Automatic Control Theory Research Articles

ПРОБЛЕМЫ РЕАЛИЗАЦИИ СИСТЕМ ПОЛУАВТОМАТИЧЕСКОГО УПРАВЛЕНИЯ, ВКЛЮЧАЮЩИХ КОНТУР ОБРАТНОЙ СВЯЗИ ПО УСИЛИЮ

The issues of force-torque sensing in semi-automatic systems are considered. The paper describes the main control principles in ergatic systems from the viewpoint of automatic control theory, considers a method for improving the control quality by introducing additional feedback for the operator. The work proposes force-torque sensing as the most promising feedback channel for the implementation, describes the relevance of this channel in the fulfilled automatic control systems, gives examples. A description of the feedback loop for the efforts on the manipulator’s working element is given. The work highlights the following as the main problems in implementing the considered semi-automatic systems: the kinematic chain influence, filtering and delay, gravity compensation, as well as the problem of the natural feedback loop.

РАЗРАБОТКА МОБИЛЬНОГО КОЛЕСНОГО РОБОТА ДЛЯ ДОСТАВКИ ПОСЫЛОК

The study objective is to develop approaches to the design of a mobile wheeled robot for transporting small-sized goods, operating autonomously without the participation of a human operator. At the same time, the main task is to develop a mathematical model of a wheeled robot that takes into account the moments of rolling friction and sliding of the driving wheels on the support surface, and which allows to study the starting operation modes of the electromechanical drive of a mobile device. The increase in the speed of the mobile robot is achieved by minimizing the acceleration time to the required speed values through the use of a 2-stage algorithm for changing the control voltage. The development of a mathematical model of a robotic system is carried out on the basis of methods of analytical mechanics and the theory of automatic control. Using the Laplace transforms, an analytical solution of differential equations describing the dynamics of a mobile robot is obtained. Numerical solution of the obtained equations is carried out in Mathcad interface. The novelty of the work consists in obtaining time dependencies for the speed and current in the circuit of the electric motor of the mobile robot wheeled drive and finding out the basic patterns of movement at its launch. The results of the conducted research can be used in the development of motion control systems for mobile robots with feedback, ensuring the stabilization of a set value of the movement speed in steady-state modes. Conclusions: a mathematical model of a mobile robotic system is developed, the starting modes of its operation and the method of combined motion control are studied, the speed of a mobile wheeled device is increased when moving along a given trajectory.

Design and implementation of a novel didactic strategy using learning styles for teaching control theory

This paper explains the design and implementation of a novel didactic strategy based on learning styles for teaching automatic control theory in engineering. Traditional research on engineering education has worked to develop teaching methodologies, educational resources, and assessment tasks without considering the learning styles of the students. However, it is important to consider the learning styles of students to increase the number of useful tools that aid students in understanding abstract ideas and difficult concepts. To demonstrate that it is possible to design excellent courses of automatic control by using class activities concerning the learning styles of students. The proposal includes knowing the learning styles of students that enable professors to design appropriate didactic strategies based on the student needs. The proposed didactic strategy is appropriate and enhances the understanding of difficult concepts related to automatic control.

Стабілізація обертання ротора Дар'є сумісними змінами довжини лопатей і траверс

With the ever-increasing prices of and demand for traditional fuels and the decreasing availability thereof, renewable energy sources, such as wind energy, are gaining enormous popularity. First of all, this branch of "green" energy is environmentally friendly. A significant increase in the use of wind power plants (WPPs) is observed all over the world. Modern WPPs are of two types: vertical- and horizontal-axis ones. Vertical-axis WPPs, in contrast to horizontal-axis ones, have a number of specific design advantages, such as, for example, insensitivity to the wind direction, which significantly simplify their design and increase their reliability. The operation of vertical-axis WPPs involves the need to stabilize their operating regimes, the main objective of which is to stabilize electricity production in conditions of a variable wind speed using appropriate stabilization systems (SSs). In SS development, use is made of various control algorithms, which make a basis for harnessing physical principles of SS construction. Recently, SSs based on blade swept area variation have become widespread. Such systems, unlike systems based on, for example, generator load variation, actually use the adaptation of WPPs to a variable wind speed, and they dispense with the need for mechanical dissipation of excess energy by resistance forces and, to some extent, with the need to transfer it to the support. The last point significantly reduces the load on the rotor-to-generator transmission systems and alleviates the requirements for anchor systems in the case of WPPs installed on floating platforms. In terms of design, the stabilization of vertical-axis WPPs by swept area variation can be performed in three ways: by varying the blade length, varying the length of the traverses whereby the blades are attached to the rotor shaft, and by simultaneously varying the length of the blades and the traverses, i.e., by varying WPP rotor configuration. The elaboration of approaches to the development of algorithms for the stabilization of vertical-axis WPPs controlled by rotor configuration variation is an important and promising task. The goal of this paper is to develop efficient algorithms for stabilizing the variable-configuration WPP rotor speed providing the stability and operability of the channels of blade and traverse length variation in their simultaneous operation. The problem is solved using methods of the classical theory of automatic control and mathematical simulation. The novelty lies in extending the concept of control by swept area variation to Darrieus vertical-axis WPPs, synthesizing efficient algorithms for stabilizing the rotor speed of Darrieus vertical-axis WPPs controlled by rotor configuration variation, and determining conditions for their stability and operability. The algorithms and approach developed may be used in substantiating design solutions for Darrieus vertical-axis WPPs.

INCREASING THE RELIABILITY OF THE SYSTEM OF AUTOMATIC VOLTAGE REGULATION OF LOW-VOLTAGE CIRCUITS OF ELECTRICAL DIRECT CURRENT MOVEMENT COMPONENTS

Purpose. The purpose of this work is the analysis of possible directions for improving the performance indicators of electric rolling stock of direct current railways. The work is devoted to the improvement of systems of automatic voltage regulation of low-voltage circuits where the power source is a direct current generator. The number of electric locomotives and electric trains of railways and their units, which have exhausted their service life, but will be in service for a long time, preserves the relevance of research into possible directions of modernization and the specifics of system operation. Methodology. The work uses the analysis and generalization of previously performed research. The methodological basis of the research is the mathematical apparatus of the theory of automatic control and the theory of reliability. The object of research is the process of functioning of low-voltage control circuits of electric rolling stock of direct current railways with direct current generators as an energy source. The subject of the study is a voltage regulator for own needs based on a modern element base. Findings. A variant of the system of automatic voltage regulation of low-voltage circuits with generator power sources for electric rolling stock of direct current is offered. The basis of the system is the voltage regulation node, which in the existing structure is made on the basis of a carbon vibration regulator on a strip. As an alternative, a system based on operational amplifiers and the use of proportional or proportional-integral laws of the regulator in the structure is proposed. Modeling of dynamic processes indicates the structural stability of the system and qualitative transition processes. A comparison of the no-failure indicators of the nodes indicates a possible increase in terms between services and cost savings. The comparison is made for systems that are in operation for a long time and those that are offered. Originality. It is proposed to implement the node of the system of automatic voltage regulation on a modern elemental basis, which allows to improve the reliability of the system and implement a small, economical, modernization of rolling stock of railways with an exhausted service life. Practical value. The obtained results can be used by enterprises that carry out major repairs of electric trains and direct current electric locomotives with extended service life. The implementation of the proposed units makes it possible to replace existing contact-based relay systems with fast contact wear, frequent maintenance and debugging. As a result, new units can be transferred to service during current repairs due to the introduction of non-contact systems and increase the probability of trouble-free operation and use the personnel who are always present in locomotive depots. This reduces the cost of maintenance due to the introduction of a modern element base and exclusion from the technological process of maintenance of existing units.

Parametric Correlation Analysis between Equivalent Electric Circuit Model and Mechanistic Model Interpretation for Battery Internal Aging

In modern electric vehicle applications, understanding the evolution of the internal electrochemical reaction throughout the aging of batteries is as relevant as knowing their state of health. This article demonstrates the feasibility of correlating a mechanistic model of the battery internal electrochemical reactions with an equivalent electrical circuit (EEC) model, providing a practical and understandable interpretation of the internal reactions for electrical specialists. By way of electrochemical impedance spectroscopy analysis and automatic control theory, a methodology for correlating the resistance and capacitance variations of the EEC model and how they reflect the electrochemical reaction changes is proposed. These changes are represented through the time constants of the three RC parallel arrays from an EEC model. PS-260 lead–acid batteries were analyzed throughout the SOC and their useful life to validate this methodology. The result analysis allows us to establish that the first RC array corresponds to the negative electrode reactions in the range of 1.48 Hz to 10 kHz, the second RC array to the positive electrode reactions and generation of sulfates in the range of 0.5 to 1.48 Hz, and the third RC array to the generation of sulfates and their diffusion in the range of 0.01 to 0.5 Hz.

Application of two-step input to reduce overshoot of the transient response at automated control systems

The problems of quality improving for technology control are very important and are considered in works on the theory of automatic control and related fields. Various approaches to solving the problems are known especially by the decreasing overshoot of step response. To provide this the most of existing methods require: to adjust a controller parameters; development of a mathematical model of a controlled object; additional filters applications, that as a whole is difficult to implement under industrial conditions. The authors have proposed another approach to solving the above problems, contrary to the known ones. Namely, to apply two successive inputs with lower amplitudes and delay in time instead of the known one step input. The response of the controlled system on the complex two step inputs was considered and the optimal time delay was defined. The investigations were conducted by the modelling a typical classic linear automation control system that consists of a static control object of the first order with time delay, proposal - integration - difference controllers. The modelling results for a transient under the various applied one and two step inputs, including their ramp variation were obtained. It was shown that the two-step inputs with their ramp application gives the decreasing of the maximum displacement for a transient in a typical control system: more than 3 times increase was shown comparing with the one-step approach. The optimal time interval between the steps was determined that leads to the maximum effectiveness of the technology application. The procedure to define the details of the approach application was developed

Comprehensive degree of nonlinearity in the dynamic response of high-speed Maglev train

The aim of this study is to propose a method for evaluating the comprehensive degree of nonlinearity in the dynamic response of high-speed maglev train system through mathematical modeling and numerical simulation. A model of a typical high-speed maglev vehicle is established based on the principles of maglev vehicle dynamics, and control models for the suspension magnet and the guide magnet are developed using principles from the electromagnetism and automatic control theory. The vibration responses of the vehicle system, including acceleration and electromagnetic forces are calculated using a fast numerical integration method. This calculation is performed for various control parameters and track harmonic excitations. The Hilbert-Huang transform (HHT) is adopted to decompose the response signal and derive the local mean frequency (amplitude) and instantaneous frequency (amplitude) of the response, based on which the Degree of Nonlinearity (DN) of the vibration response of a single component is obtained by calculating the deviation between the instantaneous frequency and the mean frequency. The Comprehensive Degree of Nonlinearity (CDN) of the vibration response in the maglev train system is proposed and defined by incorporating the DNs of the vertical and lateral vibrations of the carbody, bogie, suspension magnet and guide magnet, and by quantitatively evaluating them. The effects of the electromagnet control parameters and harmonic irregularities (wavelength and amplitude) of the track on the DN of each component and the CDN of the entire vehicle system are analyzed in detail. The analysis results show that the DN and CDN can demonstrate the extent of instability in the vehicle system and can be applied for safety warning on maglev vehicles.

Research of the regulator of an expander-generator unit

The relevance of research is determined by the tasks of increasing the efficiency of alternative and renewable energy power plants. The purpose of the work is to develop a method of coordinating the settings of the automatic excitation regulators and the speed of rotation of the rotor of the generator from the vortex installation of the expander-generator unit, which is part of the autonomous power consumption network. To achieve the goal, the methods of mathematical modelling in the MATLAB environment, physical modelling, processing of experimental data, theory of automatic control, theory of magnetic field, theory of electric machines, programming of microprocessor devices were used. Considering the need to expand the base of alternative energy sources, the task of controlling the energy plant for the utilization of excess pressure of gas transportation networks was considered. The study of the regulator of the expander-generator unit was based on a model reflecting the interaction of mechanical and electrical processes. A set of nonlinear differential equations corresponded to the description of these processes. Accurate consideration of nonlinearities of the considered control object complicates the implementation of the corresponding microprocessor control systems. Modelling is aimed at achieving a compromise between the required accuracy of object control and the possibilities of simplifying the object control structure. The use of experimental and datasheet data of the devices made it possible to evaluate the dynamics of turbine rotation and voltage generation, forming the factors for the untying of the control circuits. The use of MATLAB with the Lookup Table option made it possible to perform a multi-point linearization of the nonlinear description of the process, speeding up the modelling and adjustment of the regulator. This is important to incoordinate the settings of the frequency control loops and the output voltage, given the trade-off between the speed of the regulator and the minimization of oscillations in the generation frequency. Based on the obtained results, a regulator of the expander-generator unit was developed, which ensures the stabilization of the initial parameters of the unit under the conditions of electrical load disturbances. In practice, the obtained data can be used in the integration of renewable energy sources into the general energy system through the optimization of the operation of generators

Research on the application of automatic control theory in automatic driving technology

Autonomous driving technology has been widely used and studied in depth in recent years, and has become a hot field in the automotive industry. As one of the core methods to realize automatic driving, automatic control theory provides an important theoretical basis and practical guidance for automatic driving systems. This paper aims to explore the application of automatic control theory to autonomous driving and analyze its potential impact on improving driving safety, comfort and efficiency. This paper first introduces the basic principles and components of the autonomous driving system. Among them, automatic control theory plays an important role in decision-making and execution. Secondly, this paper discusses the specific application of automatic control theory in automatic driving. These include PID controller-based vehicle stability control, model predictive control (MPC) for path planning and trajectory tracking. These applications enable autonomous driving systems to respond in real time to environmental changes and maintain vehicle stability and safety. Finally, the paper discusses the challenges and future directions of automatic control theory in autonomous driving. Future research should focus on further improving the robustness and adaptability of automatic control algorithms to cope with complex driving scenarios and uncertainties. To sum up, automatic control theory plays an important role in automatic driving and has broad application prospects. Through continuous improvement and innovation, automatic control theory will make an important contribution to the realization of safer, more efficient, and more intelligent autonomous driving technology.

СИНТЕЗ ЭЛЕКТРОПРИВОДА КОМПРЕССОРНОЙ УСТАНОВКИ ЭЛЕКТРОВОЗА

The study objective is to improve the reliability and energy efficiency of the electric locomotive compressor drive. To achieve this, the required power of the electric motor was calculated the performance of the compressor unit, the volume of the main tanks and the selected electric motor were checked to start and adjust the capacity at low supply voltage. The task to which the paper is devoted is to design an electric drive for a compressor motor. A vector model of an asynchronous motor was made. The process of direct start-up and starting an asynchronous electric motor with the use of a scalar control system and IR compensation were modeled. Research methods: systematic approach; provisions of the theory of automatic control and electrical engineering; numerical PC simulation using Matlab software package. The novelty of the work is in the use of a frequency-controlled electric drive to start the asynchronous electric motor of the compressor unit instead of the normally installed starting capacitors. This design solution will significantly reduce the amplitude of the starting currents, which in turn will reduce the wear of the winding insulation. The study results are presented, based on the results of the constructed models, as graphs of the dependencies of speed and current during direct start of the electric motor and with the control system. Conclusions: the scalar control system, thanks to the introduction of an intensity setter, as well as IR compensation diagram, allow extending the transition time and controlling the value of the inrush current in acceptable values. Such an approach to make an electric drive compressor motor is able to significantly increase its reliability and service life, as well as to increase the overall energy efficiency of the system.

Active Filters for Standard-Compliant Power Quality in Electrical Networks

The article is devoted to the analysis of three circuits of modular multilevel converters (MMCS) with cascade connection of single-phase bridge and half-bridge voltage converters, each of which operates in pulse width modulation (PWM) mode. The main feature of active filters based on MMS is the possibility of selective high-speed harmonic filtering in on–line mode: AF allows the suppression of any given set of harmonics, including the negative harmonic of the fundamental frequency (reverse sequence), with a given degree of suppression - to zero or a normalized value - by an appropriate task in the control program. For the practical implementation of MMS in solving problems of normalization of electricity quality indicators, the so-called DSB control algorithm of MMS was developed, based on the traditional "classical" theory of automatic control and the theory of three-phase circuits. A comparative assessment of the use of various MMC schemes for symmetry and reactive power compensation has been carried out. It is shown that the problem of voltage symmetry using MMS is a special one, requiring the use of special algorithms to solve it, ensuring the reactive nature of branches of MMS circuits.

System of automated monitoring and forecasting of the remaining resource of pipeline transport

This article presents a system of automated monitoring and forecasting of the residual resource of pipeline transport, consisting of a developed and manufactured information and diagnostic complex for monitoring the technical condition of pipeline transport and software. Informative frequency ranges for monitoring the technical condition of pipeline transport are determined. Experimental studies have been conducted to confirm the effectiveness of the developed technical solution. The paper considers the problems of reliability of pipeline transport. The analysis of existing methods for assessing the technical condition of pipelines is carried out. A system of automated monitoring and forecasting of the residual resource of pipeline transport has been developed. Experimental studies have been conducted. The methods of circuit and simulation modeling, the theory of automatic control, experimental planning, decision-making, probabilistic and statistical methods of mathematical processing and the method of finite element analysis were used in the performance of the work. Based on the resultsof the study, a new methodology for assessing the technical condition of pipeline transport has been developed.

Analysis of the State of Moisture Control to Ensure and Regulate the Quality of Grain and Grain Products

The article discusses the methods for determining the maturity of grain and describes its behavior during harvesting, to optimize the selection of the grain moisture state, discusses the requirements for the choice of measurement method and the design of moisture control measuring devices, as well as its high accuracy and the possibility of measuring from field conditions, collection, storage, transportation, and industrial processing and release of finished products of granular materials. The purpose of the study is to improve the efficiency of control and management of complex technological processes and moisture control devices for granular bulk materials of plant origin through the development of systems for automatic and automated control of the electrophysical characteristics of grain products and to increase the reliability of quantitative and qualitative assessments of production and technological measurement information. To achieve this goal, it is necessary to conduct analytical and experimental studies of the possibility of creating an express method for controlling the moisture content of grain and products of their industrial processing and the development of a moisture meter for automated control of raw material parameters during acceptance and storage at grain processing enterprises. The article discusses the scientific and methodological foundations for measuring the electrophysical characteristics of grain products of agricultural production and the implementation on this basis of the functional subsystem of information support by the Automated Process Control System for Controlling the Mass Ratio of Moisture of Plant Origin Materials. A critical analysis of the current state of the theory and practice of automatic control of electrophysical characteristics of grain products and the identification of the trend of their further development and improvement are carried out. A mathematical model of the interaction of a high-frequency field with a granular material has been constructed, where the influence of the elastic properties of the grain on the electrical characteristics of the electromagnetic wave, which distinguishes its behavior in the field of a high-frequency wave from many other dielectrics, has been substantiated, and the influence of a large number of various disturbing factors has been studied, often the measurement results cannot be applied in the control of the technological process due to the uneliminated error, which is the cause of inaccurate information. Primary measuring transducers of electrophysical parameters of grain products are proposed, and their mathematical models are considered. A functional scheme of the measuring device based on the dielcometric method of moisture control of grain and granular materials has been developed, and metrological characteristics have been given.

THE MEDIAN TREE

Mathematical models in which objects have a finite discrete structure are used to solve a wide range of practical problems. Such are, for example, many problems in auto-matic design, operation research, control theory, network planning, and computational geometry. Often, oriented or non-oriented graphs are considered as such models, which can adequately describe the structure of the problem of interest to us. Among these tasks, a certain place is occupied by tasks related to network issues of optimal placement of ware-houses, certain service points, emergency, medical services, etc. When studying such issues, it becomes necessary to identify, in a certain sense, the central objects in the networks un-der consideration, and in order to find them, the concept of the shortest path between these two given elements plays an essential role. A definition of the medial vertex of a graph is provided in the article – the vertex whose sum of distances to the others is minimal. The median of a non-oriented tree con-sisting of medial vertices is considered, and it is proved that the median of each such tree has either one vertex or two connected by an edge. This result is a definite generalization of a similar property of the center of a tree consisting of central vertices. The question of the relationship between the center and median of the same tree is also studied. The examples of trees with ten vertices show that such a direct connection does not exist, and there can be all four logically possible cases: the same tree can contain one or two central and one or two medial vertices.

Methodological features of the development of intelligent information technology for the transportation process in railway transport

The article presents methodological features of the development of intelligent information technology (hereinafter referred to as IIT) for implementation in the transportation process in railway transport. The purpose of this study is to integrate intelligent information technology into the railway transportation process using the IDEF0 functional modeling methodology. The implementation of IIT will ensure monitoring of the condition of wagons and cargo from the moment of loading to the moment of unloading along the entire route. Methods: Analysis of the current state of the subject area, synthesis of solutions, mathematical modeling, provisions of the theory of automatic control are applied. Results: World experience in the use of intelligent technologies in railway transport was analyzed, a diagram of a control system for the process of accepting a car for transportation and a mathematical model of the problem that IIT solves was developed. The role of IIT in the transportation process is determined using the IDEF0 functional modeling methodology. The importance of integrating IIT into the process of freight transportation by rail in increasing their efficiency through the use of new methods is shown.

Automatic Control and System Theory and Advanced Applications—Volume 2

The aim of the Special Issue on Automatic Control and System Theory and Advanced Applications, the second volume of a previous paper selection, is to emphasize the role of new inventions in the area of automatic control applications [...]

Алгоритми стабілізації швидкості обертів ротора Дар’є вітро-енергетичної установки, керованого змінами довжини лопатей

The world’s power engineering features ever increasing attention to the development of renewable power sources. Difficulties in provision with traditional energy sources (gas, coal, and oil products) and the global trends of transition to green sources call for replacing the traditional sources with new ones. Among the alternative energy sources, wind power plants (WPPs) installed in suitable territories have received widespread use. Modern WPPs are of two types: vertical- and horizontal-axis ones. Vertical-axis WPPs, as distinct from horizontal-axis ones, have a number of specific advantages, such as, for example, insensitivity to wind direction changes, which significantly simplify the WPP design and increase the WPP reliability. Both WPP types are dynamically complex systems, which operate in different regimes depending on their dynamic and technological features. The task of matching these features is assigned to control systems, which control the rotor operation using additional devices, for example, generators of different types. For horizontal-axis WPPs, approaches to the solution of a number of system control problems have been developed on the basis of the principle of swept area variation. The development of a similar approach for vertical-axis WPPs seems to be an important and promising task. The goal of this paper is to develop efficient algorithms of WPP rotor speed stabilization using the principle of swept area variation, namely, telescopic blades. The problem is solved using methods of the classical automatic control theory and mathematical simulation. The novelty lies in extending the concept of control by swept area variation to Darrieus vertical-axis WPPs, synthesizing efficient algorithms for stabilizing the rotor speed of Darrieus vertical-axis WPPs controlled by blade length variation, and determining conditions for their stability. The algorithms may be used in substantiating design solutions for Darrieus rotor vertical-axis WPPs.

Development of an algorithm for controlling the suspension of a heavy-duty vehicle using the technology of systems embedding

BACKGROUND: The article is devoted to the development of an algorithm for controlling the suspension of a heavy-duty vehicle. The paper presents a suspension control system for a heavy-duty vehicle. The relevance is linked to the fact that by 2025, industry cooperation between representatives of the high-tech industry and scientists in the field of developing intelligent vehicle control systems is planned within the Autonet ecosystem. The control systems of modernized units with a high degree of electrification and digitalization are of the greatest interest to Russian automakers. This paper describes the results of a study of the active suspension of a heavy-duty vehicle from the side of control theory.
 AIM: Development of an algorithm for controlling the suspension of a heavy-duty vehicle. A technical requirement for the monotony of the transition process was formed, since this is the main indicator of improvement of the operational properties of a vehicle, which becomes obvious especially clearly in the smoothness of the suspension.
 METHODS: In the study, the fundamentals of the theory of automatic control, the theory of linear algebra, the concept of the state space, as well as methods of systems embedding based on modern achievements of algebra were used. Computer simulation was carried out in the environment of the MATLAB/Scilab/SimInTech kind.
 RESULTS: A mathematical and computer model of a half of a four-point suspension of a heavy-duty vehicle has been developed. The paper presents a suspension control system for a heavy-duty vehicle. The control algorithm is developed using the systems nesting technology. The properties of the synthesized control system more than doubled the quality of the system compared to the characteristics of the control object.
 CONCLUSION: The practical value lies in the ability of using the results of the study in the production and testing of adaptive suspension of a heavy-duty vehicle.

Stages and main tasks of the century-long control theory and system identification development

The article provides a review of the mathematical description of the dynamics of continuous and discrete linear stationary systems and objects, used at the development stage of the classical theory of automatic control in the form of mathematical models of the «input-output» type. The time and frequency characteristics of continuous and discrete control systems are described, typical links of stationary systems are considered, parametric discrete models of objects as part of typical digital control loops are presented. Stochastic discrete autoregressive models of stationary time series used to describe the dynamic objects in the synthesis of digital control systems are considered. A review of standard control laws for the implementation of continuous and discrete controllers has been completed. A method for synthesizing discrete controllers for multidimensional controlled objects with different, unknown and changing delays is considered, through which variable delays are compensated in the characteristic equation of a closed-loop control system. A common technique for synthesizing one-dimensional and multidimensional controllers for stochastic objects with delays based on ARMAX models is considered. An analysis of approaches to identifying delays in controlled objects is carried out and a method for identifying delays when using input-output models is considered, based on the calculation and comparison of impulse responses for extended and non-extended models of the controlled object. An analysis of the advantages and disadvantages of «input-output» type models is given, as well as the possibilities of their application for solving various classes of control theory problems.