On the Dynamics of the Furuta Pendulum

Abstract

The Furuta pendulum, or rotational inverted pendulum, is a system found in many control labs. It provides a compact yet impressive platform for control demonstrations and draws the attention of the control community as a platform for the development of nonlinear control laws. Despite the popularity of the platform, there are very few papers which employ the correct dynamics and only one that derives the full system dynamics. In this paper, the full dynamics of the Furuta pendulum are derived using two methods: a Lagrangian formulation and an iterative Newton-Euler formulation. Approximations are made to the full dynamics which converge to the more commonly presented expressions. The system dynamics are then linearised using a Jacobian. To illustrate the influence the commonly neglected inertia terms have on the system dynamics, a brief example is offered.

Morap

“…Figure 6 shows the physical setup of a Furuta pendulum [5], a pendulum mounted at the end of a single jointed link. This experiment is a classic inverted pendulum problem, where a control algorithm has to be developed in order to keep the pendulum in an upright stabilized position.…”

“…The angle of the pendulum is measured by an MPU-9150 inertial measurement unit, con- nected on the main data bus through a slip ring, allowing for full 360 continuous rotation. As part of the case study, we model the pendulum in Modelyze using the explicit equations described by Cazzolarto et al [5], simulate it using the Modelyze simulator, and animate it in MATLAB (see Figure 7). Equation-based modeling showed that controlling the pendulum worked in simulation.…”

Control De Un Péndulo De Furuta. Una Revisión Del Estado Del Arte.

“…En el año 2010 apareció nuevamente interés en el modelado del péndulo de Furuta, así se realizó un estudio (reporte técnico de la universidad de Adelaida, Australia) [41] donde se obtuvo el modelo matemático del péndulo invertido rotacional por medio de dos métodos, el primero es a partir de la formulación del Lagrangiano y el otro con el método iterativo de Newton-Euler. Se realizaron aproximaciones a la dinámica completa la cual converge a la expresión comúnmente presentada para el modelo, el trabajo fue presentado por Ben S. Cazzolato y Zebb Prime.…”

Dynamic Analysis of the Tilted Furuta Pendulum

“…These works highlighted the complexity of the dynamic model and the necessity to simplify based on several assumptions. The authors of [1,4] proposed a linearized model based on a small angle assumption. Others neglected one or more of the cross coupling terms relating the two rotations [1].…”

“…Others neglected one or more of the cross coupling terms relating the two rotations [1]. The authors of [2,4] showed, through simulations, that this assumption is not acceptable and it could have an important effect on the dynamic response. To the best knowledge of the authors, there is no work in the literature that carries time-extended experimental tests and validates the results against the deduced model.…”