Title: Sliding mode control design with a class of piecewise smooth switching surfaces

Authors: Yu Yao, Kai Zheng, Kemao Ma, Tielong Shen

Addresses: Simulation and Control Center, Harbin Institute of Technology, Building-E Science Park, Harbin, Heilongjiang, 150001, China. ' Simulation and Control Center, Harbin Institute of Technology, Building-E Science Park, Harbin, Heilongjiang, 150001, China. ' Simulation and Control Center, Harbin Institute of Technology, Building-E Science Park, Harbin, Heilongjiang, 150001, China. ' Department of Engineering and Applied Sciences, Sophia University, Kioicho 7-1, Chiyoda-ku, Tokyo, 102-8554 Japan

Abstract: In order to achieve more flexibility, a new design method is proposed to construct the switching surface of sliding mode control. We first prove that the available switching surface is not unique for the fixed reaching phase design. A new switching surface is developed by the combination of these available switching surfaces. Unlike typical sliding mode control design, the new switching surface is continuous, in other words, piecewise smooth. Furthermore, a method is provided to obtain the sliding motion on the non-smooth region of the switching surface, where a high-dimensional cross product is introduced to calculate the direction of the trajectories on the smooth half surfaces with respect to the non-smooth regions. Based on this method, we show that the sliding motion is still smooth on the non-smooth switching surface.

Keywords: sliding mode control; switching surfaces; Filippov solution; non-smooth analysis.

DOI: 10.1504/IJMIC.2009.027216

International Journal of Modelling, Identification and Control, 2009 Vol.7 No.3, pp.294 - 304

Published online: 17 Jul 2009 *

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