Sliding order and sliding accuracy in sliding mode control

TLDR

Sliding mode control steers nonlinear systems to a desired manifold and maintains them there, typically via high‑frequency switching of the control input. The paper introduces a new class of sliding modes and defines the concept of sliding mode order. The proposed algorithms employ bounded, time‑continuous control with discontinuities confined to the control derivative. The authors show that sliding accuracy is proportional to the switching time delay, and for the new algorithms it scales with the square of that delay. Contributors: ARIE LEVANT (formerly L.

Abstract

Abstract The synthesis of a control algorithm that stirs a nonlinear system to a given manifold and keeps it within this constraint is considered. Usually, what is called sliding mode is employed in such synthesis. This sliding mode is characterized, in practice, by a high-frequency switching of the control. It turns out that the deviation of the system from its prescribed constraints (sliding accuracy) is proportional to the switching time delay. A new class of sliding modes and algorithms is presented and the concept of sliding mode order is introduced. These algorithms feature a bounded control continuously depending on time, with discontinuities only in the control derivative. It is also shown that the sliding accuracy is proportional to the square of the switching time delay. Additional informationNotes on contributorsARIE LEVANTFormerly, L. V. Levantovsky