Conventional and high order sliding mode control

• Published in: Journal of the Franklin Institute Vol. 357; no. 15; pp. 10244 - 10261
• Main Authors: Utkin, Vadim, Poznyak, Alex, Orlov, Yury, Polyakov, Andrey
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.10.2020; Elsevier Science Ltd
• Subjects: Control systems; Documents; Equations of motion; Manifolds (mathematics); Numerical analysis; Sliding mode control; Studies
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2020.06.018

Term “Conventional” sliding mode control (SMC) was introduced in the book Sliding Mode Control and Observation [1] by the authors, working in the area of high order sliding mode (HOSM) control. The term is related to all publications on n-dimensional systems with m- dimensional control and with sliding modes and state trajectories in a manifold of order n-m. Most of publications on HOSM control studied a new phenomenon for systems with a scalar control (m = 1), specifically, the existence of sliding modes in manifolds of dimension lower than n-1 with a finite reaching time. Along with implementation issues, it was natural to discuss to what extent the main principles of the conventional theory were to be revised (definitions, existence conditions, motion equations), what new properties of systems with HOSM can be expected. Partially these questions were discussed in [2] along with several international workshops on SMC and CDC in 2018. In this paper we demonstrate that main concepts are similar for both types of SMC, discuss new developments needed for HOSM control, compare the potential to suppress chattering, complexity of the both methods.