundary control laws are given. To solve the problem of varying payload, an adaptive boundary controller is developed. Furthermore, based on the theory of barrier Lyapunov function and the adaptive algorithm, state constraints and output control under vibration condition can be achieved. The stability of the closed-loop system is carried out by the Lyapunov stability theory. Numerical simulations are given to illustrate the performance of the closed-loop system.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Korayem, M. H. , and Ghariblu, H. , 2004, “ Analysis of Wheeled Mobile Flexible Manipulator Dynamic Motions With Maximum Load Carrying Capacities,” Rob. Auton. Syst., 48(2–3), pp. 63–76. [CrossRef]
Korayem, M. H. , Irani, M. , and Nekoo, S. R. , 2011, “ Load Maximization of Flexible Joint Mechanical Manipulator Using Nonlinear Optimal Controller,” Acta Astronaut., 69(7–8), pp. 458–469. [CrossRef]
Hashemi, S. M. , Abbas, H. S. , and Werner, H. , 2012, “ Low-Complexity Linear Parameter-Varying Modeling and Control of a Robotic Manipulator,” Control Eng. Pract., 20(3), pp. 248–257. [CrossRef]
Wai, R. J. , Huang, Y. C. , Yang, Z. W. , and Shih, C. Y. , 2010, “ Adaptive Fuzzy-Neural-Network Velocity Sensorless Control for Robot Manipulator Position Tracking,” IET Control Theory Appl., 4(6), pp. 1079–1093. [CrossRef]
Chen, C. S. , 2011, “ Supervisory Adaptive Tracking Control of Robot Manipulators Using Interval Type-2 TSK Fuzzy Logic System,” IET Control Theory Appl., 5(15), pp. 1796–1807. [CrossRef]
Huang, J. S. , Wen, C. Y. , Wang, W. , and Jiang, Z. P. , 2014, “ Adaptive Output Feedback Tracking Control of a Nonholonomic Mobile Robot,” Automatica, 50(3), pp. 821–831. [CrossRef]
Korayem, M. H. , Rahimi, H. N. , and Nikoobin, A. , 2012, “ Mathematical Modeling and Trajectory Planning of Mobile Manipulators With Flexible Links and Joints,” Appl. Math. Modell., 36(7), pp. 3229–3244. [CrossRef]
Hu, Q. , and Zhang, J. , 2015, “ Maneuver and Vibration Control of Flexible Manipulators Using Variable-Speed Control Moment Gyros,” Acta Astronaut., 113, pp. 105–119. [CrossRef]
Shawky, A. , Zydek, D. , Elhalwagy, Y. Z. , and Ordys, A. , 2013, “ Modeling and Nonlinear Control of a Flexible-Link Manipulator,” Appl. Math. Modell., 37(23), pp. 9591–9602. [CrossRef]
Dubay, R. , Hassan, M. , Li, C. , and Charest, M. , 2014, “ Finite Element Based Model Predictive Control for Active Vibration Suppression of a One-Link Flexible Manipulator,” ISA Trans., 53(5), pp. 1609–1619. [CrossRef] [PubMed]
Feng, Y. , Bao, S. , and Yu, X. , 2004, “ Inverse Dynamics Nonsingular Terminal Sliding Mode Control of Two-Link Flexible Manipulators,” Int. J. Rob. Autom., 19(2), pp. 91–102.
Zhang, X. , Xu, W. , Nair, S. S. , and Chellaboina, V. , 2005, “ PDE Modeling and Control of a Flexible Two-Link Manipulator,” IEEE Trans. Control Syst. Technol., 13(2), pp. 301–312. [CrossRef]
Zhang, L. , and Liu, J. , 2012, “ Observer-Based Partial Differential Equation Boundary Control for a Flexible Two-Link Manipulator in Task Space,” IET Control Theory Appl., 6(13), pp. 2120–2133. [CrossRef]
Tian, L. , and Collins, C. , 2005, “ Adaptive Neuro-Fuzzy Control of a Flexible Manipulator,” Mechatronics, 15(10), pp. 1305–1320. [CrossRef]
Zhang, L. , and Liu, J. , 2013, “ Adaptive Boundary Control for Flexible Two-Link Manipulator Based on Partial Differential Equation Dynamic Model,” IET Control Theory Appl., 7(1), pp. 43–51. [CrossRef]
Pradhan, S. K. , and Subudhi, B. , 2012, “ Real-Time Adaptive Control of a Flexible Manipulator Using Reinforcement Learning,” IEEE Trans. Autom. Sci. Eng., 9(2), pp. 237–249. [CrossRef]
Feliu, V. , Rattan, K. S. , and Brown, H. B. , 1989, “ Adaptive Control of a Single-Link Flexible Manipulator in the Presence of Joint Friction and Load Changes,” IEEE International Conference on Robotics and Automation (ICRA), Scottsdale, AZ, May 14–19.
He, W. , and Ge, S. S. , 2015, “ Vibration Control of a Flexible Beam With Output Constraint,” IEEE Trans. Ind. Electron., 62(8), pp. 5023–5030. [CrossRef]
He, W. , Ge, S. S. , and Huang, D. , 2015, “ Modeling and Vibration Control for a Nonlinear Moving String With Output Constraint,” IEEE/ASME Trans. Mechatronics, 20(4), pp. 1886–1897. [CrossRef]
Clason, C. , and Kaltenbacher, B. , 2014, “ Optimal Control of a Singular PDE Modeling Transient MEMS With Control or State Constraints,” J. Math. Anal. Appl., 410(1), pp. 455–468. [CrossRef]
Meirovitch, L. , 2001, Fundamentals of Vibrations, McGraw-Hill, New York. [PubMed] [PubMed]
Tee, K. P. , Ge, S. S. , and Tay, E. H. , 2009, “ Barrier Lyapunov Functions for the Control of Output-Constrained Nonlinear Systems,” Automatica, 45(4), pp. 918–927. [CrossRef]
Willis, H. R. , 1981, Advanced Process Control, McGraw-Hill, New York.
LaSalle, J. , and Lefschetz, S. , 1961, Stability by Lyapunov's Direct Method, Academic Press, New York.

Figures

Grahic Jump Location
Fig. 1

Configuration of the flexible manipulator

Grahic Jump Location
Fig. 2

Schematic illustration of a symmetrical barrier Lyapunov function

Grahic Jump Location
Fig. 8

Boundary deflection speed regulation (y˙(L,t)=0)

Grahic Jump Location
Fig. 9

Elastic deflection of the flexible manipulator

Grahic Jump Location
Fig. 10

Control inputs: (a) control input τ(t) and (b) control input F(t)

Grahic Jump Location
Fig. 3

Angle and its speed constraints: (a) angle constraint and (b) angle speed constraint

Grahic Jump Location
Fig. 4

Boundary deflection and its speed constraints: (a) boundary deflection constraint and (b) boundary deflection speed constraint

Grahic Jump Location
Fig. 5

Angle regulation (θ(t))

Grahic Jump Location
Fig. 6

Angle speed regulation (θ˙(t))

Grahic Jump Location
Fig. 7

Boundary deflection regulation (y(L,t)=0)

Grahic Jump Location
Fig. 11

α and α̂ under different conditions

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In