In this paper, we consider hybrid models of mechanical systems undergoing impacts — Lagrangian hybrid systems, and study their periodic orbits in the presence of Zeno behavior, where an infinite sequence of impacts converges in finite time. The main result of this paper is explicit conditions under which the existence of stable periodic orbits for a Lagrangian hybrid system with perfectly plast...

The search for ever smaller violations of Einstein’s weak equivalence principle continues to be an important experimental goal at the close of the 20th century, with string theory providing new motivations. Currently, the most sensitive laboratory and terrestrial-scale tests are carried out with instrumentation based on the 18th century concept of the torsion pendulum, but not with 18th century...

The sway motion of crane can be successfully suppressed by properly shaping the reference command. Input shaping is a one type of feed-forward shaping method that is based on linear superposition. In this paper, we present the impact of double pendulum type overhead crane (DPTOC) system on the effectiveness of input shaping. An unshaped bang-bang input force is used to determine the characteris...

This paper addresses the problem of estimating human body dynamics from 3-D visual data. That is, our goal is to estimate the state of the system, joint angle trajectories and velocities, and the control required to produce the observed motion from indirect noisy measurements of the joint angles. For a two-link chain in the human body, we show how two independent spherical pendulums can be comp...

Inverted pendulum system is a complicated, unstable and multivariable nonlinear system. In order to control the angle and displacement of inverted pendulum system effectively, a novel double-loop digital PID control strategy is presented in this paper. Based on impulse transfer function, the model of the single linear inverted pendulum system is divided into two parts according to the controlle...

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...

We have built and tested a 3.5 m high-finesse Fabry-Perot prototype inteferometer with a precision ellipsometer for the QED test and axion search (Q & A) experiment. We use X-pendulum-double-pendulum suspension designs and automatic control schemes developed by the gravitational-wave detection community. Verdet constant and Cotton-Mouton constant of the air are measured as a test. Double modula...

A control system combining input shaping and feedback is applied to a double-pendulum bridge crane subjected to external disturbances. The external disturbances represent naturally occurring forces, such as gusting winds. The proposed control method achieves fast point-to-point response similar to open-loop input-shaping control. It also minimizes transient deflections and disturbance-induced r...

We have built and tested a 3.5 m high-finesse Fabry-Perot prototype inteferometer with a precision ellipsometer for the QED test and axion search (Q & A) experiment. We use X-pendulum-double-pendulum suspension designs and automatic control schemes developed by the gravitational-wave detection community. Verdet constant and Cotton-Mouton constant of the air are measured as a test. Double modula...

The natural sway of crane payloads is detrimental to safe and efficient operation. Under certain conditions, the problem is complicated when the payloads create a double-pendulum effect. Most crane control research to date has focused on single-mode dynamics. For example, several researchers have shown that signal-mode oscillations can be greatly reduced by properly shaping the inputs to the cr...