Исследование реакции поверхности жидкости на импульсное воздействие наклонной газовой струи при малых числах Рэйнольдса

A mathematical description of the motion of a cavity on the liquid surface under an oblique action of a gas jet is obtained using the well-known expressions for the movement of a gas bubble in a liquid. The boundary of the viscous drag force domination over the form drag force is determined. The impingement of the gas jet on the liquid surface is considered as a dynamic object of the automatic control theory. It is found that the dynamic properties of the two-phase system "gas jet - liquid" are described by the integrator equations. Using a specially designed setup, the transient response of the "gas jet - liquid" system were experimentally obtained for the aerodynamic action at angles of 20º and 50º to the surfaces of liquids with the viscosities of 0.71 and 26.1 Pa•s (Reynolds number Re < 2). The research results are necessary for the analysis of the non-contact aerodynamic method of liquid viscosity measurements.

CURRENT STATE OF SCIENTIFIC AND TECHNICAL DEVELOPMENTS IN THE FIELD OF IMPROVING THE EFFICIENCY OF VIBRATION EQUIPMENT AND TECHNOLOGIES

The article considers the state of scientific and technical developments in the field of improving the efficiency of vibration technology. Production activity in most branches of industrial production is provided by the work of various technological machines and vehicles. The operation of machines, equipment, mechanisms, apparatus and devices in the conditions of the need to ensure high productivity is often accompanied by significant dynamic loads, vibration processes and manifestations of shock interactions of machine elements. Ensuring the reliability and safety of machines requires at all stages of their life cycle serious attention to compliance with certain restrictions on the parameters of the dynamic state of technical objects, the development of methods and means of assessing control and management of dynamic interactions. Modern mechanical engineering is a scientific basis for solving the main problems of machine dynamics, which, in general, is based on scientific potential created by domestic and foreign scientists in the field of theoretical and applied mechanics, theory of mechanisms, dynamics and strength of machines, development of scientific directions in automatic control theory. applied system synthesis, etc. The results of scientific research are reflected in the works of famous scientists. The formed practice of pre-design researches of the created machines, the equipment and the equipment is based on wide use of means of mathematical modeling, application of means of computer engineering. The choice of equipment in production is based on cost, productivity, size, energy consumption, etc. In this regard, there is a question of the need to find and develop new approaches, methods and means to ensure the efficiency and reliability of technological machines and equipment.

Advanced Mathematics and Computational Applications in Control Systems Engineering

Control-systems engineering is a multidisciplinary subject that applies automatic-control theory to design systems with desired behaviors in control environments [...]

On the conditions for cycles existence in a second-order discrete-time system with sector-nonlinearity

In this paper, a second-order discrete-time automatic control system is studied. This work is a continuation of the research presented in the author’s papers “On the Aizerman problem: coefficient conditions for the existence of a four-period cycle in a second-order discrete-time system” and “On the Aizerman problem: coefficient conditions for the existence of threeand six-period cycles in a second-order discrete-time system”, where systems with two- and three-periodic nonlinearities lying in the Hurwitz angle were considered. The systems with nonlinearities subjected to stronger constraints are discussed in this paper. It is assumed that the nonlinearity not only lies in the Hurwitz angle, but also satisfies the additional sector-condition. This formulation of the problem is found in many works devoted to theoretical and applied questions of the automatic control theory. In this paper, a system with such nonlinearity is explored for all possible values of the parameters. It is shown that in this case there are parameter values for which a system with a two-periodic nonlinearity has a family of four-period cycles, and a system with a three-periodic nonlinearity has a family of three- or six-period cycles. The conditions on the parameters under which the system can have a family of periodic solutions are written out explicitly. The proofs of the theorems provide a method for constructing nonlinearity in such a way that any solution of the system with initial data lying on some definite ray is periodic.

Lever ties: possibilities of creating dynamic conditions in mechanical oscillation systems

The paper considers the possibilities to assess, create and change dynamic conditions of mechanical oscillation systems with additional ties in tasks of dynamics that are typical to technological and transport objects. The aim of the paper is in development of methodological basics of system analysis, detailed elaboration of notions about shapes, peculiarities and possibilities of functions interaction of elements in oscillation systems in the presence of dynamic ties in the shape of lever mechanisms. The paper uses methods of structural mathematical modeling based on analytical apparatus of automatic control theory. The authors developed a method of creating mathematical models obtained with the use of the Laplace transformations of the original equations formed on the basis of the Lagrange formalism. They propose a technology of creating structural mathematical models with the exception of intermediate coordinates. They also consider the introduction of new type transfer functions surrounding the distribution of the oscillation amplitudes of the mass-inertial element in the form of a rigid body performing plane motion and variants of appearance of specific dynamic modes in a connected motion under the influence of external disturbances. The study shows the possibilities of interpreting the modes of dynamic absorption of oscillations through a connection with definition of a node (or centre) of oscillations. As a result, the authors propose a number of analytical ratios to evaluate peculiarities of the dynamic conditions of vibrational interactions and present the results of numeric modeling.

ESTIMATION OF MEASUREMENT ERRORS IN A SINGLE-CHANNEL PLATFORM ANGULAR POSITIONING CONTROL SYSTEM BASED ON AN ANGULAR VELOCITY SENSOR

This work is devoted to the important problem of the contemporary automatic control theory – creation of integrated technologies of design of ACS (Automatic Control Systems). Such technologies must provide complex solution of the controlled object’s state evaluation and synthesis of the control law. The main practical result would be ACS accuracy increase. The new concept of ACS design for realization of integrated technologies conditions the urgency to confirm its efficacy’s by applied results in creation of concrete working systems. Research in this direction of automatic control theory is at its initial stage, at which it is important to evaluate possibilities of new technologies on simple ACS’ functioning models. The author presents a model of a one-channel attitude control system for a platform based on an angular velocity sensor providing instantaneous posterior estimation of platform’s rotation angle error. Values of the disturbance torque, acting on the platform, and angular velocity measurement errors on the considered observation interval are set as random numbers that stay constant on this interval. The author presents the analysis of control and state evaluation for the object of control, implemented by the synthesized system for two versions of the object: in the absence and in the presence of its own damping torque. The author demonstrates a modification of adjuster’s structure to achieve accuracy increase for the platform’s parameters evaluation.