A Multi-Axial Electromechanically-Coupled Homogenized Energy Model for Ferroelectric Materials

2017 ◽  
Author(s):  
William S. Oates ◽  
Ralph C. Smith
Keyword(s):  
Large Scale ◽  
Three Dimensional ◽  
Ferroelectric Materials ◽  
Energy Model ◽  
Three Dimensions ◽  
Real Time Control ◽  
Proportional Loading ◽  
Time Control ◽  
Homogenized Energy Model ◽  
Applied Fields

In this paper, we discuss the development and implementation of a 3-D electromechanically coupled homogenized energy model (HEM) for ferroelectric materials. A stochastic-based methodology is introduced and applied to problems involving large scale switching of ferroelectric and ferroelastic materials. Switching criteria for polarization variants are developed using density distributions in three dimensions to accommodate both electrical and mechanical loading and their coupled response. The theory accommodates non-proportional loading and major/minor loop hysteresis. Such formulations are known to accelerate computations for real-time control of nonlinear and hysteretic actuators. The proposed formulation maintains superior computational efficiency in the three dimensional case through the application of density formulations that are based on internal distributions of stress and electric field to produce a distribution of polarization switching events over a range of applied fields and stresses.

The Homogenized Energy Model for Characterizing Magnetization and Strains in Ferromagnetic Materials

2012 ◽  
Author(s):  
Lucus Van Blaircum ◽  
Ralph C. Smith
Keyword(s):  
Model Calibration ◽  
Ferromagnetic Materials ◽  
Energy Model ◽  
Real Time Control ◽  
Macroscopic Models ◽  
Time Control ◽  
Rate Dependent ◽  
Homogenized Energy Model ◽  
Domain Level ◽  
Control Implementation

Ferromagnetic materials exhibit rate-dependent hysteresis, creep and constitutive nonlinearities due to their inherent domain structure. For model-based control applications, these non-linear attributes must be incorporated in a models in a manner that facilitates model calibration and real-time control implementation. In this paper, we present a homogenized energy model for these materials. This is a multiscale framework that quantifies energy at the domain level and then employs stochastic homogenization techniques to provide macroscopic models that are highly efficient to implement. The accuracy of models will be validated using a variety of experimental data.

Motion control of a cable-suspended robot using image recognition with coordinate transformation

2020 ◽  
Vol 235 (1) ◽  
pp. 52-67
Author(s):  
Jonqlan Lin ◽  
Cheng-Kai Chiang
Keyword(s):  
Image Recognition ◽  
Coordinate Transformation ◽  
Large Scale ◽  
Material Handling ◽  
Three Dimensional ◽  
Real Time Control ◽  
Spatial Image ◽  
Time Control ◽  
Pick And Place ◽  
Vertical Height

This study will concern the implementation of a vision-based controller for cable-suspended robots, and especially for the pick-and-place function. This work will develop a novel algorithm that combines cable-suspended robot coordinate transformation with image recognition to manipulate the suspended gripper to the desired position for material-handling tasks. Two webcams sense the position of the end-effector; one will be used to calculate the horizontal planar coordinate of the target, and the other will be used to determine the vertical height of the target. Accordingly, the two-dimensional spatial image can be converted into three-dimensional image coordinates. Based on the sensed information, the robot can convert the position of the target to required cable lengths and then drive the servomotor to retract (or release) the cables to move the suspended gripper to the desired position. Various experiments will be conducted to verify the proposed methodology. The framework that is developed herein is easily implemented for real-time control and is suitable for inclusion in mechatronic kits in a university control course. The large variety of ideas that are addressed in this work apply to cranes, aerostats, and other large-scale manufacturing equipment that requires cable-driven robots.

Multi-Axial Homogenized Energy Model for Ferroelectric Materials

Aerospace ◽  
2006 ◽  
Author(s):  
William S. Oates ◽  
Ralph C. Smith
Keyword(s):  
Domain Switching ◽  
Three Dimensional ◽  
Ferroelectric Materials ◽  
Energy Model ◽  
Modeling Framework ◽  
Multi Scale ◽  
Modeling Approach ◽  
Scale Modeling ◽  
Multi Scale Modeling ◽  
Homogenized Energy Model

A multi-axial homogenized energy model is developed to account for nonlinear and hysteretic ferroelectric constitutive behavior induced by multi-axial electric field loading. The modeling approach extends a one-dimensional multi-scale modeling framework developed for ferroic materials [1, 2]. A three-dimensional energy function is introduced at the mesoscopic length scale and subsequently approximated as piecewise polynomial approximations to improve computational efficiency. Multi-scale field relations are then developed by introducing a distribution of effective electric fields and coercive fields that govern the nucleation of localized domain switching in polycrystalline ferroelectric materials. The distribution of field relations is used to relate the localized domain switching processes to observed macroscopic behavior by utilizing a stochastic homogenization technique. It is demonstrated that a simplified stochastic distribution of effective fields and coercive fields is sufficient to predict multi-axial ferroelectric switching in ferroelectric ceramics. Examples are given to validate the model in comparison to multi-axial loading experiments given in the literature. The model reduction provides a simple and efficient multi-scale modeling approach that is important for developing reliable piezoelectric actuator systems as well as implementation in model-based control of two and three dimensional structures.

A real-time control method-based simulation for high-speed trains on large-scale rail network

2017 ◽  
Vol 28 (10) ◽  
pp. 1750126 ◽  
Author(s):  
Yutong Liu ◽  
Chengxuan Cao ◽  
Yaling Zhou ◽  
Ziyan Feng
Keyword(s):  
Real Time ◽  
Traffic Flow ◽  
High Speed ◽  
Large Scale ◽  
Simulation Method ◽  
Real Time Control ◽  
Rail Network ◽  
Time Control ◽  
High Speed Trains ◽  
Rail Traffic

In this paper, an improved real-time control model based on the discrete-time method is constructed to control and simulate the movement of high-speed trains on large-scale rail network. The constraints of acceleration and deceleration are introduced in this model, and a more reasonable definition of the minimal headway is also presented. Considering the complicated rail traffic environment in practice, we propose a set of sound operational strategies to excellently control traffic flow on rail network under various conditions. Several simulation experiments with different parameter combinations are conducted to verify the effectiveness of the control simulation method. The experimental results are similar to realistic environment and some characteristics of rail traffic flow are also investigated, especially the impact of stochastic disturbances and the minimal headway on the rail traffic flow on large-scale rail network, which can better assist dispatchers in analysis and decision-making. Meanwhile, experimental results also demonstrate that the proposed control simulation method can be in real-time control of traffic flow for high-speed trains not only on the simple rail line, but also on the complicated large-scale network such as China’s high-speed rail network and serve as a tool of simulating the traffic flow on large-scale rail network to study the characteristics of rail traffic flow.

Synthetic reflection seismograms in three dimensions by a locked‐mode approximation

Geophysics ◽  
1989 ◽  
Vol 54 (3) ◽  
pp. 350-358 ◽  
Author(s):  
G. Nolet ◽  
R. Sleeman ◽  
V. Nijhof ◽  
B. L. N. Kennett
Keyword(s):  
Finite Difference ◽  
Born Approximation ◽  
Large Scale ◽  
Layered Medium ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Realistic Model ◽  
Three Dimensions ◽  
Acoustic Response ◽  
Many Sources

We present a simple algorithm for computing the acoustic response of a layered structure containing three‐dimensional (3-D) irregularities, using a locked‐mode approach and the Born approximation. The effects of anelasticity are incorporated by use of Rayleigh’s principle. The method is particularly attractive at somewhat larger offsets, but computations for near‐source offsets are stable as well, due to the introduction of anelastic damping. Calculations can be done on small minicomputers. The algorithm developed in this paper can be used to calculate the response of complicated models in three dimensions. It is more efficient than any other method whenever many sources are involved. The results are useful for modeling, as well as for generating test signals for data processing with realistic, model‐induced “noise.” Also, this approach provides an alternative to 2-D finite‐difference calculations that is efficient enough for application to large‐scale inverse problems. The method is illustrated by application to a simple 3-D structure in a layered medium.

scholarly journals A Survey on the Computation of Quaternions From Rotation Matrices

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Soheil Sarabandi ◽  
Federico Thomas
Keyword(s):  
Three Dimensional ◽  
Rotation Matrix ◽  
Three Dimensions ◽  
Attitude Dynamics ◽  
Euler Parameters ◽  
Four Dimensions ◽  
Rotation Matrices ◽  
Spacecraft Attitude Dynamics ◽  
Applied Fields ◽  
Quaternion Representation

The parameterization of rotations is a central topic in many theoretical and applied fields such as rigid body mechanics, multibody dynamics, robotics, spacecraft attitude dynamics, navigation, three-dimensional image processing, and computer graphics. Nowadays, the main alternative to the use of rotation matrices, to represent rotations in ℝ3, is the use of Euler parameters arranged in quaternion form. Whereas the passage from a set of Euler parameters to the corresponding rotation matrix is unique and straightforward, the passage from a rotation matrix to its corresponding Euler parameters has been revealed to be somewhat tricky if numerical aspects are considered. Since the map from quaternions to 3 × 3 rotation matrices is a 2-to-1 covering map, this map cannot be smoothly inverted. As a consequence, it is erroneously assumed that all inversions should necessarily contain singularities that arise in the form of quotients where the divisor can be arbitrarily small. This misconception is herein clarified. This paper reviews the most representative methods available in the literature, including a comparative analysis of their computational costs and error performances. The presented analysis leads to the conclusion that Cayley's factorization, a little-known method used to compute the double quaternion representation of rotations in four dimensions from 4 × 4 rotation matrices, is the most robust method when particularized to three dimensions.

Modeling, Model Reduction, and Control of a Hands-Free Two-Wheeled Self-Balancing Scooter

2020 ◽  
pp. 185-202
Author(s):  
Qiong Li ◽  
Wangling Yu ◽  
H. Henry Zhang
Keyword(s):  
Model Reduction ◽  
Large Scale ◽  
Power Transmission ◽  
System Response ◽  
Real Time Control ◽  
Time Control ◽  
Iteration Period ◽  
Synergistic Approach ◽  
Model Reduction Technique ◽  
And Control

Designing a two-wheeled self-balancing scooter involves in the synergistic approach of multidisciplinary engineering fields with mutual relationships of power transmission, mass transmission, and information transmission. The scooter consists of several subsystems and forms a large-scale system. The mathematical models are in the complex algebraic and differential equations in the form of high dimension. The complexity of its controller renders difficulties in its realization due to the limit of iteration period of real time control. Routh model reduction technique is employed to convert the original high-dimensional mathematical model into a simplified lower dimensional form. The modeling is derived using a unified variational method for both mechanical and electrical subsystems of the scooter, and for the electronic components equivalent circuit method is adopted. Simulations of the system response are based on the reduced model and its control design. A prototype is developed and realized with Matlab-Labview simulation and control environment.

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