VSC Approach Angle Based Boundary Layer Thickness: A New Variation Law and Its Stability Proof

A major drawback on the use of sliding mode controllers is their inherent intense control activity. A usual strategy to cope with this problem is to use a boundary layer around the switching surface. The boundary layer thickness choice is based on a compromise between smoothness in the control action and tracking error. Since this compromise may be difficult to achieve, several boundary layer thickness variation laws (BLTVL) have been proposed in literature. In a recent study [1] an interesting BLTVL was proposed, based on the approach angle of the state to the switching surface. Although innovative, that study does not provide a proof of the stability of the controller. Furthermore, the BLTVL definition varies according to the system order and sliding surface definition. This paper extends the work done in [1] by presenting a new BLTVL based on a generalised definition of the approach angle that can be applied to systems of any order using any sliding surface. Furthermore, an innovative stability proof of a variable structure controller (VSC) using the new BLTVL is provided. Experimental results obtained in a servopneumatic system validate the usefulness of this approach.