Mathematical modeling trajectory of a ship as a control object in global planning

In the article proposes the decomposition of the global planning task in local planning. It is proposed to combine the segment method and the sector method of division of the circle to construct the ship’s trajectory in local planning. Corrective coefficients were selected for the correct geometry of the turning trajectory, combining the segment method and the sector method of constructing the ship’s trajectory. The article uses formulas of spherical trigonometry; the trajectory of the turn depends on the rudder angle, which in turn depends on the turning ability of the vessel under the given conditions. In determining the value of the angle of the rudder, the control device must take into account the ship’s turning ability in the conditions set, the value of the angle of the turn and the constrained water area. The combination of all factors allows to differentiate the ship’s turning ability such as: high HG, middle MD or low LW with regard to passage area. The ME shifting operating modes matrix proposed in the article works as a filter of modes of operation and is completely dependent on the readings of pressure, temperature and vibration sensors. The ship’s trajectory is constructed using calculations in MS Excel and graphic simulations in the MATLAB environment.

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TASKS STATEMENT FOR MODERN AUTOMATIC CONTROL THEORY OF UNDERWATER COMPLEXES WITH FLEXIBLE TETHERS

EUREKA Physics and Engineering ◽

10.21303/2461-4262.2016.00158 ◽

2016 ◽

Vol 5 ◽

pp. 25-36 ◽

Cited By ~ 3

Author(s):

Valery Dudykevych ◽

Blintsov Oleksandr

Keyword(s):

Mathematical Modeling ◽

Automatic Control ◽

Control Systems ◽

Motion Control ◽

Control Object ◽

Synthesis Methods ◽

Automatic Control Systems ◽

Control Automation ◽

Control Under Uncertainty ◽

Consistent Solution

The definition of a new class of control objects is proposed. It is an underwater complex with flexible tethers (UCFT) for which there is the need to automate motion control under uncertainty and nonstationarity of own parameters and external disturbances. Classification of marine mobile objects and characteristics of the flexible tethers as UCFT elements is given. The basic UCFTs configurations that are used in the implementation of advanced underwater technologies are revealed. They include single-, double- and three-linked structures with surface or underwater support vessels and self-propelled or towed underwater vehicles. The role of mathematical modeling in tasks of motion control automation is shown. The tasks of UCFT mathematical modeling are formulated for synthesis and study of its automatic control systems. Generalized structures of mathematical models of UCFT basic elements are proposed as the basis for the creation of simulating complex to study the dynamics of its motion. The tasks of UCFT identification as a control object are formulated. Their consistent solution will help to obtain a UCFT mathematical model. The basic requirements for UCFT automatic motion control systems are determined. Their satisfaction will ensure implementation of selected underwater technology. Areas of development of synthesis methods of UCFT automatic control systems are highlighted.

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Mathematical modeling and parametric identification of a model using the example of a water-heating unit

Pedagogy and Psychology ◽

10.51889/2020-1.2077-6861.13 ◽

2020 ◽

Vol 42 (1) ◽

pp. 103-109

Author(s):

Sarsenbek Zhusupbekov ◽

◽

Laulasyn Abzhanova ◽

Olzhas Nauryzbaev ◽

◽

...

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Least Squares ◽

Least Squares Method ◽

Mimo System ◽

Control Object ◽

Real Object ◽

Water Heating ◽

Heating Unit ◽

The Mathematical Model

The article is devoted to systemic issues related to the principles of mathematical modeling of technological objects, and the degree of adequacy of certain mathematical descriptions to real processes in these systems. In the article using the least squares method (least squares), a model of a water-heating unit is constructed as a MIMO system. The analysis of the process as a complex multi-connected control object. Based on the experimental data, a mathematical model is obtained in the state space of the water path. The adequacy of the mathematical model to the real object was established by directly comparing the output values of the object with the output values of the model. The results of a comparative assessment of the transition characteristics of the constructed mathematical model and the control object are presented. From the transient characteristics of the object and the mathematical model, it follows that the mathematical model fairly accurately and qualitatively describes the properties of the modeled object, i.e., it is adequate to the modeled object. The material presented allows you to teach a student to study processes by the method of mathematical modeling, including the preparation of a mathematical description, the choice of a solution method, software implementation of the model and verification of the model’s adequacy to a real object.

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Mathematical modeling of overhead crane under conditions of stress-strain state of metal structure as a control object

IOP Conference Series Materials Science and Engineering ◽

10.1088/1757-899x/1103/1/012018 ◽

2021 ◽

Vol 1103 (1) ◽

pp. 012018

Author(s):

A G Lenivtsev ◽

I V Dudanov ◽

A S Fadeev

Keyword(s):

Mathematical Modeling ◽

Strain State ◽

Control Object ◽

Metal Structure ◽

Overhead Crane ◽

Stress Strain ◽

Stress Strain State

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Моделирование акустико-электрического неразрушающего контроля дефектности диэлектрических материалов

Дефектоскопия ◽

10.31857/s0130308221020019 ◽

2021 ◽

pp. 3-14

Author(s):

А.А Беспалько ◽

А.П. Суржиков ◽

Д.Д. Данн ◽

Г.Е. Уцын ◽

М.В. Петров ◽

...

Keyword(s):

Mathematical Modeling ◽

Solid State ◽

Field Strength ◽

Electric Field ◽

Acoustic Impedance ◽

Acoustic Pulse ◽

Control Object ◽

Electromagnetic Response ◽

Electromagnetic Responses ◽

Electromagnetic Signals

The influence of defects in solid-state dielectric samples on the parameters of the electromagnetic response under deterministic acoustic influence on the control object is shown. The regularities of changes in the parameters of electromagnetic signals with variations and increases in the electric field strength vector relative to the contact of the sample materials and the defect are presented. It is shown that the amplitude-frequency parameters of the emitted electromagnetic signals are directly related to the acoustic impedance and conductivity of the contacting medium and the defect. The amplitudes of electromagnetic responses correspond to the distribution in time and space determined by mathematical modeling of mechanical stresses that occur in a defective system during the propagation of an acoustic pulse. Data on changes in the parameters of electromagnetic signals with an increase in the size of model defects in similar samples are presented.

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STABILITY ANALYSIS OF SOFTWARE MANIPULATOR MOVEMENTS USING MATHCAD

Journal of Rocket-Space Technology ◽

10.15421/451908 ◽

2019 ◽

Vol 27 (4) ◽

pp. 52-57

Author(s):

Natalya Sergeevna Ashchepkova

Keyword(s):

Mathematical Modeling ◽

Control System ◽

Stability Analysis ◽

Linear Equations ◽

Control Object ◽

Design Stage ◽

Extended Object ◽

The Matrix ◽

The Stability ◽

Conditions Of Stability

Abstract. The method of the stability analysis of the manipulator program movements with use of Mathcad applied programs package is offered. On the basis of the manipulator’s kinematic scheme, the matrices of homogeneous transformations of Denavit Hartenberg are formed and a mathematical model of the extended control object is drawn up. An outline of an extended object control system consisting of a manipulator and an actuator is presented. For example, the linear equations of the manipulator, actuators, meter and controller are considered. The task of synthesizing the manipulator control algorithm is to determine the coefficients of the matrix transfer function of the controller that satisfy the conditions of stability and quality of transients. Mathematical modeling of manipulator programmatic movements was performed using the Matchad application package. The analysis of simulation results allows us to evaluate: manipulator workspace, control system performance, grip positioning accuracy, dependence of grip positioning error on the nature of load and the law of motion. A change in the dynamic characteristics of an extended control object causes a change in the controllability of systems, for the considered example rang Q = 2, i.e. the system is fully controllable. This method can be used to analyze the manipulation of the manipulator at the design stage; allows to determine the influence of design, kinematic and dynamic parameters on the manipulation of the manipulator and perform mathematical modeling of the manipulator motion. Calculation examples are given that confirm the expediency and effectiveness of using the Mathcad application software package to solve this type of problem.

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