Sliding Mode Control for Systems with Fast Actuators: Singularly Perturbed Approach

Abstract

Singularly perturbed relay control systems with second order sliding modes are considered for the modeling of sliding mode control systems with fast actuators. For sliding mode control systems with fast actuators, sufficient conditions for the exponential decreasing of the amplitude of chattering and unlimited growth of frequency are found. The connection between the stability of actuators and the stability of the plant on the one hand and the stability of the sliding mode system as the whole on the other hand is investigated. The algorithm for correction of sliding mode equations is suggested for taking into account the presence of fast actuators. Algorithms are proposed to solve the problem of eigenvalues assignment or optimal stabilization for sliding motions using the additional dynamics of fast actuators.