Sliding mode control of class of linear uncertain saturated systems

Abstract

This chapter 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 it is subject to constant limitations in amplitude. The uncertainty is being norm bounded reported on both dynamic and control matrices. In general, sliding mode control strategy consists on two essential phases. The design of the sliding surface is the first phase which 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. The controller design is the second phase of the sliding mode control design, which leads to the development of a continuous and non-linear control law. This nonlinear control law is build by choosing switched feedback gain capable of forcing the plant state trajectory to the sliding surface and maintaining a sliding mode condition. To give provider of robustness of the proposed nonlinear control, an approximation on the trajectory deviation of the uncertain saturated system compared to the ideal behavior is proposed. Finally, the validity and the applicability of this approach are illustrated by a multivariable numerical example of a robot pick and place.