Nonlinear control with friction compensation to swing-up a Furuta pendulum

• Published in: ISA transactions 2023-08, Vol.139, p.713-723
• Main Authors: Antonio-Cruz, Mayra, Hernandez-Guzman, Victor Manuel, Merlo-Zapata, Carlos Alejandro, Marquez-Sanchez, Celso
• Format: Article
• Language: English
• Subjects: Friction compensation; Furuta pendulum; Lyapunov method; Nonlinear control; Swing-up
• ISSN: 0019-0578; 1879-2022
• DOI: 10.1016/j.isatra.2023.05.007

Different works in literature have reported that nonlinear controllers based on the energy approach are not effective to completely swing-up an inverted pendulum subjected to friction. Most studies trying to solve this issue consider static friction models in the design of controllers. This consideration is mainly because the stability proof of the system with dynamic friction in closed-loop is difficult. Hence, this paper presents a nonlinear controller with friction compensation to swing-up a Furuta pendulum with dynamic friction. With this aim, we consider that only the active joint of the system is subjected to friction, which is represented via a dynamic model, namely, the Dahl model. We first present Furuta Pendulum dynamic model with dynamic friction. Then, by slightly modifying an energy-based controller that has been previously reported in literature and by including friction compensation, we propose a nonlinear controller that allows to swing-up completely a Furuta pendulum subjected to friction. The unmeasurable friction state is estimated through a nonlinear observer and a stability analysis of the closed-loop system is accomplished with the direct Lyapunov method. Finally, successful experimental results are presented for a Furuta pendulum prototype built by authors. This shows the effectiveness of the proposed controller in achieving a complete swing-up of the Furuta pendulum, in a time feasible for experimental implementation, and ensuring closed-loop stability. [Display omitted] The present paper proposes a nonlinear controller with dynamic friction compensation that experimentally achieves a complete swing-up for the Furuta pendulum in a short time, whose stability analysis is accomplished with the Lyapunov method •A nonlinear control to swing-up a Furuta pendulum with dynamic friction is proposed.•Control is an improved modification of an energy control previously reported.•Modification allows formally demonstrating swing-up accomplishment despite friction.•Three problems by friction in swinging-up inverted pendulums in practice are solved.•Improved performance of the control is successfully verified in practical application.