Analysis and design of systems driven by finite-time convergent controllers: practical stability approach

摘要

A concept of the practical stability margins for systems driven by finite-time convergent (FTC) controllers, including sliding-mode/higher order sliding-mode (HOSM) controllers, is proposed. These margins are based on the system's tolerance to self-sustained oscillations with certain amplitude and frequency limits. The practical stability margins are introduced as the maximal gain increase or/and the maximal phase lag added to the frequency characteristic of the linear part of the open-loop system that yields acceptable loss of system's stability/performance in terms of admissible parameters of self-sustaining oscillations. It is proposed using the describing function-harmonic balance technique for the identification of the practical stability margins. To ensure the desired practical stability margins, linear dynamics compensators are designed and added in cascade to FTC controllers. The proposed approach is verified on numerous examples.