Adaptive Multi-Input Super Twisting Control for a Quadrotor: Singular Perturbation Approach

Abstract

Singular perturbations easily result in the problem of high gain. Instead of high gain feedbacks, this work proposes an adaptive two-time-scale (TTS) super twisting control (STWC) algorithm for the attitude tracking of a singularly perturbed quadrotor system (SPQS). The bounds of uncertainties are assumed to be perturbed around their nominal values. First, a nominal STWC with slow and fast control gains is designed to achieve the finite-time attitude tracking for the nominal SPQS. The finite-time stability of the close-loop system is proven by utilizing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -dependent Lyapunov method. Then, dynamically adapted slow and fast control gains initialized at their nominal values are used for the accurate finite-time convergence of tracking errors to the region around the origin, which avoids overestimating the values of control gains. Experimental results demonstrate the performance of the proposed controller in terms of attitude stabilization and tracking, and robustness to external disturbances.