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

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.