Joint swing-up and stabilization of the Reaction Wheel Pendulum using Discontinuous Integral algorithm

• Published in: Nonlinear analysis. Hybrid systems Vol. 41; p. 101042
• Main Authors: Gutiérrez-Oribio, Diego, Mercado-Uribe, Ángel, Moreno, Jaime A., Fridman, Leonid
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2021
• Subjects: Finite-time stability; Nonlinear systems; Robust control; Uncertain Systems; Robust control; Uncertain Systems; Finite-time stability; Nonlinear systems
• ISSN: 1751-570X
• DOI: 10.1016/j.nahs.2021.101042

In this paper, a third-order discontinuous integral controller is designed to jointly swing-up and robustly stabilize in finite-time the upright position of the Reaction Wheel Pendulum (RWP) system, despite some uncertainties and perturbations. To show this, a numerical estimation of the domain of attraction of the controller is used. The control algorithm produces a continuous control signal, thus reducing the usual chattering effect of the sliding-mode controllers. The theoretical results of the paper are verified by simulations and experiments in a laboratory setup. •Global transformation of the RWP model to a global third-order chain of integrators.•A Third-Order Discontinuous Integral Algorithm (3-DIA) is designed.•Homogeneous Lyapunov function ensures (theoretically) local finite-time convergence.•3-DIA’s attraction domain allowing to cover both the upright and downward position.•Simulations and experiments are presented to provide evidence of the controller.•A comparison with a linear controller is also presented.