This paper summarizes the mechanical and control design concepts of an inverted or unstable pendulum where stabilization is achieved by a moment exchange generated by a controlled symmetric rotation of a rotational inertia attached to the pendulum. The proposed design of the pendulum has a fixed bottom rotation or point of support as opposed to the usual vertically or horizontally moving point ...

This paper concerns active vibration damping of a frictionless physical inverted pendulum with a radially moving mass. The motion of the inverted pendulum is restricted to an admissible set. The proposed Proportional Derivative linear controller damps the inverted pendulum (which is anchored by a torsion spring to keep it in a stable upright position), excerting a force on the radially moving m...

To use numerical investigation of functional differential equations it is very important to know if difference analogues of the considered differential equations have the reliability to preserve some general properties of these equations, in particular, property of stability. This problem is considered here by investigation of a difference analogue of the linear mathematical inverted pendulum. ...

In this paper we present a coordinating control law for a network of mechanical systems with unstable dynamics. The control law is derived using the Method of Controlled Lagrangians together with potential shaping designed to couple the mechanical systems. The coupled system is Lagrangian with symmetry, and energy methods are used to prove stability and coordinated behavior. The class of mechan...

This paper proposes a fuzzy classifier system (FCS) using fuzzy rules given by hyper-cone membership functions. The hyper-cone membership function is expressed by a kind of radial basis function, and its fuzzy rules can be flexibly located in input and output spaces. Therefore, The FCS can generate excellent rules which have the best location and shape of membership functions. We apply the FCS ...

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...

The mixed μ synthesis is proposed for mechanical systems. In this method, both the real parametric and the complex uncertainties are handled together. A compensator that achieves nominal performance and meets robust stability specifications can be designed. The method will be illustrated for an inverted pendulum device as an educational example and a suspension design problem as a practical exa...

This paper describes a procedure for incorporating artificial gyroscopic forces in the method of controlled Lagrangians. These energy-conserving forces provide additional freedom to expand the basin of stability and tune closed-loop system performance. We also study the effect of physical dissipation on the closed-loop dynamics and discuss conditions for stability in the presence of natural dam...

Properties of simple strategies for swinging up an inverted pendulum are discussed. It is shown that the behavior critically depends on the ratio of the maximum acceleration of the pivot to the acceleration of gravity. A comparison of energy-based strategies with minimum time strategy gives interesting insights into the robustness of minimum time solutions. ! 1999 Elsevier Science Ltd. All righ...

This work seeks to improve dynamic accuracy of viewpoint tracking for Augmented Reality. Using an inverted pendulum to model the head, dynamic orientation sensing in a vertical plane is achieved using only a dual axis accelerometer. A unique solution is presented as conventional approaches to solve the model equations fail to produce stable results due to ill conditioning. Accuracy is limited b...