Terminal Sliding Mode Control of the Flexible Manipulator

Abstract:

Aimed at the finite-time stabilization problem of a class of flexible manipulators, a stabilization controller based on terminal sliding mode control was proposed in this paper. Firstly, the nonlinear model of flexible manipulators was transformed into linear system through the exact state feedback linearization. Based on the finite time stabilization control method of the linear system, a stabilization controller based on terminal sliding mode control was designed for the flexible manipulators. Furthermore, it was proved that all the states of flexible manipulators could be stabilized to equilibrium in finite time with the proposed controller. The simulation results showed that the performance of the flexible manipulators with the proposed finite-time state feedback controller was effective. At last, the analysis and comparison of the proposed controller and the finite-time state feedback controller were given.

• Periodical: Applied Mechanics and Materials (Volumes 530-531)
• Pages: 1026-1031
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.530-531.1026
• Online since: February 2014
• Authors: Sheng Li*, Yi Qing Wang, Bao Lin Hou
• Keywords: Exact State Feedback Linearization, Finite Time Control, Flexible Manipulators, Terminal Sliding Mode Control

References

[1] Shihua Li, Shihong Ding, Yuping Tian. A Finite-time State Feedback Stabilization Method for a Class of Second Order Nonlinear Systems. Acta Automatic Sinica, Vol. 33(2007), p.101~103(in Chinese).

DOI: 10.1360/aas-007-0101

[2] Bhat S P, Bernstein D S: Geometric homogeneity with applications to finite-time stability[J]. Mathematics of Control, Signals, and Systems, Vol. 17(2005), p.101~127.

DOI: 10.1007/s00498-005-0151-x

[3] Bhat S P, Bernstein D S: Finite-time stability of continuous autonomous systems [J]. SIAM Journal of Control and Optimization, Vol. 38(2000), p.751~766.

DOI: 10.1137/s0363012997321358

[4] Bhat S P, Bernstein D S: Lyapunov analysis of finite-time differential equations. Proceeding. American Control Conference, Seattle, WA, June 1995, 1831~1832.

DOI: 10.1109/acc.1995.531201

[5] Yiguang Hong: Finite-time stabilization and stabilizability of a class of nonlinear systems, Systems & Control Letters, Vol. 46(2002), p.231~236.

DOI: 10.1016/s0167-6911(02)00119-6

[6] Yiguang Hong , GW Yang, DZ Cheng, Spurgeon S: Journal of Control Theory and Applications, 2004, p.69~74.

[7] Y Feng, XH Yu, Zhihong Man: Non-singular terminal sliding mode control of rigid manipulators[J]. Automatica, Vol. 38(2002), p.2159~2167.

DOI: 10.1016/s0005-1098(02)00147-4

[8] Sin C K: On the Synthesis of the fixed order stabilizing controller. Texas A&M University, (2005).

[9] Marino R, Tomei P. Nonlinear Control Design-Geometric, Adaptive and Robust. Prenctice Hall, London, (1995).

[10] Nersesov S G, Haddad W M, Hui Q. Finite-Time Stabilization of Nonlinear Dynamical Systems via Control Vector Lyapunov Functions[J]. Journal of the Franklin Institute, 2008, 345: 819-837.

DOI: 10.1016/j.jfranklin.2008.04.015

[11] Wang Yiqing, Chen Qingwei, Hou Baolin. Research on finite-time control method for the flexible manipulator[J]. Applied Mechanics and Materials, 2012, 220-223: 1772-1777.

DOI: 10.4028/www.scientific.net/amm.220-223.1772

[12] L Liu, J Sun. Finite-time stabilization of linear systems via impulsive control[J]. International Journal of Control, 2008, 81(6): 905-909.

DOI: 10.1080/00207170701519060

[13] Nersesov S G, Haddad W M. Finite-Time Stabilization of Nonlinear Impulsive Dynamical Systems[J]. Nonlinear Analysis: Hybrid Systems, 2008, 2: 832-845.

DOI: 10.1016/j.nahs.2007.12.001

[14] J Li, CJ Qian: Global finite-time stabilization by output feedback for a class of linearly unobservable systems. Proceedings of the American Control Conference, 2006: 4987~4992.

DOI: 10.1109/acc.2006.1657511