scholarly journals An approximate mathematical model for estimating the influence of vibrations on attached elements of a mobile robot video system

2021 ◽  
pp. 20-26
Author(s):  
A. A. Lobaty ◽  
M. М. Tatur ◽  
A. K. Ibrahim
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Mobile Robot ◽  
Random Process ◽  
Random Vibration ◽  
Experimental Studies ◽  
Mobile Platform ◽  
Special Equipment ◽  
Video System ◽  
Vibration Process

The problem of constructing and applying of mathematical model for assessing the influence of vibrations on the attached elements of the video system of a mobile robot is solved. This robot is considered as a mobile platform for placing of the special equipment for various purposes. The analysis of mathematical models and the results of experimental studies of vibrations of multi-support wheeled machine and its structural elements has been conducted. On the basis of this analysis, the form of a stochastic mathematical model of vibrations of the structure of a mobile robot has been substantiated. The vibration model is specified as a correlation function or spectral density of a random process for various conditions of the robot’s movement. Differential equations of the shaping filter for modeling а random vibration process with given characteristics are presented. Differential equations for the probabilistic moments of the vibration process are presented. Based on the equations for the probabilistic moments and the proposed formula, an assessment of events, which consist in exceeding the vibration amplitude of a given level was carried out. These events are named as outliers of a random process and characterize the range within the basic properties of the equipment installed on the mobile platform are preserved. An analytical study of a mathematical model to determine the intensity of emissions of a random vibration process has been carried out. The probabilistic characteristics of the vibration process and the intensity of emissions are determined. The obtained theoretical results make it possible to assess the performance of the elements of a video system installed on a mobile platform and to formulate the basic requirements for tolerances for their parameters. The results of computer modeling clearly showed the efficiency of the proposed mathematical model for assessing the influence of vibrations.

All-mode Validation of Calculations in the Analysis of Electric Power

2020 ◽  
Vol 11 (11) ◽  
pp. 28-37
Author(s):  
Aleksey A. SUVOROV ◽  
◽  
Alexander S. GUSEV ◽  
Mikhail V. ANDREEV ◽  
Alisher B. ASKAROV ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Power System ◽  
Electric Power ◽  
Field Data ◽  
Transient Stability ◽  
Experimental Studies ◽  
Electric Power System ◽  
Adequate Model ◽  
Simulation Results

The transient stability is the main condition for reliability and survivability operation of electric power system. The transient stability analysis is an extremely complex problem. It uses the results of numerical integration of differential equations that form a mathematical model of the power system. However, the mathematical model of a large-scale power system contains a rigid nonlinear system of extremely high-order differential equations. Such system cannot be solved analytically. The simplifications and limitations are used for improving the conditionality of the power system mathematical model in time-domain simulation. It decreases the reliability and accuracy of the simulation results. In this regard, it becomes necessary to validate them. The most reliable way of validation is to compare simulation results with field data. However, it is not always possible to receive the necessary amount of field data due to many power system states and a large amount of disturbances leading to instability. The paper proposes an alternative approach for validation: using an adequate model standard instead of field data. The prototype of Hybrid Real Time Power System Simulator having the necessary properties and capabilities has been used as the reference model. The appropriate sequence of actions has been developed for validation. The adequacy of proposed approach is illustrated by the fragments of the experimental studies

scholarly journals Mathematical and Analytical Evaluation of Paste Products Quality

2021 ◽  
Vol 4 (2) ◽  
pp. 332-344
Author(s):  
Victor Guts ◽  
Olga Koval ◽  
Svitlana Bondar
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Analytical Approach ◽  
Experimental Studies ◽  
Control Sample ◽  
Poultry Meat ◽  
Analytical Evaluation ◽  
Organoleptic Evaluation ◽  
Quality Of Food

Topicality. In modern conditions, the society feels a growing demand in products made from natural ingredients of high nutritional value. Such products include meat pastes, the quality of which depends on their recipe, technological processes, equipment, and modes of its operation. With the implementation of innovative technological regimes and new equipment, there is a necessity to determine and prognosticate the quality of food products at all stages of their production and sale. According to the mentioned above, as well as economic feasibility of using automated systems for technological processes management, there is a need to elaborate a new mathematical and analytical approach to assessing and prognosticating changes in the quality of meat paste with various additives. Aim and research methods. The aim of this research is to elaborate a method for modeling the material system state, based on differential equations of kinetics of biochemical processes, assessment, and prognostication of food quality. Research methods. The method of mathematical and analytical evaluation of the paste products quality is grounded on modified mathematical models, differential equations, visualisation of research results in the form of 3D graphs, obtained by using symbolic computer mathematics. The quality of new meat paste products is compared with the quality of the paste, which is assumed to be relatively optimal according to the main organoleptic parameters of sensory quality assessment and control sample. The control sample of the paste is cooked according to the classical technology, and the recipe (GSTU 4424:2005). The prototype samples are cooked according to the innovative technology, which involves adding mechanically deboned poultry meat to the main raw material. Results. New results of analytical and experimental studies of the quality of meat paste products, cooked according to the classic recipe with the use of mechanically deboned poultry meat, are offered. The method for determining the coefficients, included in the mathematical model for assessing the meat paste products quality, their analytical relation with the optimization parameter, is elaborated. The expediency of using modern methods of symbolic computer mathematics for solving and analysing differential equations, presenting results in 3D graphs, is proved. The conducted research makes it possible to prognosticate the quality of food products, to control possible changes in their recipe while using various additives, to carry out elaborating new paste products. Conclusions and discussion. Based on the results of theoretical and experimental studies, a new mathematical model for estimating the quality of meat paste products in the form of the first-order differential equation, is offered. Its analogue is the equations, recommended for modeling the processes of biochemical kinetics. It is proved that the computer programme of mathematical and analytical research and prognostication the foodstuff quality (Goots et al., 2018) is universal. The offered mathematical model makes it possible to envision the quality of meat paste products, based on organoleptic evaluation. With its help, it becomes possible to determine the vector of possible changes in product quality and its optimisation, while elaborating the 3D graph. Mathematical and analytical assessment of the new paste products quality highlights that the partial replacement of the main meat raw by mechanically deboned poultry meat, and in pastes, made according to classical technology and the GSTU recipe (4424:2005), does not really reduce the parameters of organoleptic evaluation. In some cases, they are even higher than in the control paste samples, and very close to optimal ones. This new mathematical and analytical approach to assessing the paste products quality is promising in new culinary products elaboration in the restaurant business.

scholarly journals MODELING OF THE MANAGEMENT SYSTEM OF A FULL-DRIVE FOUR-WHEEL AGRICULTURAL MOBILE ROBOT

2019 ◽  
Vol 4 (5) ◽  
pp. 147-154
Author(s):  
Т. Круглова ◽  
Tat'yana Kruglova ◽  
А. Власов ◽  
A. Vlasov
Keyword(s):  
Mathematical Model ◽  
Mobile Robot ◽  
High Precision ◽  
Management System ◽  
Mobile Platform ◽  
Control Algorithms ◽  
Modern Trend ◽  
Precision Control ◽  
Differential Drive ◽  
State Trajectory

Widespread robotization is a modern trend in the development of agriculture. Currently, various designs of robots are being actively implemented. They are aimed to replace a human when performing various tasks. Most of these robots are wheeled mobile platform, for which it is necessary to ensure high maneuverability and accuracy of control. This problem can be solved by developing optimal high-precision control algorithms, for the study of which it is advisable to use a mathematical model of a mobile agricultural robot. This article presents the results of modeling the movement of a four-wheel mobile robot with a differential drive that moves across a rectangular field along a “snake state” trajectory that is optimal by speed

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Identification and Model Predictive Position Control of Two Wheeled Inverted Pendulum Mobile Robot

2015 ◽  
Vol 73 (6) ◽  
Author(s):  
Amir A. Bature ◽  
Salinda Buyamin ◽  
Mohamad N. Ahmad ◽  
Mustapha Muhammad ◽  
Auwalu A. Muhammad
Keyword(s):  
Mathematical Model ◽  
System Identification ◽  
Mobile Robot ◽  
Inverted Pendulum ◽  
Position Control ◽  
Superior Performance ◽  
System A ◽  
Wheeled Inverted Pendulum ◽  
Simulation Results ◽  
Real Plant

In order to predict and analyse the behaviour of a real system, a simulated model is needed. The more accurate the model the better the response is when dealing with the real plant. This paper presents a model predictive position control of a Two Wheeled Inverted Pendulum robot. The model was developed by system identification using a grey box technique. Simulation results show superior performance of the gains computed using the grey box model as compared to common linearized mathematical model. 

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

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