N. Derbel and A.M. Alimi
Variable structure, sliding mode control, fuzzy control, automatic rule design
This paper is concerned with a framework that unifies sliding mode control (variable structure control) and fuzzy logic control. The result is a hybrid sliding-and-fuzzy logic controller design that eliminates some major limitations of the two individual controls while retaining the merits of both. The object of this work is to realize a sliding mode controller by fuzzy logic without the computation of the so-called equivalent control, which is usually complex to express analytically. The proposed method concerns systems ill-defined or difficult-to-express models describing their dynamical behaviour. It consists in subdividing the state space into cells. The main idea is to consider the centre point of each state cell and apply different possibilities of control values to the system starting from the cell centre point. Then, the system will enter to an adjacent cell. Next a graph is constructed for which each cell is represented by a node and each arc between two cells is labelled by the control and pondered by the corresponding cost. This graph will be simplified and optimized by dynamic programming, with the minimization of the norm of the generalized error, in order to obtain the fuzzy logic rules. This results in fuzzy rules that express adequate control giving a fuzzy sliding mode controller. This approach is validated by considering the trajectory control of robot manipulators.
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