ISSN 1991-2927
 

ACP № 2 (56) 2019

Author: "Olga Alekseevna Peregudova"

Aleksandr Sergeevich Andreev, Ulyanovsk State University, Doctor of Sciences in Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Tashkent State University; Head of the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks, and a monograph in the field of stability theory and the motion control of mechanical systems. [e-mail: AndreevAS@ulsu.ru]A. Andreev,

Olga Alekseevna Peregudova, Ulyanovsk State University, Doctor of Sciences in Physics and Mathematics, Associate professor; graduated from the Faculty of Mechanics and Mathematics of Ulyanovsk State University; Professor of the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks, a monograph in the field of the theory of stability and motion control of mechanical systems. [e-mail: peregudovaoa@gmail.com]O. Peregudova

Robust Motion Stabilization of a Mobile Robot with Omny-Wheels 56_9.pdf

The modelling as well as the design and widespread use of wheeled mobile robots in the industrial and social spheres is one of the areas of rapid development of robotics. A sufficiently large class of such robots consists of wheeled robots with roller-bearing or omni-wheels. A distinctive feature of the design of such wheels consisting in the fact that the rollers are fixed to them according to a certain scheme allows the robot to move in any direction without a prior turn. This achieves high maneuverability compared to other wheeled carriages. The paper investigates the trajectory tracking control problem of a mobile robot with three omni-wheels and with an offset center of mass, i.e. when it is assumed that the center of mass of the robot does not coincide with the geometric center of the platform. Previously, such a problem was not considered. The paper substantiates the control structure that provides tracking of a given trajectory, including taking into account the delay and discreteness of the signal in the feedback. At the same time the control has the property of robustness which consists in the fact that its parameters do not depend directly on the mass-inertial parameters of the system and the tracked trajectory. The controller is constructed only by using the values of the system parameters bounds. The result has been achieved on the basis of the development of direct Lyapunov method in the study of the stability of non-autonomous systems obtained in the previous papers of the authors. The results of numerical modeling of the problem studied are presented.

Wheeled mobile robot, robust control, stabilization, trajectory tracking, Lyapunov functional.

2019_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.



Aleksandr Sergeevich Andreev, Ulyanovsk State University, Doctor of Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Tashkent State University; Head of the Faculty of Mathematics, Information and Aviation Technologies at Ulyanovsk State University; Head of the Department of Information Security and Control Theory; an author of papers, textbooks, and a monograph in the field of stability theory and the motion control of mechanical systems. [e-mail: AndreevAS@ulsu.ru]A. Andreev,

Olga Alekseevna Peregudova, Ulyanovsk State University, Doctor of Physics and Mathematics, Associate Professor; graduated from the Faculty of Mechanics and Mathematics of Ulyanovsk State University; Professor at the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks, and a monograph in the field of stability theory and the motion control of mechanical systems. [e-mail: peregudovaoa@sv.ulsu.ru]O. Peregudova

On Motion Control of the Mechanical System on the Basis of Actuator Dynamics 000_3.pdf

The problem of stabilization of the holonomic mechanical system program motion is solved taking into account the actuator dynamics. As it is known, the implementation of control forces and moments for the mechanical systems occurs with the help of actuators (drives), their dynamics affects the motion process. Therefore, the requirement of control implementation precision for modern mechanical systems makes it necessary to take into account the actuator dynamics. The complexity of the problems of constructing the control laws for the mathematical models of mechanical systems with actuators involves the fact that the degrees of freedom of such a system has a higher dimension with respect to the vector of control signals. The paper presents a model of a mechanical system with a drive in the form of a cascade connection of two subsystems: the mechanical one and drives. Herewith, the vector of control for the mechanical subsystem is the state of the subsystem drives. Such representation allows to solve the control problem in the form of a two-step procedure. The first step includes construction of the mechanical subsystem control law in the form of a continuously differentiable time function of time, coordinates and velocities, which carries out the stabilization of the given program motion. After that, on the second step, the relay control law is constructed for a drive subsystem that ensures the asymptotic stability of a stabilizing control law. The specificity of the obtained result involves the use of the definite Lyapunov function, which significantly simplifies the calculations for justification of the relay control law and the terms of its implementation. As an example, the problem on stabilization of a program motion is solved for a space three-link manipulator controlled by three independent DC drives.

Mechanical system, stabilization, program motion, actuator dynamics, definite lyapunov function.

2016_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling.


Aleksandr Sergeevich Andreev, Ulyanovsk State University, Doctor of Physics and Mathematics, Professor; graduated from the Faculty of Mechanics and Mathematics of Tashkent State University; Head of the Faculty of Mathematics, Information and Aviation Technologies at Ulyanovsk State University; Head of the Department of Information Security and Control Theory; an author of papers, textbooks, and a monograph in the field of stability theory and the motion control of mechanical systems. [e-mail: AndreevAS@ulsu.ru]A. Andreev,

Olga Alekseevna Peregudova, Ulyanovsk State University, Doctor of Physics and Mathematics, Associate Professor; graduated from the Faculty of Mechanics and Mathematics at Ulyanovsk State University; Professor at the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks, and a monograph in the field of stability theory and the motion control of mechanical systems. [e-mail: peregudovaoa@sv.ulsu.ru]O. Peregudova

Two-link Manipulator Control Synthesis Without Velocity Measuring 000_9.pdf

The paper investigates the way to treat the problem of two-link manipulator program motion stabilization without velocity measuring. Most familiar strategies for mechanical system motion control including robot manipulators are based on the assumption that both coordinates and velocities of the mechanical system are available to measure. However, certain difficulties relating to practical application arise. These difficulties include, for example, inability of the velocity sensors installation due to various constraints. Another difficulty is connected with the fact that the operation of these sensors involves the problem of noise occurrence and, in consequence, the accuracy of the control problem solution can be decreased. The main approaches to the control problem of mechanical systems (such as manipulators) without measuring velocities apply approximate differentiation of the system coordinates as well as observer construction. These approaches are not fully developed for the problem of non-local stabilization of the manipulator non-stationary program motions because of such difficulties like non-linearity and non-stationarity of the system. The article provides the method of piecewise non-linear continuous control synthesis on the basis of both the construction of the observer and the application of the Lyapunov vector functions method. The novelty of the results consists in constructing the observer which dimension is smaller than the dimension of the system by a factor of two in order to solve the stabilization problem of a wide class of manipulator non-stationary motions without system linearization. The article presents the results of numerical simulation that prove obtained theoretical results.

Two-link manipulator, stabilization, program motion, control law without measuring velocity, comparison system, lyapunov vector function.

2015_ 4

Sections: Mathematical modeling

Subjects: Mathematical modeling.


Olga Alekseevna Peregudova, Ulyanovsk State University, Doctor of Physics and Mathematics, Associate Professor; graduated from the Faculty of Mechanics and Mathematics at Ulyanovsk State University; Professor at the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks, and a monograph in the field of stability theory and the motion control of mechanical systems. [e-mail: peregudovaoa@sv.ulsu.ru]O. Peregudova,

Denis Sergeevich Makarov, Ulyanovsk State University, a Post-Graduate Student; graduated from the Faculty of Mathematics and Information Technologies of Ulyanovsk State University; Junior Researcher at the Department of Scientific Research of Ulyanovsk State University; an author of articles in the field of the motion control of mechanical systems. [e-mail: prostodenis18@mail.ru]D. Makarov

Control Synthesis for Three-link Manipulator 000_12.pdf

A stabilization problem of the three-link manipulator program motion by providing continuous nonlinear control with direct and feedback communication is solved in this paper. The manipulator consists of three totally rigid links. The first link is fastened on a horizontal base and can pivot about a vertical axis. The second one is interconnected with the first and the third links by the ideal cylindrical hinges. Relative movements of the second and the third links are performed in a vertical place that pivots about a vertical axis due to the first link motion. Thus, the manipulator can perform three-dimensional motion. The manipulator motions are described by the system of Lagrange equations of the second kind. The problem on synthesis of the motion control of such system involves the control moment construction that allows the manipulator to carry out the .motion given by the program in real conditions of external and internal disturbances, and the inaccuracy of the model itself. A mathematical model of the manipulator controlled motion is constructed in this paper in case of control actions in the form of continuous control actions. By applying Lyapunov’s vector functions and the comparison systems the implementation of the built control laws in the stabilization task of the spectrum of the manipulator program motions was proved. The novelty of the results includes solving the stabilization problem of the non-stationary and nonlinear formulation, without using a linearized model, as well as the ability to stabilize not just one but a whole family of program motions. A numerical solution of the received system of differential equations using both continuous and discontinuous control laws is found. The corresponding graphs for the coordinates of the manipulator links proving the theoretical results are built.

Three-link manipulator, stabilization, program motion, continuous control, comparison system, lyapunov’s vector function.

2015_ 2

Sections: Mathematical modeling

Subjects: Mathematical modeling.


Olga Alekseevna Peregudova, Ulyanovsk State University, Doctor of Physics and Mathematics, Associate Professor; graduated from the Faculty of Mechanics and Mathematics at Ulyanovsk State University; Professor at the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks, and a monograph in the field of stability theory and the motion control of mechanical systems. [e-mail: peregudovaoa@sv.ulsu.ru]O. Peregudova,

Denis Sergeevich Makarov, Ulyanovsk State University, a post-graduate student; graduated from the Faculty of Mathematics and Information Technologies of Ulyanovsk State University; Junior Researcher at the Department of Scientific Research of Ulyanovsk State University; an author of articles in the field of the motion control of mechanical systems. [e-mail: prostodenis18@mail.ru]D. Makarov

Control Synthesis for Double-link Manipulator 38_4.pdf

A stabilization problem of a doubl-link manipulator program motion on a fixed base is solved in this paper. Totally rigid manipulator links are interconnected by an ideal cylindrical hinge and via the same hinge the first element is fastened to the base. Thus, the manipulator can perform motions in a vertical plane only. The manipulator motions are described by the system of Lagrange equations of the second kind. The problem on synthesis of the motion control of such system involves the construction of the laws of a control moments change that allow the manipulator to carry out the motion given by the program in real conditions of external and internal disturbances, and the inaccuracy of the model itself. A mathematical model of the manipulator controlled motion is constructed in this paper in case of control actions in the form of continuous and discontinuous functions bounded in modulus. By applying Lyapunov’s vector-functions and the comparison systems we justified the implementation of the built control laws in the stabilization task of the spectrum of the manipulator program motions. The novelty of the results includes solving the stabilization problem of the non-stationary and nonlinear formulation, without changing to a linearized model, as well as the ability to stabilize not just one but a whole family of program motions. With the help of Maple’s mathematical package a numerical solution of the received system of differential equations using both continuous and discontinuous control laws is found. The corresponding graphs for the coordinates and velocities of the manipulator links proving the theoretical results are built.

Multi-link manipulator, stabilization, program motion, relay control, comparison system, lyapunov’s vector-function.

2014_ 4

Sections: Automated control systems

Subjects: Automated control systems, Mathematical modeling.


Olga Alekseevna Peregudova, Ulyanovsk State University, Doctor of Physics and Mathematics, Associate Professor, graduated from the Mechanics and Mathematics Department of Ulyanovsk State University; Professor at the Department of Information Security and Control Theory of Ulyanovsk State University; an author of articles, textbooks, and a monograph on the theory of stability and motion control of mechanical systems. [e-mail: peregudovaoa@sv.ulsu.ru]O. Peregudova,

Konstantin Valerievich Pakhomov, Ulyanovsk State University, Post-graduate student; graduated from the Faculty of Mathematics and Information Technologies of Ulyanovsk State University; Junior Researcher of the Research Department of Ulyanovsk State University; an author of articles in the field of motion control of mechanical systems. [e-mail: pakhomovkv@yandex.ru]K. Pakhomov

Constructing of Piecewise Constant Control in the Problem of Dynamic Positioning of Ship 36_1.pdf

The paper deals with the results of solving the problem of control synthesis performing dynamic positioning of ship in a point. The problem of simple dynamic positioning, which is in alignment with the center of mass of the vessel with given point waters (center position) for the given requirements for the orientation course is considered. The solution of this problem is provided by use of control on the basis of feedback that asymptotically stabilizes the position and orientation of the ship. To justify the control law, which is based in a discrete form, Euler discrete approximation of the original continuous system is constructed and the method of recursive procedure of backstepping is applied. This procedure allows to build a controlled system that can be represented as a cascade connection of several subsystems. For each subsystem, the stabilizing control and the Lyapunov function are built. At the final step of the recursive procedure, a control law for the entire system and the corresponding Lyapunov function is constructed. Thus, the structure of the found control law essentially depends on the Lyapunov function used at each stage of the procedure. We justify the use of a new class of Lyapunov functions in the form of vector norms for solving this problem, which is used in comparison to previously known works with class of quadratic Lyapunov functions and allows us to simplify the control structure and improve its properties, such as the speed of convergence of the process at a given position. The results of numerical simulations, confirming a higher effectiveness of the proposed control law in comparison with the known results are obtained.

Dynamic positioning, piecewise constant control, backstepping technique, lyapunov function.

2014_ 2

Sections: Automated control systems

Subjects: Automated control systems, Architecture of ship's system.


Olga Alekseevna Peregudova, Ulyanovsk State University, Doctor of Physics and Mathematics, Associate Professor, graduated from the Faculty of Mechanics and Mathematics at Ulyanovsk State University; Professor of the Department of Information Security and Control Theory at Ulyanovsk State University; an author of articles, textbooks, and a monograph in the field of the theory of stability and motion control of mechanical systems. [e-mail: peregudovaoa@sv.ulsu.ru]O. Peregudova,

Konstantin Valerevich Pakhomov, Ulyanovsk State University, Post-graduate student, graduated from the Faculty of Mathematics and Information Technologies at Ulyanovsk State University; a research assistant at the Office of Scientific Research of Ulyanovsk State University; an author of articles in the field of motion control of mechanical systems. [e-mail: pakhomovkv@yandex.ru]K. Pakhomov

On the Stabilization of Nonlinear Systems With Piecewise Constant Control Using a Back Stepping Method 34_6.pdf

A method of solving a stabilization problem of nonlinear systems with piecewise constant control on the basis of a sampling system using a back stepping method and Lyapunov’s functions of vector norms type is proved in the paper. Sufficient stabilization conditions with the initial deviations estimation are obtained. A specific example illustrates the effectiveness of the results in comparison with the known ones.

Nonlinear system, piecewise constant control, back stepping, lyapunov’s function, matrix norm.

2013_ 4

Sections: Mathematical modeling, calculi of approximation and software systems

Subjects: Mathematical modeling, Operational research.


Olga Alekseevna Peregudova, Ulyanovsk State University, Doctor of Physics and Mathematics, Associate Professor, graduated from the Faculty of Mechanics and Mathematics at the Ulyanovsk State University, Associate Professor of the Chair Information Security and Control Theory at the Ulyanovsk State University; author of articles, text-books, a monograph in the field of theory of stability and control of mechanical-system movement. [e-mail: peregudovaoa@sv.ulsu.ru]O. Peregudova

About Stabilization of Software Movement of Non-linear Mechanical Systems Using Piece-wise Continuous Controls 23_11.pdf

The article deals with tasks of navigation-parameter filtering and simultaneous discrimination of hypotheses and evaluation of changing parameters of ships communications and control systems. It cites examples of the successful use of the indicated statistics methods.

Non-linear mechanical system, piece-wise continuous control, lyapunov vector-function, breakdown principle.

2011_ 1

Sections: Mathematical modeling, calculi of approximations and software systems

Subjects: Mathematical modeling.


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