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Fractional Order Sliding Mode Control Based on Fractional Order Reaching Law: Reaching Condition Analysis and Experimental Validation

[+] Author Affiliations
Chun Yin

University of Electronic Science and Technology of China, Chengdu, ChinaUniversity of California, Merced, Merced, CA

Zhuo Li, YangQuan Chen

University of California, Merced, Merced, CA

Shou-ming Zhong

University of Electronic Science and Technology of China, Chengdu, China

Paper No. DETC2013-12724, pp. V004T08A021; 9 pages
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 18th Design for Manufacturing and the Life Cycle Conference; 2013 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5591-1
  • Copyright © 2013 by ASME


In this paper, a novel fractional order (FO) reaching law with an FO sign function is proposed. It is used to guarantee the the occurrence of reaching phase in finite time. Since the traditional integer order (IO) reaching law can be considered as a special case of the FO reaching law, it is more likely for the FO reaching law to obtain better performance. The properties of the FO sign function are used to prove the capability of states to approach the switching manifolds. Compared with the IO sign function in the classical reaching law, the states reach the switching manifolds faster with the FO reaching law. It will be shown that the reaching time under the FO SMC can be reduced by analyzing the FO sign function under appropriate conditions. Moreover, the sliding dynamics can arrive at the equilibrium point more rapidly by applying the FO reaching law. Simulation results including comparisons between the FO SMC and the IO SMC are presented to illustrate the advantages of the proposed scheme. Finally, a fractional horsepower dynamometer is utilized as a real time simulation platform to demonstrate the effectiveness of the proposed FO reaching law.

Copyright © 2013 by ASME



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