Higher order super-twisting algorithm

Generalization of the Super-Twisting algorithm (STA) for r relative degree system with respect to output, ensuring finite time convergence to the set σ, σ̇,..., π^(r) where σ represents the output via absolutely continuous control signal using information of σ, σ̇,..., π^(r)-1 are discussed. The convergence conditions for the 3-STA algorithm are proposed. The formula for algorithm of arbitrary order is suggested. The simulations results are confirmed the efficiency of the proposed algorithm.

I. Introduction

The sliding mode control [1] methodology is one such robust control technique which has its roots in the relay control. One of the most intriguing aspects of sliding mode is the discontinuous nature of the control action whose primary function is to switch between two distinctively different structures about some predefined manifold such that a new type of system motion called sliding mode exists in a manifold. This peculiar system characteristic is claimed to result in a superb system performance which includes insensitivity to parameter variations and complete rejection of certain class of disturbances. Furthermore, the system possess new properties which are not present in original system.