Geometric Modeling and Robust Control of a Gyroscopic System

Gyroscopic systems are multi-body systems which present coupled three dimensional motion. The configuration space and the state space are differentiable manifolds, and differential geometric concepts are frequently useful in the process of modeling. This paper deals with a Control Moment Gyroscope (CMG), which is not asymptotically stable, so it needs a stabilizing control law. We apply a new methodology of modeling kinematics and dynamics of rigid multi-body systems, based in the concept of Cartan’s connection and covariant derivative. The systems has two inputs (torques) and two outputs (angles) that will be controlled by a robust linear closed-loop control technique (LQG/LTR). Experimental results are presented in order to validate the proposal.

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Geometric Modeling and Simulation of Mechanical Assemblies With Elastic Components

20th Design Automation Conference: Volume 1 — Dynamic Mechanical Systems; Geometric Modeling and Features; Concurrent Engineering ◽

10.1115/detc1994-0046 ◽

1994 ◽

Author(s):

Yong Fang ◽

F. W. Liou

Keyword(s):

Finite Element Method ◽

Geometric Modeling ◽

Three Dimensional ◽

Elastic Behavior ◽

Elastic Analysis ◽

Simulation Tool ◽

Body System ◽

Mechanical Assembly ◽

Mechanical Assemblies ◽

Multi Body

Abstract In this paper, the implementation of a modeling system for the simulation of three dimensional mechanical assemblies with elastic components is presented. A mechanical assembly is modeled as a multi-body system with changing topologies. The elastic behavior can be automatically modeled using finite element method. With this simulation tool, a designer can interactively create an assembly of mechanical components ready for dynamic and elastic analysis. This paper presents a prototype of the modeling system.

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The FPGA-Based Phase-Locked Loop Speed Control System of BLDCM for Magnetically Suspended Control Moment Gyroscope

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.80-81.1249 ◽

2011 ◽

Vol 80-81 ◽

pp. 1249-1257

Author(s):

Bang Cheng Han ◽

Dan He ◽

Fang Zheng Guo ◽

Yu Wang ◽

Bing Nan Huang

Keyword(s):

Control System ◽

Integrated Circuit ◽

High Speed ◽

Speed Control ◽

Phase Locked Loop ◽

Buck Converter ◽

Current Loop ◽

Loop Control ◽

Control Moment Gyroscope ◽

Control Moment

A phase-locked loop (PLL) control system based on field programmable gates array (FPGA) is proposed through analyzing the model of three-phase unipolar-driven BLDCM (brushless direct current motor) to enhance the reliability and accurate steady-state speed for magnetically suspended control moment gyroscope (MSCMG). The numerical operation module, PLL module and current-loop control module are designed based on FPGA using very-high-speed integrated circuit hardware description language (VHDL) to realize the control law of the digital system. The pulse width modulation (PWM) generating module for Buck converter, the commutation signal generating module for the inverter and ADC module are designed for driving the motor and sampling the current signal. The PLL is analyzed and optimized in the paper and all the modules are verified using the software of ModelSim and the experiments. The simulation and experiment results on BLDCM of MSCMG show that the stability of the motor velocity can reach 0.01% and 0.02% respectively by the PLL technology based on FPGA, which is difficult to be obtained by conventional proportion integral different (PID) speed control.

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Using Origami to Promote Geometric Communication

Mathematics Teaching in the Middle School ◽

10.5951/mtms.9.4.0222 ◽

2003 ◽

Vol 9 (4) ◽

pp. 222-229

Author(s):

Rebecca R. Robichaux ◽

Paulette R. Rodrigue

Keyword(s):

Geometric Modeling ◽

Spatial Reasoning ◽

Mathematics Classroom ◽

Three Dimensional ◽

Middle School Mathematics ◽

Mathematics Lesson ◽

Mathematical Arguments ◽

Spatial Sense ◽

Teaching Geometry ◽

Geometric Concepts

Rigami has been used frequently in teaching geometry to promote the development of spatial sense; to make multicultural connections with mathematical ideas; and to provide students with a visual representation of such geometric concepts as shape, properties of shapes, congruence, similarity, and symmetry. Such activities meet the Geometry Standard (NCTM 2000), which states that students should be engaged in activities that allow them to “analyze characteristics and properties of twoand three-dimensional geometric shapes and develop mathematical arguments about geometric relationships” and to “use visualization, spatial reasoning, and geometric modeling to solve problems” (p. 41). This article begins with an explanation of the importance of communication in the mathematics classroom and then describes a middle school mathematics lesson that uses origami to meet both the Geometry Standard as well as the Communication Standard.

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Coupled Simulation Study on the Working Device of the Excavator Based on VL Motion

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.229-231.1679 ◽

2012 ◽

Vol 229-231 ◽

pp. 1679-1683

Author(s):

Shao Xun Jin ◽

Hui Peng Chen ◽

Guo Jin Chen

Keyword(s):

Hydraulic System ◽

Three Dimensional ◽

Three Dimensional Model ◽

Coupled Simulation ◽

Device Structure ◽

Loop Control ◽

Closed Loop Control System ◽

Loop Control System ◽

Multi Body ◽

Working Device

On the foundation of analyzing the excavator’s working device structure, this paper built its three-dimensional model in Catia embedded in the VL Motion, created the bodies, defined the joints and corresponding drive interface to produce the multi-body dynamic model. According to the analysis on the hydraulic system of the working device, it built the electro-hydraulic system with the interface of Motion in AMEsim and then performed the coupled simulation between the Motion and AMEsim. Aiming at the working device’s performance defects, such as the worse displacement tracking, the slow respond, it designed the PID closed loop control system to improve the system’s performance. The simulation results show that the working device’s combination performance has been improved greatly, respond speed becomes fast and the ability of displacement tracking is better.

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