Micro-Machined Gyroscope Mathematical Model and Error Analysis

2014 ◽  
Vol 609-610 ◽  
pp. 1144-1152
Author(s):  
Miao Wen Deng ◽  
Bing Mo ◽  
Chao Dong Ling ◽  
Rong Hai Huang ◽  
Su Ki Kim
Keyword(s):  
Mathematical Model ◽  
Angular Velocity ◽  
Theoretical Analysis ◽  
Error Analysis ◽  
Coriolis Force ◽  
Fabrication Technology ◽  
Measuring Accuracy ◽  
Mathematical Expressions ◽  
Micromachined Gyroscope ◽  
Important Significance

Abstract:The micro-machined gyroscope that uses Coriolis force to measure angular velocity has non-linear error,which makes the amplitude of angular velocity have a relationship with its frequency,and fabrication technology error,which leads gyroscope’s drive shaft and detection shaft not to be vertical.All kinds of errors severely restrict this kind of gyroscope’s measuring accuracy and application range.This article obtained the reason for the formation of all kind of gyroscope’s errors and their mathematical expressions through analyzing the principle of micromachined gyroscope,which uses Coriolis force to measure angular velocity.At the same time,the gyroscope mathematical model was established and used to emulate to analyze each error’s influence on the angular velocity measured by gyroscope.The conclusion obtained by theoretical analysis and simulation provides the basis for gyroscope’s error analysis and elimination,and it has an important significance in improving the measuring accuracy of gyroscope.

On the displacements of the contours of the optic-electronic space images. Mathematical modeling of displacement

2017 ◽  
Vol 992 (4) ◽  
pp. 32-38 ◽  
Author(s):  
E.G. Voronin
Keyword(s):  
Mathematical Modeling ◽  
Remote Sensing ◽  
Mathematical Model ◽  
Point Of View ◽  
Design Features ◽  
Space Images ◽  
Electronic Imaging ◽  
Measuring Accuracy ◽  
Physical Laws

The article opens a cycle of three consecutive publications dedicated to the phenomenon of the displacement of the same points in overlapping scans obtained adjacent CCD matrices with opto-electronic imagery. This phenomenon was noticed by other authors, but the proposed explanation for the origin of displacements and the resulting estimates are insufficient, and developed their solutions seem controversial from the point of view of recovery of the measuring accuracy of opticalelectronic space images, determined by the physical laws of their formation. In the first article the mathematical modeling of the expected displacements based on the design features of a scanning opto-electronic imaging equipment. It is shown that actual bias cannot be forecast, because they include additional terms, which may be gross, systematic and random values. The proposed algorithm for computing the most probable values of the additional displacement and ways to address some of the systematic components of these displacements in a mathematical model of optical-electronic remote sensing.

Mathematical Model Establishment and Analysis on the Pipe Deformation under External Pressure with the Ovality

2013 ◽  
Vol 760-762 ◽  
pp. 2263-2266
Author(s):  
Kang Yong ◽  
Wei Chen
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Yield Strength ◽  
Residual Stresses ◽  
Numerical Simulations ◽  
Significant Influence ◽  
External Pressure ◽  
Pipe Diameter ◽  
Axial Loads ◽  
The Stability

Beside the residual stresses and axial loads, other factors of pipe like ovality, moment could also bring a significant influence on pipe deformation under external pressure. The Standard of API-5C3 has discussed the influences of deformation caused by yield strength of pipe, pipe diameter and pipe thickness, but the factor of ovality degree is not included. Experiments and numerical simulations show that with the increasing of pipe ovality degree, the anti-deformation capability under external pressure will become lower, and ovality affecting the stability of pipe shape under external pressure is significant. So it could be a path to find out the mechanics relationship between ovality and pipe deformation under external pressure by the methods of numerical simulations and theoretical analysis.

Attenuation of pulsations in the reciprocating compressor piping system with an elbow-shaped surge tank

2018 ◽  
Vol 233 (5) ◽  
pp. 1677-1689
Author(s):  
Quyang Ma ◽  
Guoan Yang ◽  
Mengjun Li
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Frequency Analysis ◽  
Transfer Matrix Method ◽  
Piping System ◽  
Pulsation Frequency ◽  
Reciprocating Compressor ◽  
Pressure Pulsations ◽  
Surge Tank ◽  
The Mathematical Model

An elbow-shaped surge tank is proposed to suppress the pressure pulsations. The transfer matrix method was developed and the mathematical model was established to predict the distribution of pressure pulsations in the piping system (on which a surge tank was already installed) with an elbow-shaped surge tank. Simulation work of the whole piping system was performed. The results show that the elbow-shaped surge tank has good performance to attenuate the pressure pulsations. The frequency analysis shows that the amplitude for the first pulsation frequency is attenuated to a low level. The impulse response was analyzed to examine the efficiency of suppressing pulsations by using the suppressor. The theoretical analysis showed that there exists the optimal suppression performance when setting the distance between the elbow-shaped surge tank and the existing one. Meanwhile, modifying the ratio of length to diameter with a fixed surge volume could also impact the pressure pulsations. The analysis results can be used as a reference in designing and installing the elbow-shaped surge tank.

scholarly journals A Mathematical Model and Error Analysis of Shearer Cutting Path Based on Its Attitude

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Shi-bo Wang ◽  
Shijia Wang ◽  
Zhaoliang Ge
Keyword(s):  
Mathematical Model ◽  
Error Analysis ◽  
Inertial Navigation System ◽  
Coordinate Frame ◽  
Medium Thickness ◽  
Position Errors ◽  
Working Face ◽  
Coordinate Position ◽  
Thin Seam ◽  
Cutting Path

The horizon control system is the key technology in the automation of a shearer. The achievement of accurate shearer cutting path plays an important role for horizon control. A mathematical model of cutting path in the local geographic coordinate frame was built. Error analysis based on genetic algorithm (GA) was studied to guarantee the accuracy of the shearer cutting path. Parameters from a MG1000/2660-WD shearer and data from a working face were used to obtain the shearer cutting path with reference to the local geographic coordinate frame. Also, with error analysis based on GA, the desired sensors were chosen, which allowed coordinate position errors of a shearer’s cutting path to be less than 0.01 m. The desired accuracies of the inertial navigation system and encoders mounted on the different shearers used in thin seam, medium-thickness seam, and thick seam were calculated.

scholarly journals Allan variance in dynamically tuned inertial-unit gyro error analysis

2019 ◽  
pp. 69-77
Author(s):  
M. A. Sharova ◽  
S. S. Diadin
Keyword(s):  
Angular Velocity ◽  
Error Analysis ◽  
Output Signal ◽  
Allan Variance ◽  
Measurement Information ◽  
Noise Component ◽  
Velocity Sensor ◽  
Signal Noise ◽  
Variance Method ◽  
Inertial Unit

The purpose of the study was to consider an algorithm for obtaining the measurement information from a dynamically tuned gyroscope in the mode of an angular velocity sensor and output signal noise component estimate, the algorithm being based on the Allan variance method. The results obtained were evaluated

Constant Speed Motion Simulation and Error Analysis of Planar Non-Circular Curve Parts

2012 ◽  
Vol 220-223 ◽  
pp. 1559-1563
Author(s):  
Rui Wu ◽  
Li Bao ◽  
Yuan Kui Xu
Keyword(s):  
Mathematical Model ◽  
Error Analysis ◽  
Relative Error ◽  
Plane Curve ◽  
Simulation System ◽  
Constant Speed ◽  
Motion Simulation ◽  
Production Practice ◽  
The Mathematical Model ◽  
Circular Curve

The relative direction for a constant speed can be determined according to the planar non-circular curve parts. To establish the mathematical model, a constant speed motion simulation system is designed. The parameters of (vH=5mm/s, δ<3") is commonly used for the simulation system to simulate the movement of drawing the error curve. The results show that by controlling the movement of the plane curve parts in mathematical model can derive the basic constant speed, the relative error of constant speed is less than 3%, it provides a reliable bias when apply to production practice.

Velocity Control of a Cylindrical Rolling Robot by Surface-Morphing

2015 ◽  
Author(s):  
Michael Puopolo ◽  
J. D. Jacob
Keyword(s):  
Mathematical Model ◽  
Angular Velocity ◽  
Velocity Profile ◽  
Average Velocity ◽  
Equations Of Motion ◽  
Angular Position ◽  
Velocity Control ◽  
Control Scheme ◽  
Rolling Robot ◽  
Angular Velocity Profile

A mathematical model is developed for a rolling robot with a cylindrically-shaped, elliptical outer surface that has the ability to alter its shape as it rolls, resulting in a torque imbalance that accelerates or decelerates the robot. A control scheme is implemented, whereby angular position and angular velocity are used as feedback to trigger and define morphing actuation. The goal of the control is to direct the robot to follow a given angular velocity profile. Equations of motion for the rolling robot are formulated and solved numerically. Results show that by automatically morphing its shape in a periodic fashion, the rolling robot is able to start from rest, achieve constant average velocity and slow itself in order to follow a desired velocity profile with significant accuracy.

scholarly journals Theoretical Analysis and Adaptive Synchronization of a 4D Hyperchaotic Oscillator

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
T. Fonzin Fozin ◽  
J. Kengne ◽  
F. B. Pelap
Keyword(s):  
Mathematical Model ◽  
Adaptive Control ◽  
Theoretical Analysis ◽  
Electronic Circuit ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Exponential Nonlinearity ◽  
Dynamical Properties ◽  
Hyperchaotic Systems ◽  
Good Agreement

We propose a new mathematical model of the TNC oscillator and study its impact on the dynamical properties of the oscillator subjected to an exponential nonlinearity. We establish the existence of hyperchaotic behavior in the system through theoretical analysis and by exploiting electronic circuit experiments. The obtained numerical results are found to be in good agreement with experimental observations. Moreover, the new technique on adaptive control theory is used on our model and it is rigorously proven that the adaptive synchronization can be achieved for hyperchaotic systems with uncertain parameters.

Motion Control of an Electromechanical Micro Robot

2020 ◽  
Vol 63 (6) ◽  
pp. 57-65
Author(s):  
Ruzil Safiullin ◽  
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Motion Control ◽  
Elastic Element ◽  
Human Life ◽  
Robotic Systems ◽  
System Of Equations ◽  
Functional Modules ◽  
Innovative Technologies ◽  
Micro Robot

Currently, the development of innovative technologies in the field of electromechanics are microelectrome-chanical systems. They are widely used both in various industries and in domestic conditions of human life. An algorithm and a mathematical model of the design of an electromechanical composite microrobot have been developed. A system of equations of mechanics and electrodynamics was used to describe its metrological char-acteristics. By solving this system of equations, a theoretical analysis of the operation of its engine with a spiral secondary elastic element is carried out. Using the mechatronic approach, the buoyancy and coordination of its functional modules are studied. The results of this article will be useful for engineers involved in the design and operation of micro robots using robotic systems in the fields of biotechnology and biomechanics.

Fractional Order Modeling and Analysis of Buck-Boost Converter

2015 ◽  
Vol 789-790 ◽  
pp. 842-848
Author(s):  
Li Feng Yi ◽  
Kai Ru Zhang ◽  
Jun Liu
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Fractional Calculus ◽  
Simulation Model ◽  
Fractional Order ◽  
Theoretical Foundation ◽  
Boost Converter ◽  
Modeling And Analysis ◽  
Simulation Results ◽  
Conduction Mode

Considered the theoretical foundation of fractional order, the fractional mathematical model of the Buck-Boost converter in continuous conduction mode operation is built and analyzed in theory. Based on the improved Oustaloup fractional calculus for filter algorithm, the simulation model is framed by using the Matlab/Simulink software. And the simulation results are compared with that of integer order. It proves the correctness of the fractional order mathematical model and the theoretical analysis.

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