Lyapunov’s direct method for stabilization of the Furuta pendulum
نویسندگان
چکیده
This paper presents a novel stabilization result for the Furuta pendulum for a large region of attraction including almost all of the upper half plane. The solution is obtained via constructing a Lyapunov function after set of coordinate changes. Then, a set of differential equations are solved to achieve asymptotic stability which is proved in accordance with La Salle’s invariance principle. The effectiveness of the proposed stabilization method is illustrated with simulation studies.
منابع مشابه
A controller for swinging-up and stabilizing the inverted pendulum
The hybrid solution to the pendulum swinging-up and stabilizing problem introduced by Åström and Furuta is based in two steps: an energy injection and a linear stabilization around the desired inverted position. However the energy injection stage only considers the pendulum, and not the motion of the pivot. Furthermore, for the stabilization stage linear law, only a very small basin of attracti...
متن کاملA Normal Form for Energy Shaping: Application to the Furuta Pendulum
In this paper we derive a nonlinear control law for stabilization of the Furuta pendulum system with the pendulum in the upright position and the rotating rigid link at rest at the origin. The control law is derived by first applying feedback that makes the Furuta pendulum look like a planar pendulum on a cart plus a gyroscopic force. The planar pendulum on a cart is an example of a class of me...
متن کاملNon-smooth Approach for Contact Dynamics and Impulse-based Control of Frictional Furuta Pendulum
School of Astronautics Department of Astronautics Engineering and Mechanics Bachelor of Engineering Non-smooth Approach for Contact Dynamics and Impulse-based Control of Frictional Furuta Pendulum by Hantian Zhang In this thesis, a non-penetrated and physically consistent non-smooth numerical approach has been proposed, by employing the Prox formulation and Moreau’s mid-point time-stepping rule...
متن کاملGeometric Formulations of Furuta Pendulum Control Problems
A Furuta pendulum is a serial connection of two thin, rigid links, where the first link is actuated by a vertical control torque while it is constrained to rotate in a horizontal plane; the second link is not actuated. The second link of the conventional Furuta pendulum is constrained to rotate in a vertical plane orthogonal to the first link, under the influence of gravity. Methods of geometri...
متن کاملA linear differential flatness approach to controlling the Furuta pendulum
The aim of this work is to motivate the use of linear flatness, or controllability, to design a feedback control law for the rather challenging mechanism known as the ‘Furuta pendulum’. This is achieved by introducing three feedback controller design options for the stabilization and rest-to-rest trajectory tracking tasks: a direct pole placement approach, a hierarchical high-gain approach and ...
متن کامل