Practical stability margins in continuous higher order sliding mode control systems

Abstract

The finite time convergence of a sliding variable to zero in systems of arbitrary relative degree can be provided by Continuous Higher Order Sliding Mode (C-HOSM) control regardless of external bounded perturbations and without artificially increasing relative degree. In this work, metrics of robustness are introduced for C-HOSM control with respect to cascade unmodeled dynamics that are presented in any practical system. The frequency domain analysis of chattering in a dynamically perturbed system controlled by the C-HOSM controller is accomplished numerically using the Describing Function-Harmonic Balance technique via Newton–Raphson method. The robustness of C-HOSM controller to cascade unmodeled dynamics is quantified in terms of Practical Stability Phase and Gain Margins using the parameters of chattering (frequency and amplitude of the main harmonic) that may occur due to the unmodeled dynamics. The proposed methodologies are validated via simulations.