本論文提出以適應性模糊終端滑模控制器用於機器手臂之設計方法，此控制方法在無法得知受控系統參數情形下，仍可保證閉迴路控制系統穩定。終端滑模控制器優勢為可驅使系統追蹤誤差在有限時間內收斂為零、且閉迴路控制系統為無限穩定。適應性模糊終端滑模控制器結合了模糊終端滑模控制器及適應性結構，其設計仍保有終端滑模控制的優勢，且減緩了終端滑模控制的顫動現象。藉由李亞普諾夫（Lyapunov）穩定準則導出之適應性法則，可調整模糊控制器之輸出正規化係數及補償控制器之輸出量。如此，所提出的控制器於完全無系統參數狀況下，仍可驅使系統穩定或追蹤誤差收斂。模擬的結果顯示所提出的適應性模糊終端滑模控制器性能優於典型的適應性模糊滑模控制器。

　　A new design approach of an adaptive fuzzy terminal sliding-mode controller (AFTSMC) for robotic manipulators is developed in this thesis. This control algorithm makes the closed-loop controlled system stable, although the detailed system parameters of the robot is unknown. The terminal sliding-mode controller (TSMC) is designed to drive the system tracking errors to reach and retain in the terminal sliding-mode, the system tracking error converges to zero in finite time and the closed-loop system is infinite stable. The AFTSMC, incorporating the fuzzy logic controller (FLC), the TSMC, and adaptive scheme, is designed to retain the advantages of the TSMC and to reduce the chattering. The adaptive law is designed based on the Lyapunov stability criterion. The normalization factor of output variable in the fuzzy mechanism and the output value of compensator are adapted on-line to improve the performance of the fuzzy terminal sliding-mode controller (FTSMC). Thus, it does not require the detailed system parameters for the presented AFTSMC. The simulation results demonstrate that the AFTSMC can provide much better tracking performance than that of the classical adaptive fuzzy sliding-mode controller (AFSMC).

References

[1]J. Y. Hung, W. Gao, and J. C. Huang, “Variable structure control: a
survey,” IEEE Trans. Ind. Electron., Vol. 40, NO. 1, pp. 2-22, Feb.1993.
[2]W. Gao, and J. C. Hung, ” Variable Structure Control of Nonlinear Systems:
A New Approach,” IEEE Trans. Indust. Electr.., Vol.40,NO. 1, pp. 45-55,
Feb.1993.
[3]K. S. Yeung, and Y. P. Chen, “A New Controller Design for Manipulators
Using the Theory of Variable Structure Systems,” IEEE Trans. Auto. Contr.,
Vol. 33, NO. 2, pp 200-206, Feb.1988.
[4]L. C. Fu, and T. L. Liao, “Globally Stable Robust Tracking of Nonlinear
Systems Using Variable Structure Control and with an Application to a
Robotic Manipulator,” IEEE Trans. Auto. Contr., Vol. 35, NO. 12, pp. 1345-
1350, Dec. 1990.
[5]T. P. Leung, Q. J. Zhou, and C. Y. Su,” An Adaptive Variable Structure
Model Following Control Design for Robot Manipulators,” IEEE Trans. Auto.
Contr., Vol. 36, NO. 3, pp. 347-352, March 1991.
[6]T. L.Chern, and Y. C. Wu, “Integral Variable Structure Control Approach
for Robot Manipulators,” IEE Proceedings, Vol.139,NO.2,pp. 161-166, March.
1992.
[7]B. Yao, W. B. Gao, and M. Cheng, “VSC Coordinated Control of Two
Manipulator Arms in the Presence of Environmental Constraints,” IEEE
Trans. Auto. Contr., Vol. 37, NO. 11, pp. 1806-1812, Nov. 1992.
[8]C. Y. Su, and T. P. Leung,”A Sliding Mode Controller with Bound Estimation
for Robot Manipulators,” IEEE Trans. Robot. Auto., Vol.9, NO.2, pp. 208-
214, April 1993.
[9]E. M. Jafarov, M. N. A. Parlakci, and Y. Istefanopulos,” A New Variable
Structure PID-Controller Design for Robot Manipulators,” IEEE Trans.
Robot. Auto., Vol.9, NO.2, pp. 208-214, April 1993.
[10]X. Yu, and M. Zhihong, “On Finite Time Mechanism: Terminal Sliding
Modes,” IEEE Workshop on Variable Structure Systems, pp. 164-167, Aug.
1996.
[11]M. Zhihong and X. H. Yu, “Terminal sliding mode control of MIMO linear
systems,” IEEE Trans. Circ. Syst., Vol. 44, NO. 11, pp. 1065-1070,
Nov.1997.
[12]S. Yu, and X.Yu, “Robust Global Fast Terminal Sliding Mode Controller for
Rigid Robotic Manipulators,” Proceeding of IEEE TENCON’02, pp. 1335-
1338,2002.
[13]H. Yu, and X. Yu, “Robust Global Terminal Sliding Mode Control of SISO
Nonlinear Uncertain Systems,” Preceedings of the 39th IEEE Conference on
Decision and Control Sydney, Australia, pp. 2198-2203,Dec. 2000.
[14]Y. Wu, X. Yu, and Z. Man, “Terminal Sliding Mode Control Design for
Uncertain Dynamic Systems,” ELSEVIER Systems & Control Letters, 34, pp.
281-287, 1998.
[15]D. Yue, S. Xu, and Y. Liu, ”Terminal Sliding Mode Control of High-Order
Systems,” Proceeding of The IEEE International Conference on Industrial
Technology, pp. 811-814, 1996.
[16]M. Zhihong, A. P. Paplinski, and H. R. Wu, “A robust MIMO terminal
sliding mode control scheme for rigid robotic manipulators,” IEEE Trans.
Automat. Contr., Vol. 39, NO. 12, pp. 2464-2469, Dec. 1994.
[17]X. H. Yu and M. Zhihong, “Fast terminal sliding-mode control design for
nonlinear dynamical systems,” IEEE Trans. Circ. Sys., Vol. 49, NO. 2, pp.
261-264, Feb. 2002.
[18]Y. Feng, X. Yu, and Z. Man, “ Adaptive Fast Terminal Sliding Mode
Tracking Control of Robotic Manipulator,” Proc. of the 40th IEEE
Conference on Decision and Control, Florida, USA, pp. 4021-4026, Dec. 2001.
[19]C.W. Tao, J. S. Taur, and M. L. Chan, “Adaptive fuzzy terminal sliding
mode controller for linear systems with mismatched time-varying
uncertainties,” IEEE Trans. Sys. Man. Cyber., Vol. 34, NO. 1, pp. 255-
262, Feb. 2004.
[20]L. X. Wang, A course in fuzzy systems and control, Prentice Hall, NJ,
1997.
[21]J. Yen and R. Langari, Fuzzy logic intelligence, control, and information,
Prentice Hall, NJ, 1999.
[22]G. J. Klir, U. S. Clair, and B. Yuan, Fuzzy set theory foundations and
applications, Prentice Hall, NJ, 1997.
[23]S. Y. Yi, and M. J. Chung, “ A Robust Fuzzy Logic Controller for Robot
Manipulators with Uncertainties,” IEEE Trans. Syst., Man, Cybern., Vol.
27, NO. 4, pp. 706-713, Aug. 1997.
[24]C. H. Tsai, C. H. Wang, and W. S. Lin, “ Robust Fuzzy Model-
FollowingControl of Robot Manipulators,” IEEE Trans. Fuzzy Syst., Vol.8,
NO. 4, pp. 462-469, Aug. 2000.
[25]H. Lee, E. Kim, H. J. Kang, and M. Park,” Design of a Sliding Mode
Controller with Fuzzy Sliding Surfaces,” IEE Proc. Control Theory Appl.,
Vol. 145, NO.5, pp. 411-418, Sept. 1998.
[26]J. H. Li, Design of Fuzzy Sliding-Mode Controllers and Their Applications
to a class of Mechatronic Systems,Ph.D. Dissertation, National Cheng Kung
University, 2003
[27]Y. C. Hsu, G. Chen, and H. X. Li, “A fuzzy adaptive variable structure
controller with applications to robotic manipulators,” IEEE Trans. Syst.,
Man, Cybern., Vol.31, NO. 3, pp. 331-340, June 2001.
[28]Y. Guo and P. Y. Woo, “An adaptive fuzzy sliding mode controller for
robotic manipulators,” IEEE Trans. Syst., Man, Cybern., Vol. 33, NO. 2,
pp. 149-159, March 2003.
[29]S. Y. Yi and M. J. Chung, “A robust fuzzy logic controller for robot
manipulators with uncertainties,” IEEE Trans. Syst., Man, Cybern., Vol.
27, NO. 4, pp. 706-713, Aug. 1997.
[30]F. C. Sun, Z. Q. Sun, and G. Feng, “An adaptive fuzzy controller based on
sliding mode for robot manipulators,” IEEE Trans. Syst., Man Cyber., Vol.
29, NO.4, pp. 661-667, Aug.1999.
[31]B. K. Yoo and W. C. Ham, “Adaptive control of robot manipulator using
fuzzy compensator,” IEEE Trans. Fuzzy Sys., Vol. 8, NO. 2, pp. 186-199,
April 2000.
[32]E. Kim, “Output feedback tracking control of robot manipulators with
model uncertainty via adaptive fuzzy logic,” IEEE Trans. Fuzzy Syst. Vol.
12, NO. 3, pp. 368-378, June 2004.
[33]S. J. Huang, and J. S. Lee,” A Stable Self-Organizing Fuzzy Controller
for Robotic Motion Control,” IEEE Trans. Indus. Electr. Vol. 47, NO. 2,
pp. 421-428, April. 2000.
[34]C. H. Tsai, C. H. Wang, and W. S. Lin,” Robust Fuzzy Model-Following
Control of Robot Manipulators,” IEEE Trans. Fuzzy Syst. Vol.8, NO. 4,
pp. 462-469, Aug. 2000.
[35]K. Erbatur, and O. Kaynak,” Use of Adaptive Fuzzy Systems in Parameter
Tuning of Sliding-Mode Controllers,” IEEE/ASME Trans. Mechatron., Vol.6,
NO.4, pp. 474-482, Dec.2001.
[36]L. K. Wong, F. H. F. Leung, and P. K .S. Tam, “A fuzzy sliding controller
for nonlinear systems,” IEEE Trans. Indus. Electr. Vol. 48, NO. 1, pp. 32-
37, Feb. 2001.
[37]Y. Liu, A. W. Hoover, and I. D. Walker,” A Timing Model for Vision-Based
Control of Industrial Robot Manipulators,” IEEE Trans. Robotics, Vol.20,
NO.5, pp. 891-898, Oct. 2004.
[38]V. P. Vega, S. Arimoto, Y.H. Liu, G. Hirzinger, and P. Akella, “ Dynamic
Sliding PID Control for Tracking of Robot Manipulators: Theory and
Experiments,” IEEE Trans. Robotics and Auto., Vol.19, NO.6, pp. 967-976,
Dec. 2003.
[39]J. J. E. Slotine and W. Li, Applied nonlinear control, Prentice Hall, NJ,
1991.
[40]G. Tao, Adaptive Control Design and Analysis, John Wiley, NJ, 2003.
[41]M. Zak, “Terminal attractors for addressable memory in neural networks,”
Physics Letters A, Vol.133, NO.1,2, pp. 18-22, 1988.
[42]M. Zak, “Terminal attractors in neural networks,” Neural Networks,
Vol.2, pp. 259-274, 1989.
[43]F.J. Chang, S. H. Twu, and S. Chang, “Adaptive chattering alleviation of
variable structure systems control,” Proc, Inst. Elect. Eng. D, Vol.137,
pp. 31-39, Jan. 1990.