Discrete-time sliding mode control of a class of linear uncertain saturated systems

Abstract

This paper proposes a new design approach of discrete-time sliding mode control of a class of linear uncertain systems in presence of saturation constraint. 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 quasi-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 optimisation. The solution to this problem is therefore numerically tractable via linear matrix inequalities optimisation. The controller design is the second phase of the sliding mode control design, which leads to the development of a continuous and nonlinear control law. An approximation on the trajectory deviation of the uncertain saturated system compared to the ideal behaviour 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.