Robust Sliding Mode Control of Class of Linear Uncertain Saturated Systems

B. Torchani(1*), A. Sellami(2), G. Garcia(3)

(1) Unit of Research C3S, ESSTT, Tunis, Tunisia
(2) Unit of Research C3S, ESSTT, Tunis, Tunisia
(3) University of Toulouse, LAAS-CNRS, Toulouse, France
(*) Corresponding author

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This paper proposes a new design approach of continuous sliding mode control of linear systems in presence of uncertainty and saturation. The saturation constraint is reported on inputs vector and uncertainty being norm bounded reported on both dynamic and control matrices. In a first step, the design of the sliding surface is formulated as a pole assignment of linear uncertain and saturated system in a specific region through convex optimization. The solution to this problem is therefore numerically tractable via linear matrix inequalities (LMI) optimization, which leads to the development of a continuous and non-linear control law. In a second step, an approximation on the trajectory deviation of the uncertain saturated system compared to the ideal behavior is proposed to provide robustness of the nonlinear control. Finally, the validity and the applicability of this approach are illustrated by a multivariable numerical example of a robot pick and place.
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Sliding Mode Control; Norm Bounded Uncertainty; Saturation; Robustness

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