The dynamics of a bead sliding without friction along a periodically pulsating wire is under consideration. If the arc length of the wire is taken as the relevant coordinate, the motion of the bead is described by a periodic newtonian equation. Sufficient conditions are derived assuring that a given equilibrium is of twist type, a property that implies its nonlinear stability as well as a KAM s...

A classical control approach to stabilizing a dual inverted pendulum system with linear control is presented, along with measured results of the completed system. The emphasis of this work is on both the system’s implementation details and its role in a feedback course at the Massachusetts Institute of Technology. The control method includes a variety of techniques that makes this system not on...

The purpose of this paper is to present the design and program implementation of a general procedure which yields the mathematical model for a classical or rotary inverted pendulum system with an arbitrary number of pendulum links. Lagrange equations of the second kind with an integrated Rayleigh dissipation function are employed in model design, and the energetic balance relations, derived for...

−Inverted Pendulum is a well established benchmark problem that produces many challenges to a control engineer. It is a nonlinear, unstable, non minimumphase and under actuated system.Itrequires a controller which canadapt in different disturbance conditions and work appreciably well when compared to conventional controllers. In this paper Interval type-2 Fuzzy logic controllerfor inverted pend...

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 ...

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In this paper, we will propose a nonlinear passivity based controller fur a double inverted pendulum system, consisting of a two-link pendulum mounted on a pad which is moved by a linear induction motor so that the double pendulum points straight-up The proposed controller nut only can drive the double pendulum from its “natural stable hanging position” tu its “unstable upright inverted positio...

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 purpose of this article is to perform an indepth analysis of the classical double inverted pendulum system using the Inverted Pendula Modeling and Control (IPMaC), a Simulink block library designed by the authors of the paper. The custom function blocks included in the IPMaC offer comprehensive program support for the modeling, simulation and control of classical and rotary inverted pendula...