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 ...

Inverted pendulum control is a well-known and challenging problem, which is generally associated to attitude control of a rocket during take off. This system consists of one input generating the cart driving force, and two outputs (linear position of the cart and angular position of the rod). The objective of this experimental design is to swing up the pendulum rod using an appropriate open loo...

The inverted pendulum is a simple system in which both stable and unstable configurations are easily observed. The upward inverted state is unstable, though it has long been known that a simple rigid pendulum can be stabilized against small disturbances in its inverted state by oscillating its pivot in an up-and-down motion. Numerical simulations of the inverted pendulum are employed to investi...

A torsion pendulum allows ground-based investigation of the purity of free-fall for the LISA test masses inside their capacitive position sensor. This paper presents recent improvements in our torsion pendulum facility that have both increased the pendulum sensitivity and allowed detailed characterization of several important sources of acceleration noise for the LISA test masses. We discuss he...

A pendulum is a bob of mass , attached to a frictionless pivot point via a massless rod of length . The bob is free to swing from side to side in a vertical plane. Let  denote the acceleration due to gravity. Let  denote the angle between the rod and a vertical axis. The pendulum has two equilibrium positions, a stable one at  = 0 (bottom) and an unstable one at  =  (top). Assume further...

We present a detailed account of our 2004 experiment to measure the Newtonian constant of gravitation with a suspended laser interferometer. The apparatus consists of two simple pendulums hanging from a common support. Each pendulum has a length of 72 cm and their separation is 34 cm. A mirror is embedded in each pendulum bob, which then in combination form a Fabry-Perot cavity. A laser locked ...

This paper obtains feedback stabilization of an inverted pendulum on a rotor arm by the “method of controlled Lagrangians”. This approach involves modifying the Lagrangian for the uncontrolled system so that the Euler-Lagrange equations derived from the modified or “controlled” Lagrangian describe the closed-loop system. For the closed-loop equations to be consistent with available control inpu...

In this paper we discuss theoretical and experimental investigations of the use of eddy current damping for multi-stage pendulum suspensions such as those intended for use in Advanced LIGO, the proposed upgrade to LIGO (the US laser interferometric gravitational-wave observatory). The design of these suspensions is based on the triple pendulum suspension design developed for GEO 600, the German...

This paper discusses Hamel’s formalism and its applications to structure-preserving integration of the ndimensional spherical pendulum. It utilizes redundant coordinates in order to eliminate multiple charts on the configuration space of the pendulum as well as nonphysical artificial singularities induced by local coordinates, while keeping the minimal possible degree of redundancy and avoiding...