scholarly journals SPECIAL VEHICLE MOTION STABILIZATION SYSTEM

2021 ◽  
pp. 37-41
Author(s):  
M. V. Lyashenko ◽  
V. V. Shekhovtsov ◽  
P. V. Potapov ◽  
A. A. Shvedunenko
Keyword(s):  
Pid Controller ◽  
Deflection Angle ◽  
Angular Displacement ◽  
Dynamic Equations ◽  
Engine Torque ◽  
Special Vehicle ◽  
Vehicle Motion ◽  
Motion Stabilization ◽  
The Deflection Angle ◽  
The Mathematical Model

The system of special vehicle (SV) motion stabilization during moving on a straight surface is modeled on the base of dynamic equations of the mathematical model. The movement is stabilized by using a PID controller, the angular displacement of the mass is selected to ensure a given speed of movement, and the deflection angle is stabilized by controlling the engine torque.

Modeling of Conductive Shape Memory Polymer Nanocomposites Based Structure From a Control Perspective

2013 ◽  
Author(s):  
He Shen ◽  
Yunjun Xu ◽  
Fei Liang ◽  
Jihua Gou ◽  
Bob Mabbott
Keyword(s):  
Shape Memory ◽  
Pid Controller ◽  
Shape Control ◽  
Deflection Angle ◽  
Shape Memory Polymer ◽  
Shape Memory Polymers ◽  
Unknown Parameters ◽  
Macro Scale ◽  
The Deflection Angle ◽  
Scale Behavior

Shape memory polymers (SMPs) can recover their original shape under external stimulus such as light, heat, pH, humidity, and electric power. However, the applications of SMPs are limited by the number of shapes they can memorize and whether or not these shapes can be precisely and repeatedly controlled. Although a vision based PID controller has been shown by the authors to be capable of controlling the deflection angle of a SMP structure, the repeatability and precision are still low. In order to enhance the robustness and repeatability of the SMP shape control system, in this paper, the macro-scale behavior model of the SMP structure from the control perspective is proposed and the unknown parameters are identified using real-time vision, temperature, and resistance signals.

scholarly journals Quantitative evaluation indexes of the spatial steering effect of directional perforation hydraulic fractures

2021 ◽  
pp. 014459872110102
Author(s):  
Lu Weiyong ◽  
He Changchun
Keyword(s):  
Quantitative Evaluation ◽  
Hydraulic Fracture ◽  
Deflection Angle ◽  
Hydraulic Fractures ◽  
Principal Stress Direction ◽  
Perforation Hole ◽  
Evaluation Indexes ◽  
Initiation Pressure ◽  
The Deflection Angle ◽  
Bending Fracture

To better evaluate the spatial steering effect of directional perforation hydraulic fractures, evaluation indexes for the spatial steering effect are first proposed in this paper. Then, these indexes are used to quantitatively evaluate existing physical experimental results. Finally, with the help of RFPA2D-Flow software, the influence of perforation length and azimuth on the spatial steering process of hydraulic fracture are quantitatively analysed using four evaluation indexes. It is shown by the results that the spatial deflection trajectory, deflection distance, deflection angle and initiation pressure of hydraulic fractures can be used as quantitative evaluation indexes for the spatial steering effect of hydraulic fractures. The deflection paths of directional perforation hydraulic fractures are basically the same. They all gradually deflect to the maximum horizontal principal stress direction from the perforation hole and finally represent a double-wing bending fracture. The deflection distance, deflection angle and initiation pressure of hydraulic fractures increase gradually with increasing perforation azimuth, and the sensitivity of the deflection angle to the perforation azimuth of hydraulic fractures also increases. With increasing perforation length, the deflection distance of hydraulic fractures increases gradually. However, the deflection angle and initiation pressure decrease gradually, as does the sensitivity.

scholarly journals OPERATOR-PRODUCT EXPANSION AND ANALYTICITY

1999 ◽  
Vol 14 (30) ◽  
pp. 4819-4840
Author(s):  
JAN FISCHER ◽  
IVO VRKOČ
Keyword(s):  
Operator Product Expansion ◽  
Deflection Angle ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Operator Product ◽  
Coupling Constant ◽  
Expectation Value ◽  
Euclidean Region ◽  
The Deflection Angle ◽  
Class Of Functions

We discuss the current use of the operator-product expansion in QCD calculations. Treating the OPE as an expansion in inverse powers of an energy-squared variable (with possible exponential terms added), approximating the vacuum expectation value of the operator product by several terms and assuming a bound on the remainder along the Euclidean region, we observe how the bound varies with increasing deflection from the Euclidean ray down to the cut (Minkowski region). We argue that the assumption that the remainder is constant for all angles in the cut complex plane down to the Minkowski region is not justified. Making specific assumptions on the properties of the expanded function, we obtain bounds on the remainder in explicit form and show that they are very sensitive both to the deflection angle and to the class of functions considered. The results obtained are discussed in connection with calculations of the coupling constant αs from the τ decay.

The precise calculations of the constant terms in the equations of motions of planets and photons of general relativity

2021 ◽  
Vol 34 (2) ◽  
pp. 183-192
Author(s):  
Mei Xiaochun
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Deflection Angle ◽  
Constant Term ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
The Deflection Angle ◽  
Equations Of Motions

In general relativity, the values of constant terms in the equations of motions of planets and light have not been seriously discussed. Based on the Schwarzschild metric and the geodesic equations of the Riemann geometry, it is proved in this paper that the constant term in the time-dependent equation of motion of planet in general relativity must be equal to zero. Otherwise, when the correction term of general relativity is ignored, the resulting Newtonian gravity formula would change its basic form. Due to the absence of this constant term, the equation of motion cannot describe the elliptical and the hyperbolic orbital motions of celestial bodies in the solar gravitational field. It can only describe the parabolic orbital motion (with minor corrections). Therefore, it becomes meaningless to use general relativity calculating the precession of Mercury's perihelion. It is also proved that the time-dependent orbital equation of light in general relativity is contradictory to the time-independent equation of light. Using the time-independent orbital equation to do calculation, the deflection angle of light in the solar gravitational field is <mml:math display="inline"> <mml:mrow> <mml:mn>1.7</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> . But using the time-dependent equation to do calculation, the deflection angle of light is only a small correction of the prediction value <mml:math display="inline"> <mml:mrow> <mml:mn>0.87</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> of the Newtonian gravity theory with a magnitude order of <mml:math display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . The reason causing this inconsistency was the Einstein's assumption that the motion of light satisfied the condition <mml:math display="inline"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> in gravitational field. It leads to the absence of constant term in the time-independent equation of motion of light and destroys the uniqueness of geodesic in curved space-time. Meanwhile, light is subjected to repulsive forces in the gravitational field, rather than attractive forces. The direction of deflection of light is opposite, inconsistent with the predictions of present general relativity and the Newtonian theory of gravity. Observing on the earth surface, the wavelength of light emitted by the sun is violet shifted. This prediction is obviously not true. Practical observation is red shift. Finally, the practical significance of the calculation of the Mercury perihelion's precession and the existing problems of the light's deflection experiments of general relativity are briefly discussed. The conclusion of this paper is that general relativity cannot have consistence with the Newtonian theory of gravity for the descriptions of motions of planets and light in the solar system. The theory itself is not self-consistent too.

Gauging the earth

2013 ◽  
Vol 97 (540) ◽  
pp. 413-420
Author(s):  
John D. Mahony
Keyword(s):  
Approximate Formula ◽  
Deflection Angle ◽  
School Science ◽  
Science Department ◽  
Measurement Apparatus ◽  
The Earth ◽  
Interesting Discussion ◽  
Simple Measurement ◽  
The Deflection Angle

In an earlier note by W. J. A. Colman [1], the reader was treated to an interesting discussion concerning a BBC programme about the earth's radius in the context of endeavours to determine it by an 11th century Persian mathematician, Al-Biruni. At the same time a modem but approximate formula that might not have been available to the ancients was proposed for the radius and, following that account, it is the purpose here to explore just how accurately one might determine the earth's radius using this formula together with a simple measurement apparatus (not a sophisticated astrolabe) that might be constructed from materials found in the garage of any DIY handyman, or indeed, in the laboratory of any school science department. A schematic for the configuration of an observer P at a height h above the earth (of radius R) where the deflection angle to the horizon is denoted by θ, is shown in Figure 1. Also shown in the figure is a ‘sighting tube’ of length L about which more will be said later.

Optimization Control of the Bullwhip Effect in Supply Chain Inventory

2014 ◽  
Vol 945-949 ◽  
pp. 3187-3190
Author(s):  
Hai Dong ◽  
Jin Hua Liu ◽  
Liang Yu Liu
Keyword(s):  
Mathematical Model ◽  
Supply Chain ◽  
Control Theory ◽  
Inventory Control ◽  
Pid Controller ◽  
Bullwhip Effect ◽  
Control Gain ◽  
Optimization Control ◽  
Suitable Combination ◽  
The Mathematical Model

The bullwhip effect was caused by fuzzy demand among the enterprises. In order to reduce this effect, control theory was applied to solve the inventory in supply chain. Firstly, inventory control in supply chain and the bullwhip effect was researched. Secondly, a kind of proportional integral differential (PID) controller was developed for inventory control in a three-level supply chain, and the mathematical model of the PID controller for inventory control was presented. Finally, the results show that the PID controller can evidently alleviate the bullwhip effect and inventory fluctuations under the suitable combination of control gain.

scholarly journals Tracking control and robustness study of shifting process

2018 ◽  
Vol 46 (2) ◽  
pp. 99-106
Author(s):  
Xin-xin Zhao ◽  
Chao Guan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Tracking Control ◽  
Pid Controller ◽  
Automatic Transmission ◽  
Good Control ◽  
Simulation Software ◽  
Control Effect ◽  
Engine Torque ◽  
Shift Quality

Heavy dump vehicles are usually working with big load changes and bad work environment, thus change the friction performance of transmission clutches, as well as great affect the shift quality seriously, which influence the vehicle performance. Many researchers developed a lot to design a useful automatic transmission control system. Using PID tracking control and Monte Carlo method, the controller based on an dynamic model was set up to analyze the shifting process of automatic transmission and its robustness in this paper．The shift process was divided into four stages, low-gear phase, torque phase, inertia phase and high-gear phase. The model presents the process from the first gear to the second gear when the torque has big change．Since the jerk and the friction work of clutch are both related to the speed of clutch which was easier to control, it was chose as the target to control the oil pressure for satisfying the requirement of shift quality．The simulation software, Maplesim and Simulink, were used to build the vehicle model and shifting controller for simulation under different working conditions, and the maximum jerk was changed from 34 m/s3 to 12 m/s3 after the optimization. In this paper the Monte Carlo has been used to quantize and evaluate the robustness of the closed-loop system for the friction coefficients and output torque of turbine variation leading by the friction feature parameters and throttle angle changed. Monte Carlo method was used to analyze the effectiveness and robustness of PID controller, which proves that it has good control effect when the throttle is ongoing minor fluctuations. When the throttle is full opening, a quadratic optimal controller based on disturbance is designed by the method of multi-objective optimization. When it changes within 20 percent, PID controller was designed under the guidance of tracking thoughts. The results also show that the controller could still obtain better effect when the friction coefficient ranged from -40 % to 40 % as well as engine torque changed from -20 % to 20 %, which indicates the robustness of controller.

scholarly journals Values estimation of deflection angle of a floating sensor for various objects (to the resistance to measuring the water surface rate)

2019 ◽  
Vol 5 (2) ◽  
pp. 181-196
Author(s):  
K. Presnyakov ◽  
G. Kerimkulova ◽  
G. Askalieva
Keyword(s):  
Water Surface ◽  
Deflection Angle ◽  
Surface Velocity ◽  
Informative Parameter ◽  
The Deflection Angle

A device is proposed for measuring the surface velocity of water, the use of which is based on the use of a new informative parameter — the deflection angle of the movable float sensor (together with the guide slide) from the vertical in the direction of the dynamic axis of the flow, allowing you to simply and reliably measure the surface velocity of water.

scholarly journals Weak Deflection Angle of some Classes of non-linear Electrodynamics Black Holes via Gauss-Bonnet Theorem

2020 ◽  
Author(s):  
Hasan El Moumni ◽  
Karima Masmar ◽  
Ali Övgün
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Lensing ◽  
Deflection Angle ◽  
Weak Field ◽  
Leading Order ◽  
Plasma Medium ◽  
Non Linear ◽  
The Deflection Angle ◽  
Bonnet Theorem

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the Gauss-Bonnet theorem for finding deflection angle in weak field limits. The effect of non-linear electrodynamics on the deflection angle in leading order terms is studied. Furthermore, we discuss the effects of the plasma medium on the weak deflection angle.

scholarly journals Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Junji Jia ◽  
Ke Huang
Keyword(s):  
Gravitational Lensing ◽  
Deflection Angle ◽  
Strong Field ◽  
Distance Effect ◽  
Critical Value ◽  
Field Limit ◽  
Perturbative Method ◽  
The Deflection Angle ◽  
The Impact ◽  
Strong Field Limit

AbstractA perturbative method to compute the deflection angle of both timelike and null rays in arbitrary static and spherically symmetric spacetimes in the strong field limit is proposed. The result takes a quasi-series form of $$(1-b_c/b)$$ ( 1 - b c / b ) where b is the impact parameter and $$b_c$$ b c is its critical value, with coefficients of the series explicitly given. This result also naturally takes into account the finite distance effect of both the source and detector, and allows to solve the apparent angles of the relativistic images in a more precise way. From this, the BH angular shadow size is expressed as a simple formula containing metric functions and particle/photon sphere radius. The magnification of the relativistic images were shown to diverge at different values of the source-detector angular coordinate difference, depending on the relation between the source and detector distance from the lens. To verify all these results, we then applied them to the Hayward BH spacetime, concentrating on the effects of its charge parameter l and the asymptotic velocity v of the signal. The BH shadow size were found to decrease slightly as l increases to its critical value, and increase as v decreases from light speed. For the deflection angle and the magnification of the images however, both the increase of l and decrease of v will increase their values.

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