Design scheme of discrete time variable structure controllers applied to multi-input-multi-output linear systems with chattering elimination

Designing discrete time variable structure control with sliding mode (SM) schemes implies finding an asymptotically stable sliding surface with a control policy which assures the existence of a SM. Based on a recently innovative approach, where the authors developed a flexible design of sliding surfaces applied to discrete time linear multi-input multi-output (MIMO) systems, a novelty controller design strategy is proposed, where a switching surface parameter is used for the adjustment of the control signal limitations and for the improvement of the controlled system dynamics against model uncertainties. It is the first time that these drawbacks are solved modifying the switching surface values because it has been always resolved via control law adjustment. Moreover, a new chattering elimination method using adjustable sigmoid functions is also implemented in the controller. The main advantages of the proposed methodology are: firstly, it can be easily applied to high-order linear MIMO systems; secondly, system dynamics coordinates representation transformations are not needed and thirdly, the non-ideal SM dynamics is considered in the design procedure. Both the sliding surface and the control law specification are included in the proposed methodology. An illustrative example is included.