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Abstract

Sliding mode control is a nonlinear feedback control technique which provides good robustness against modeling uncertainties and external disturbances. However, as the uncertainties or disturbances increase, a greater control input is required, and the control signal may cause an undesirable chattering phenomenon. In general, the further the system trajectory from the origin, the more violent the chattering effect. However, as the trajectory moves closer to the origin, the degree of chattering gradually reduces. As a result, even if an attempt is made to eliminate chattering by introducing a small constant boundary layer around the sliding surface, the chattering phenomenon may still take place during the transient stage. Furthermore, if the thickness of the boundary layer is increased in order to suppress chattering completely, control accuracy may be lost. Accordingly, this study proposes four different variable-thickness boundary layers designed to achieve a compromise between the desire to eliminate the chattering phenomenon and the need to retain control accuracy. In two of these boundary layers, the thickness is approximately proportional to the norm of the normalized state vector; while in the other two layers, the thickness tends toward a saturated value as the trajectory moves further from the origin. The feasibility and effectiveness of the proposed approaches are verified through their application to several representative numerical examples.

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