Frequency Domain Analysis of Second Order Sliding Modes

Abstract

Higher order sliding modes (SM) and second order sliding modes (SOSM) in particular have received a lot of attention from the control research community over the last decade (See bibliography in [1]–[7] and references therein). The main advantages of the higher order SM algorithms over the first order classical SM are: a higher accuracy of motion, and the possibility of using continuous control laws (e.g. super twisting/twisting, sub-optimal, or the prescribed control law as filters). Those attractive features of SOSM allow viewing them as superior in some aspects in comparison with the classical first order SM. However, the main motivation for the development of SOSM control algorithms was eliminating chattering, which has been the main drawback of the SM [15].