scholarly journals ABOUT THE INFLUENCE OF VIBRATIONS OF THE CONVEYED LIQUID ON THE AREA OF STABILITY OF A CLOSED SYSTEM AUTOMATIC VEHICLE COURSE CONTROL

2021 ◽  
pp. 29-41
Author(s):  
Yevgen Aleksandrov ◽  
Tetyana Aleksandrova ◽  
Alexander Grigoriev ◽  
Yaroslav Morhun
Keyword(s):  
Mathematical Model ◽  
Free Surface ◽  
Pid Controller ◽  
Low Frequency ◽  
Forced Oscillations ◽  
Liquid Lead ◽  
Variable Parameters ◽  
Course Stability ◽  
The Stability ◽  
Stability Area

The existing publications that investigate vehicle course stability optimization were analyzed. A mathematical model, which describes the disturbed movement of a car with a tank, was compiled. This model allows to consider the liquid free surface oscillations and determine their effect on the car course stability during constant motion or emergency braking. There was described the main information regarding the car that was used to perform mathematical calculations. An algorithm was developed for deriving the characteristic equation for a complex system of differential equations describing dynamic changes in the movement parameters of a car, oscillations of partial layers of liquid in a tank and the operation of an electromagnetic drive of the control valve and an electronic PID controller for a two-circuit system for ensuring course stability. Based on the developed mathematical model, the influence of forced oscillations of the fluid on the stability area of the system built in the plane of variable parameters of the controller is investigated. It is shown that low-frequency oscillations of the free surface of a liquid lead to a significant reduction in the stability area, which indicates the need to consider such oscillations when solving problems of analysis and synthesis of this system. It was found that for a car with a tank, where low-frequency transverse oscillations of the liquid occur, which are accompanied by a redistribution of mass and disturb the movement, an increase of the speed unambiguously leads to a deterioration in directional stability. That enables exclusion of speed from the number of variable parameters and significantly simplify the problem being solved. The calculations for cases with different loading levels were performed. It was found out that the level of liquid in the tank, considering its relationship with the speed, has an ambiguous effect on the car course stability, and it is unacceptable to limit the research calculations to the case with 50 % load. Instead of this, it is necessary to find a line that bends from above the stability boundaries that correspond to many liquid levels. Keywords: fluid vibrations; exchange rate stability system; area of stability; tank; PID-controller; parameters.

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

Resonance in a mathematical model of baroreflex control: arterial blood pressure waves accompanying postural stress

2005 ◽  
Vol 288 (6) ◽  
pp. R1637-R1648 ◽  
Author(s):  
Peter E. Hammer ◽  
J. Philip Saul
Keyword(s):  
Blood Pressure ◽  
Mathematical Model ◽  
Blood Volume ◽  
Low Frequency ◽  
Pressure Waves ◽  
Central Blood Volume ◽  
Arterial Baroreflex ◽  
Arterial Blood ◽  
Gain Margin ◽  
The Stability

A mathematical model of the arterial baroreflex was developed and used to assess the stability of the reflex and its potential role in producing the low-frequency arterial blood pressure oscillations called Mayer waves that are commonly seen in humans and animals in response to decreased central blood volume. The model consists of an arrangement of discrete-time filters derived from published physiological studies, which is reduced to a numerical expression for the baroreflex open-loop frequency response. Model stability was assessed for two states: normal and decreased central blood volume. The state of decreased central blood volume was simulated by decreasing baroreflex parasympathetic heart rate gain and by increasing baroreflex sympathetic vaso/venomotor gains as occurs with the unloading of cardiopulmonary baroreceptors. For the normal state, the feedback system was stable by the Nyquist criterion (gain margin = 0.6), but in the hypovolemic state, the gain margin was small (0.07), and the closed-loop frequency response exhibited a sharp peak (gain of 11) at 0.07 Hz, the same frequency as that observed for arterial pressure fluctuations in a group of healthy standing subjects. These findings support the theory that stresses affecting central blood volume, including upright posture, can reduce the stability of the normally stable arterial baroreflex feedback, leading to resonance and low-frequency blood pressure waves.

scholarly journals Instability of Liquid-Film Flows With Temperature-Dependent properties Down A Heated Incline

2021 ◽  
Author(s):  
Syeda Rubaida Zafar
Keyword(s):  
Mathematical Model ◽  
Free Surface ◽  
Stability Analysis ◽  
Marangoni Effect ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Temperature Dependent ◽  
The Stability ◽  
Temperature Dependent Properties ◽  
Film Flows

In this thesis we investigate the stability of free-surface flow on a heated incline. We develop a complete mathematical model for the flow which captures the Marangoni effect and also accounts for changes in the properties of the fluid with temperature. We apply a linear stability analysis to determine the stability of the steady and uniform flow. The associated eigenvalue problem is solved numerically by means of a spectral colocation method.

scholarly journals STABILITY AND VIBRATIONS OF THE ELECTRONIC CLOSED SYSTEM STABILIZING THE COURSE OF A CAR WITH A TANK

2021 ◽  
pp. 44-63
Author(s):  
Yevgen Aleksandrov ◽  
Tetyana Aleksandrova ◽  
Alexander Grigoriev ◽  
Yaroslav Morhun
Keyword(s):  
Free Surface ◽  
Low Frequency ◽  
Control Valve ◽  
Maximum Speed ◽  
Liquid Lead ◽  
The Road ◽  
Emergency Braking ◽  
Directional Stability ◽  
On The Road ◽  
Discrete Mathematical Model

To describe the disturbed movement of a car with a tank, a discrete mathematical model has been compiled, which allows one to take into account the oscillations of the free surface of the liquid and determine their effect on the directional stability of the car during uniform movement and during emergency braking. Linearization is carried out and an equation is obtained for the natural frequencies of oscillations of the electrohydromechanical system, which combines dynamic changes in the parameters of the movement of a car with a tank, partial layers of liquid in a tank and the operation of an electromagnetic drive of the control valve and an electronic PID controller for a two-circuit scheme to ensure directional stability. It is shown that low-frequency oscillations of the free surface of liquid lead to a significant reduction in the stability region, which indicates the need to take such oscillations into account when solving problems of analysis and synthesis of this system. It has been established that for a car with a tank, where low-frequency transverse oscillations of the liquid occur, which are accompanied by redistribution of mass and disturb the movement, an increase in the speed unambiguously leads to a deterioration in road-holding ability. This made it possible to exclude the speed from the variable parameters and significantly simplify the task. It was found that the liquid level in the tank, taking into account its connection with the maximum speed, has an ambiguous effect on the road-holding ability of the vehicle, and it is unacceptable to limit the research to calculations for 50 % of the load. Instead of this traditional simplification, it is necessary to find a line that bends from above those stability boundaries that correspond to many liquid levels from the entire range of their variation. It is shown that the dynamics of emergency braking weakly depends on the viscosity of the liquid in the tank, but with long-term continuous operation of the brake control system, self-oscillations appear in it. A method for tuning the parameters of an electronic regulator for low-amplitude self-oscillations is proposed.

Method of Variable Parameter PID Control Applied for AMB System

2012 ◽  
Vol 150 ◽  
pp. 75-79
Author(s):  
Hao Nan Tan ◽  
Jian Sheng Zhang
Keyword(s):  
Mathematical Model ◽  
Pid Control ◽  
Pid Controller ◽  
Variable Parameter ◽  
Electromagnetic Theory ◽  
Single Degree Of Freedom ◽  
Variable Parameters ◽  
Single Degree ◽  
Simulation Results ◽  
Amb System

According to electromagnetic theory, A single degree of freedom mathematical model of AMB system was established. We design a variable parameter PID controller based on the model. And the simulation results express that the variable parameters PID controller was better in the lots of indicators compared with the traditional PID controller.

Simulation Technologies for Tamper System of Asphalt-Paver Based on AMESim

2010 ◽  
Vol 129-131 ◽  
pp. 1098-1103 ◽  
Author(s):  
Tian Hong Luo ◽  
Xin Fu Gan ◽  
Wen Jun Luo
Keyword(s):  
Mathematical Model ◽  
Simulation Model ◽  
Pid Controller ◽  
Dynamic Performance ◽  
Operating Principle ◽  
Simulation Results ◽  
The Stability ◽  
The Mathematical Model

Tamper mechanism is one of the most important parts in all of Asphalt-pavers. In this article, the mathematical model of the tamper system has been established and the stability of the system has been analyzed by using Matlab. According to the operating principle of tamper system of Asphalt-paver, the simulation model of tamper system of Asphalt-paver has been established by using AMESim. The main parameters of the model were set, and then, the simulation results were analyzed, which show that the system is stable and the dynamic performance of system will be improved, when accumulator and PID controller were equipped. Besides, the tamping frequency of hammer is very important to the performance of system. When tamping frequency of hammer over 20HZ, the performance of system will go bad.

scholarly journals Instability of Liquid-Film Flows With Temperature-Dependent properties Down A Heated Incline

2021 ◽  
Author(s):  
Syeda Rubaida Zafar
Keyword(s):  
Mathematical Model ◽  
Free Surface ◽  
Stability Analysis ◽  
Marangoni Effect ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Temperature Dependent ◽  
The Stability ◽  
Temperature Dependent Properties ◽  
Film Flows

In this thesis we investigate the stability of free-surface flow on a heated incline. We develop a complete mathematical model for the flow which captures the Marangoni effect and also accounts for changes in the properties of the fluid with temperature. We apply a linear stability analysis to determine the stability of the steady and uniform flow. The associated eigenvalue problem is solved numerically by means of a spectral colocation method.

Application of the method of mathematical modeling for forecasting channel deformations at the underwater crossing of the main pipeline

2020 ◽  
Vol 10 (6) ◽  
pp. 599-609
Author(s):  
Valery А. Gruzdev ◽  
◽  
Georgy V. Mosolov ◽  
Ekaterina A. Sabayda ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Roughness Coefficient ◽  
Computational Domain ◽  
Channel Deformations ◽  
Geological Surveys ◽  
Kuban River ◽  
The Stability ◽  
Protective Structures

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

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