The paper proposes conceptual model of a digital platform for cyber-physical management of manufacturing enterprises in the upcoming era of Industry 5.0, characterized by the vision of any business, including industrial production or logistics, as a complex adaptive system built on fundamental principles of self-organization and evolution, as well as interaction of artificial intelligence systems and people. The first part discusses principles of building a digital platform that can support operation of an enterprise within Industry 5.0 as a digital ecosystem of smart services. This part of the paper proposes typing of vasic platform services, lists the minimum set of services of each type, and gives description of their functionality. It also substantiates the leading role of multi-agent systems as a basic software architecture and technology for developing applications of the digital eco-systems. The paper provides examples of digital platforms and ecosystems of smart services for management of cargo transportation of the Russian Railways on the principles of "uberisation", life cycle of complex technical products, as well as enterprises of the plant-growing industry. It is shown that results are applicable to modern industrial corporations and enterprises in industry and agriculture, logistics, design, consulting and service.

The theory of systems of functional differential equations is a significant and rapidly developing sphere of modern mathematics which finds extensive application in complex systems of automatic control and also in economic, modern technical, ecological, and biological models. Naturally, the problems arises of stability and partial stability of the processes described by the class of the equation. The article studies the problem of partial stability which arise in applications either from the requirement of proper performance of a system or in assessing system capability. Also very effective is the approach to the problem of stability with respect to all variables based on preliminary analysis of partial stability. We suppose that the system have the zero equilibrium position. A conditions are obtained under which the uniform stability (uniform asymptotic stability) of the zero equilibrium position with respect to the part of the variables implies the uniform stability (uniform asymptotic stability) of this equilibrium position with respect to the other, larger part of the variables, which include an additional group of coordinates of the phase vector. These conditions include: 1) the condition for uniform asymptotic stability of the zero equilibrium position of the "reduced" subsystem of the original system with respect to the additional group of variables; 2) the restriction on the coupling between the "reduced" subsystem and the rest parts of the system. Application of the obtained results to a problem of stabilization with respect to a part of the variables for nonlinear controlled systems is discussed.

Operating conditions of the power facilities equipment have an impact on its technical condition. These conditions are determined by the state of the external (environment) environment. Deviations of environmental parameters from the required (normative) values can accelerate negative trends leading to failures, accidents and, accordingly, economic damage from downtime and restoration of the proper technical condition of power equipment. Therefore, taking into account the state of the environment is an important aspect of solving the problems of monitoring, diagnosis and forecasting of technical condition, as well as solving the problems of management and decision support in the operation of energy facilities. The external environment is characterized by different types of uncertainty. The different uncertainties of the external environment determine the need to choose or correct the way to achieve the goal of management or decision-making. Therefore, the paper proposes a formalized description of the environment state, which has uncertainties of different types. Synthesized operations to obtain states different from the" typical " obtained, for example, at the design stage of the diagnostic system or control of power equipment. On the basis of this implemented a method of rapid assessment of the external environment without a survey of experts based on the synthesis of the accelerated procedure. The choice of fuzzy set theory is justified as a mathematical tool for formalizing uncertainties of different types and subjectivism inherent in the opinions of domain experts. The concept of the environment state is formalized and typical operations for determining its typical states are proposed. To take into account the different types of uncertainty in the description of the current state of the environment, a modifier mechanism is proposed. Modifiers can significantly simplify calculations in the formalization of environmental conditions for use in diagnostic systems and control of power equipment. The considered computational examples show the main features of the proposed approach. The results of the application of the developed approach suggest the feasibility of its application to solve the problem of formalization of the environment in the operation of power equipment under uncertainty.

The usage of "motor-wheel" systems requires the electric vehicle control system improvement by using the characteristics of the wheel adhesion to the road surface. One of the aspects of such improvement is the enhancement of the algorithms for the functioning of the antilock braking system (ABS). In developing the ABS control algorithms, various approaches and methods of modern control theory are used, including methods based on the estimation of wheel slip, traction force, wheel friction coefficient using linear and nonlinear estimation methods, linear and nonlinear regulators. This work illustrates the application of the principle of high order integral adaptation (PIA) of Synergetic Control Theory (SCT) for constructing a robust control law for an electric vehicle wheel slip. The main features of the SCT contain: firstly, a fundamental change in the goals of the behavior of the synthesized systems; secondly, direct consideration of the natural properties of nonlinear objects; thirdly, the formation of an analytical mechanism for generating feedbacks, i.e. control laws. PIA consists in introducing nonlinear integrators into the control law that compensate for disturbances without their immediate estimation. The obtained in this work control law has a fairly simple structure, is focused on using physically accessible state variables of the braking system, and its implementation does not require immediate estimation of disturbances or building a complex neural network to calculate disturbances. The results of computer simulations of the synthesized robust control law for ABS indicate its effectiveness in functioning under conditions of external environment uncertainty.

The results of experimental investigation intended to improve movement conditions for pneumatic robots on vertical surfaces under water are discussed. Features of the movement of vacuum contact devices for the simulation of mathematical model of the vacuum contact device with surfaces under water are presented. The experimental studies made it possible to obtain additional data on the dynamics of attachment, to obtain transient processes for air-water flow through ejector and to correct the results obtained earlier. For the purpose of analytical study of dynamic processes occurring in the system of vacuum contact devices, and taking into account the complexity of the description of nonlinearities, linearized simplified models of the system "air ejector — contact device — water environment" were developed. Vacuum contact devices are designed to provide guaranteed contact with vertical surfaces, plane slopes or horizontal surfaces on which the underwater robot performs its movement, carrying out the prescribed technological tasks, for example, in dry wells of nuclear power plants, on the surfaces of ship hulls, on the surfaces of underwater structures. The models took into account the forces of adhesion to the surfaces under water — the forces from the pressure drop, the friction force, the contact and vacuum interaction, the elasticity of suction caps. As a result of the solution of the model problem, the values of mechanical parameters, as well as the values of vacuum and flow in the cavity of variable volume as functions of changing the gap between the end of the corrugated membrane and the surfaces are obtained explicitly. As a result of the study of dynamic processes occurring in simplified models of vacuum contact devices "air ejector — contact surface — water environment", the transient characteristics of the change in the operating forces and pressures over time, as well as the dependence of the normal and tangential components of the forces on the depth of immersion in water were obtained. The variants of the designs of vacuum contact devices with surfaces in the water environment are investigated, and the modernization of the laboratory test bench for testing vacuum contact devices under water is carried out.

A design scheme and a mathematical model of the dynamics of the translational motion of a solid body, which simulate the movement of an underwater platform using anchor-cable propulsion devices, are proposed, and examples of the use of such platforms during the mining and exploration of new hydrocarbon deposits on the continental shelf are given. A diagram of the underwater platform with anchor-cable propulsion devices, as well as the method of its movement. The peculiarity of the mathematical model of the process of moving a platform with this type of propulsion devices is in the dependence of the developed efforts on the position of the cables relative to the moving body and the excess of the number of control actions over the number of degrees of freedom of the mechanical system. The mathematical model describing the movement of the platform is based on geometric equations with simultaneous operation of propulsion drives on the one hand, and on the equation of the dynamics of the translational motion of the body on the other. It is shown that the task of the control system in this process is to provide the necessary balance of forces in the cables going to the propulsion anchor. As drives, DC motors and stepper motors are considered due to their ability to operate from an independent power source, such as batteries. The features of control of DC motors and stepper motors as part of anchor-cable drives drives are established. To resolve dynamic uncertainty, the necessity of introducing an additional equation into a mathematical model has been proved. In accordance with the developed mathematical model, the laws of changes in time of control actions are obtained, in particular, such as the voltage applied to the armatures of DC motors and the switching frequency of the windings when using stepping motors. A method for controlling the movement of a solid body under the influence of two drives has been developed. It can be used to study the translational movement of an underwater platform with anchor-cable propulsion devices. The features of control of DC motors and stepper motors are considered to change the length of cable drives according to a given law.

The work is devoted to improving the reliability and manufacturability of mechatronic machine designs with parallel kinematics by replacing statically indeterminable manipulators with statically determinable mechanisms. A technique is proposed in which the design of statically determinable manipulators of technological mechatronic machines with parallel kinematics is performed by modifying the structure of prototypes and includes three steps: identifying and analyzing redundant links, eliminating redundant links, checking the correctness of eliminating redundant links. To determine the number of degrees of freedom of the mechanism, identify redundant links, and verify the solution, the authors use the proposed methodology for structural analysis of parallel structure mechanisms. In structural analysis, a manipulator is represented by a hierarchical structure and is considered as a parallel connection of elementary mechanisms with an open kinematic chain; as a kinematic chain consisting of leading and driven parts; as a set of links and kinematic pairs; as a kinematic connection of the output link and the rack. The article implements the following techniques for eliminating redundant links: mobility increase in kinematic pairs; introduction of unloading links and passive kinematic pairs to the kinematic chain; exclusion of extra links and pairs from the kinematic chain; increase in mobility in some kinematic pairs simultaneously with the exclusion of other kinematic pairs that have become superfluous. The authors developed several variants of structural schemes of self-aligning manipulators based on the Orthoglide mechanism, which retain the basic functional proper ties of the prototype. To increase the number of self-aligning mechanism diagrams, the redistribution of mobilities and links within the connecting kinematic chain and between connecting kinematic chains is used. The proposed methodics allow to determine the number of degrees of freedom of the mechanism, the number and type of redundant links, eliminate redundant links and, on an alternative basis, build structural diagrams of statically determinable mechanisms of technological mechatronic machines with parallel kinematics.

The tracking system of moving objects is analyzed on the basis of a biaxial cardan suspension with MEMS gyroscopes in the control loop. The kinematics of the tracking system in one of the guidance planes is considered. A block diagram of one channel of the tracking system, consisting of correction and stabilization circuits, is given. It is shown that the time of the transition process, the bandwidth, the phase delay between the angular velocity of the accompanied object and the platform is largely determined by the quality factor of the correction circuit speed. The given numerical estimates give an idea of the characteristics of the tracking system. Relations are given that make it possible to estimate the influence of the noise of a MEMS gyroscope on the angular velocity of a stabilized platform. The occurrence of synchronous errors of the tracking system on an oscillating carrier is explained. It is shown that the influence of dry friction forces in the axes of suspension on the tracking system is equivalent to the action of the sum of harmonics with frequencies multiple to the oscillation frequency of the carrier with odd coefficients. The effect of the moment of viscous friction forces in conditions of carrier oscillations is illustrated. An experimental spectral characteristic of the tracking system model on a swinging stand is presented, confirming the theoretical conclusions. An analytical relation is given to estimate the relative synchronous error of the tracking system.

The importance of information is noted and the defects of traditional air data systems are described, implementing aerometric, aerodynamic and directional methods using straddled in the fuselage of the air pressure receiver, temperature braking receivers, sensors aerodynamic angles of attack and slip. The features of construction and advantages of the original vortex air data system with one stationary receiver of primary information and frequency-time primary informative signals based on the original vortex sensor of aerodynamic angle and true air velocity with a hole-receiver of static pressure on its streamlined surface associated with the absolute pressure sensor with frequency output are considered. It is noted that according to the results of calculations, the instrumental static errors of the measuring channels of the vortex air data system are close in magnitude to the instrumental errors of traditional air data systems. The reasons are considered, mathematical models and calculated values of methodical static errors of measuring channels of vortex air data system which testify to prospects of application of system on subsonic aircraft are received.