Analysis of Higher Order Sliding Mode Controllers with Boundary Layer Approximation.

The presence of chattering, i.e. high frequency oscillations with finite amplitude, is unavoidable in systems driven by conventional and higher order sliding mode (HOSM) control. A widely used technique to attenuate chattering is the boundary layer (BL) method; it is based on the approximation of discontinuous terms by a saturation function. However, sliding mode control (SMC) systems with BL approximation still presents chattering due to unmodeled dynamics. Amplitude and frequency of chattering can be estimated applying describing function (DF) and harmonic balance (HB) equation techniques. In this paper, HOSM controllers such as Twisting, Nested second order, and Super Twisting (ST) extension to relative degree two, with BL approximation, are analyzed. The effect of the BL value in the parameters of chattering is studied. When the BL value increments, chattering in systems driven by Twisting and Nested may decrease in amplitude, whereas in the case of ST-extension the variation in amplitude and frequency is minimum. Analysis for the case when the derivative in Twisting and ST-extension algorithms is computed via a linear differentiator is also included. Examples and simulations verifying the results are presented.