A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the spherical 2D pendulum models as special cases. The case where the rigid body is asymmetric and the center of mass is distinct from the pivot location leads to t...

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 non-linear control laws. Despite the popularity of the platform there are very few papers which employ the correct dynamics and only one that de...

A device laboratory was designed to create a commanded disturbance to the Furuta inverted pendulum. This pendulum was modified by adding a second inverted pendulum coupled to the main one by means of a semi-rigid spring. The induced motion on the second inverted pendulum causes displacement of the center of mass of the system, producing a kind of perturbation similar to that presented on mobile...

The looping pendulum is a simple physical system consisting of two masses connected by string that passes over rod. We derive equations motion for the using Newtonian mechanics, and show these can be solved numerically to give good description system's dynamics. numerical solution captures complex aspects pendulum's behavior, in agreement with experimental results.

Various kinds of motion of a rigid pendulum (including swinging with arbitrarily large amplitudes and complete revolutions) are investigated both analytically and with the help of computerized simulations. The simulation experiments reveal many interesting peculiarities of this famous physical model and complement the analytical study of the subject in a manner that is mutually reinforcing. 1. ...

Problem statement: The rotary inverted pendulum system was a highly nonlinear model, multivariable and absolutely unstable dynamic system. It was used for testing various design control techniques and in teaching modern control. The objectives of this study were to: (i) Develop a real rotary inverted pendulum which derived the mechanical model by using Euler-Lagrange and (ii) Design controller ...

The purpose of this paper is to present the design and program implementation of expansions made to the existing general algorithmic procedure which yields the mathematical model for a classical inverted pendulum system with an arbitrary number of pendulum links. The expansions include the option to define the reference position of the pendulum in a planar coordinate system, to choose the refer...

As a precursor to capsize, marginal stability, resulting from incorrect loading conditions and crew negligence, poses a serious danger to ships. Therefore, as a benchmark problem for preventing capsize, the use of an actively controlled pendulum for the stabilization of a marginally stable ship was analyzed. Lyapunov stability criteria and closed loop eigenvalues were used to evaluate the exten...

This paper presents the control of an inverted pendulum system using intelligent algorithms, such as fuzzy logic and neural networks, for advanced control education. The swing up balancing control of the inverted pendulum system was performed using fuzzy logic. Because the switching time from swing to standing motion is important for successful balancing, the fuzzy control method was employed t...

This paper proposes a swing-up control scheme for a cart-type single pendulum having a serial second pendulum as a parasitic part. The proposed control scheme swings up the first pendulum with controlling the motion of a cart and being robust to the parasitic part. In the swing-up, the second pendulum is swinging at the top of the first pendulum and the motion of the second pendulum works as st...