Synthesis Of Control Systems Research Articles

Identification of the electric motor mathematical model based on a data sample with feature engineering

The object of this study is a mathematical model of a synchronous electric motor, obtained on the basis of experimental data, which takes into account the temperature mode and uses artificial features to increase the accuracy of its operation. A characteristic feature of this work is that the model takes into account the temperature mode as a component of the technical-operational state of the object. The resulting mathematical model could make it possible to synthesize an optimal automatic control system in terms of the operational state of the object. The problem addressed was to increase the accuracy of the identified mathematical models by applying the approach of feature engineering. The results showed that the identification of mathematical models by the initial data leads to a low level of accuracy of the obtained models, namely 65–70 % for the first output channel, 80–85 % for the second, and 75–80 % for the third, fourth, and fifth output channels. Accordingly, building models with a higher threshold of accuracy requires the use of other, more significant data for identification. This paper reports a method for reformatting the original data into artificial features and provides results of their effectiveness in relation to the original channels. The resulting artificial features and the original features were used for further identification; the resulting mathematical model has on average higher accuracy thresholds, namely 82 %, 93 %, 88 %, 85 % for the corresponding output channels. The results prove the effectiveness of applying the principle of feature engineering since the accuracy of the resulting model is 5–10 % higher compared to the baseline. The scope of practical application of the results includes the synthesis of automatic control systems based on mathematical models of control objects obtained as a result of identification.

CONTROL SYSTEMS SYNTHESIS FOR ROBOTS ON THE BASE OF MACHINE LEARNING BY SYMBOLIC REGRESSION

This paper presents a novel numerical method for solving the control system synthesis problem through the application of machine learning techniques, with a particular focus on symbolic regression. Symbolic regression is used to automate the development of control systems by constructing mathematical expressions that describe control functions based on system data. Unlike traditional methods, which often require manual programming and tuning, this approach leverages machine learning to discover optimal control solutions. The paper introduces a general framework for machine learning in control system design, with an emphasis on the use of evolutionary algorithms to optimize the generated control functions. The key contribution of this research lies in the development of an algorithm based on the principle of small variations in the baseline solution. This approach significantly enhances the efficiency of discovering optimal control functions by systematically exploring the solution space with minimal adjustments. The method allows for the automatic generation of control laws, reducing the need for manual coding, which is especially beneficial in the context of complex control systems, such as robotics. To demonstrate the applicability of the method, the research applies symbolic regression to the control synthesis of a mobile robot. The results of this case study show that symbolic regression can effectively automate the process of generating control functions, significantly reducing development time while improving accuracy. However, the paper also acknowledges certain limitations, including the computational demands required for symbolic regression and the challenges associated with real-time implementation in highly dynamic environments. These issues represent important areas for future research, where further optimization and hybrid approaches may enhance the method's practicality and scalability in real-world applications.

The study of forced oscillations in the non-linear system of an individual traction drive

BACKGROUND: The processes taking place in the ‘traction electric drive – wheel – road’ system during acceleration and braking cause increased dynamic loads on drive components, which may lead to a breakdown. Therefore, it is important to control the drive in a way to minimize and to suppress the given processes. To make it possible, the control system is to be equipped with a resistance torque observer at the electric motor shaft. In addition, in any system, there is a heighten interest in study of arise of resonances, which come with abrupt increase of oscillations amplitudes. Therefore, the features of oscillation phenomena in the given non-linear system are to be studied. AIM: Identification of the peculiarities of oscillatory processes, resonance phenomena in the systems of electromechanical drive of vehicles, which are nonlinear technical systems. METHODS: The study of features of the oscillating processes and the study of capabilities of arise of resonant phenomena were conducted using analysis of the differential equations system describing the operation of the non-linear system. RESULTS: The features of the oscillating phenomena in non-linear systems of interaction between an elastic wheel and road as well as capabilities of arise of resonant phenomena were considered. It is defined that arise of the resonant phenomena in the considered systems is not possible due to breakdown of them. The behavior of modes of interaction between an elastic wheel and road during intensive acceleration and braking was analyzed. The abrupt shock behavior of change rate of wheel torque and current consumed by a drive as well as features of lowering of them when using the self-oscillating phenomena suppression were found. CONCLUSION: The practical value of the study lies in ability of using the proposed conclusions at development of units of a traction electric drive and at synthesis of vehicle motion control systems.

Structural and Parametric Synthesis of a Hybrid Repetitive Control System for Uncertain Multi-Mode Plant

Article deals with the problem of constructing a hybrid adaptive-robust repetitive control system for one class of a MIMO plants which operating with structural and parametric uncertainty and constant action of an external disturbances. A procedure for structural and parametric synthesis of a control system is proposed. At the structural synthesis stage with the help of hyperstability criterion the authors are developing a decentralized combined controller. After that using the method of continuous models the authors are built a continuous-discrete control system. The main feature of a control loop structure synthesis stage is to ensure the validity of V. M. Popov’s integral inequality. For this purpose, the authors determining the special estimates that guarantee positivity for nonlinear non-stationary part of the system under consideration. At the system’s parametric synthesis stage the authors are use the environment of engineering and technical calculations "Matlab — Simulink" to perform optimization modeling of the continuous and hybrid repetitive control systems. This action is carried out using one of the functional optimization methods — a genetic algorithm. Authors use the criterion of generalized operation for automatic control systems to form the functionality for assessing the quality of the proposed system. At the simulation stage initially for continuous repetitive system it was searched its controller parameters which ensure the minimum value of the specified functional. Then, with a given discretization step of the control loop elements, the hybrid periodic system was optimized in order to improve the quality of its operation.

Synthesis of an automatic control system for a voltage inverter as part of an autonomous power supply system with a hydrogen module

This paper examines the problem of synthesizing a two-loop control system for a three-phase voltage source inverter designed for an autonomous power supply system. This type of DC/AC converters is an essential part of power supply systems with renewable energy sources as primary sources, and, accordingly, must corresponds to the requirements for the electric power quality. These requirements are met through circuit design solutions, as well as through the construction of high-precision automatic control systems. The system integrates: a hydrogen electrolyzer, a hydrogen storage system, and a hydrogen fuel cell. The paper proposes a method for calculating the parameters of PI controllers with resonant components, based on the time-scale separation method and allowing independent adjustment of the controller components. The introduction of a resonant component ensures high tracking accuracy for a desired main voltage harmonic and selective suppression of external harmonic influences. The proposed approach allows to synthesize an automatic control system that significantly improves the quality of the voltage inverter output parameters.

Optimal Synthesis of a Satellite Attitude Control System under Constraints on Control Torques and Velocities of Reaction Wheels

The problem of optimal synthesis of a nonlinear system’s control law parameters of satellite attitude control under constraints is considered. The maximum stability degree of a system is considered as an optimality criterion. The reaction wheels’ control moments and angular velocities achievable within the drives’ physical characteristics are considered as constraints. A linear model of the system converted from the original nonlinear model was used to solve the problem. The decomposition method, based on the transition from real time to relative time, is used to separate the tasks of optimality criterion maximization and constraints consideration. A method of synthesizing the optimal form of system transient process according to the maximum stability degree criterion is developed. An analytical method for determining the optimal values of control law parameters is proposed, based on the structural features of the linear differential equations system. A method that takes into account constraints on control moments and angular velocities of reaction wheels, based on transition scale from relative time to real time and its calculation algorithm, ensuring that conditions of all constraints are met, is developed. An example of solving the problem of optimal system synthesis is considered. The results demonstrate the effectiveness and simplicity of the proposed methods and algorithm for targeted selection of a system’s technical characteristics, taking into account constraints on reaction wheels’ maximum angular velocities and control moments values.

The Method of Synthesis of a Stable Closed-Loop Object Control System with Limiters

The Method of Synthesis of a Stable Closed-Loop Object Control System with Limiters

Comparative study of PI-controller and neurocontroller performances in optimal by settling time control problems

When developing control systems, an important issue arises of choosing an operator, which forms the control function. The standard approach is to use a PI- or PID-controller, a more advanced approach involves ANNs training for this purpose. A comparative analysis of the PI- and neurocontroller performances makes it possible to establish the disadvantages and advantages of each of the compared controllers, which is an important scientific and applied problem. The purpose of the work was to conduct a comparative analysis of the performance of the PI-controller and the neurocontroller based on a set of evaluation indicators for plants of the second and third orders. Such a comparison was carried out by using an approach to the synthesis of both controllers, which involved the minimization of a complex objective function. The latter is obtained as a result of reducing the problem of optimal control with constraints to the problem of unconstrained optimization. The analysis showed that according to the settling time indicator (optimization criterion), the neurocontroller has an advantage of 6.1...96.2% for the modelled plants. At the same time, according to other indicators of the control quality, the PI-controller has an advantage. In addition, the synthesis of a neurocontroller in terms of finding the minimum of the objective function is a more difficult problem. For its solution, a bigger number of iterations of the VCT-PSO optimization algorithm is required. It is rationally to set more than 1000 iterations and swarm population in the range 30…50 particles. A comparative analysis by the settling time of the neurocontroller and PI-controller, which is tuned according to engineering methods, showed significant reserves for improving this indicator. Thus, if the requirements for settling time minimization are quite strict, then it is advisable to use a neurocontroller. The obtained results will make it possible to develop recommendations for the rational choice of the control operator when solving practical problems of the control systems synthesis

Optimization of the Parameters of a Model Predictive Control System for an Industrial Fractionator

The problem of parametric synthesis of a model predictive control (MPC) system by the chemical process of production of the kerosene fraction of an industrial fractionator under conditions of constraints and uncertainty is considered. The optimal parameters of the MPC algorithm are obtained as a result of solving the problem of multi-criteria optimization, taking into account the intervally specified parameters of the plant model.

Mathematical modeling of heat exchange for efficient automated control systems

The article deals with the problem of mathematical modeling of heat transfer processes, taking into account a large number of factors affecting these processes and a variety of mathematical modeling methods. The article discusses the idea of developing a universal and flexible model that could quickly adapt to different initial modeling conditions and take into account various parameters for further use of the mathematical model in the synthesis of automatic control systems. The paper discusses the main aspects of mathematical modeling of heat transfer and the creation of a mathematical model in distributed heat exchanger parameters with the possibility of changing the properties and parameters of the equipment. The paper analyzes previous studies and identifies the problems of existing methods of mathematical modeling of heat transfer, such as lack of versatility, complexity, and insufficient accuracy. The paper goes on to review different approaches to mathematical modeling of heat transfer, such as models with a group of parameters, models in distributed parameters, and models based on artificial intelligence. The article provides an overview of model implementation methods and their advantages and disadvantages. Based on this analysis, the authors propose a new mathematical model of heat transfer in distributed parameters, which should be universal, easy to use, and accurate in accordance with the requirements of synthesizing automated control systems. The authors also outline the methodology for achieving this goal, which includes the implementation of the geometry of the heat exchanger, the implementation of conditions and mathematical modeling, as well as the study of the influence of parameters and the formation of transients. The general conclusion of the article is that the developed mathematical model of heat transfer can be used to synthesize automatic control systems for heat exchange processes in various industries.

Control system of the electric drive of a robot with a dc motor

Problem. Robotics and flexible production systems are the most important technical basis for the intensification of production. The use of robotic systems is expanding every year. This paper considers a two-circuit servo control system using the example of a DC motor current and speed control system and examines the functional diagram of the third circuit, a digital angle control system. Using the Matlab + SIMULINK software package, the servo drive and the digital system for controlling the angular position of the robot manipulator were modelled. Goal. As a result of the analysis, the purpose of the study was highlighted: the development of a digital system for adjusting the angular position of the manipulator, improve the quality of its positioning. Tasks: to study work management systems; to study the drives of robots; to get a mathematical model of an electric motor; to develop a machine diagram of a digital electric drive; to synthesize a three-loop robot positioning control system. Methodology. The research problems should be solved by methods of analysis and synthesis of automatic control systems. Results. In the work, a three-circuit control system of the electric drive of a robot with a direct current motor was developed. Thus, as a result of modeling the operation of a digital electric drive with three control circuits for current, speed and positioning, an aperiodic transient process was provided with quality indicators. Originality. Thus, the results of simulation of the two-loop servo control system showed that the dynamic characteristics of the electric motor in terms of current and speed of rotation, which meet the requirements of the task, are provided by the PI controller in the current control circuit and the PID controller in the speed control circuit. Thus, as a result of modeling the operation of a digital electric drive with three control circuits for current, speed and positioning, an aperiodic transient process was provided with quality indicators. Practical value. The following results were obtained during the research: the best control law for the current circuit is the proportional-integral (PI) law; the best control law for the speed contour is the proportional-integral-differential (PID) law; the best control law for a digital positioning control loop is the proportional (P) law.

Estimation of Centrifugal Pump Efficiency at Variable Frequency for Irrigation Systems

The sustainability of the food production achieved with the help of irrigation systems and the sustainability of their energy consumption are major challenges of the current century. Pumping systems currently account for approximately 30% of global electrical energy consumption. As electricity prices rise, there is a growing need for technological advancements to enhance energy efficiency and reduce consumption costs effectively. This study focuses on operating centrifugal pumps at variable frequency as an effective means of achieving this goal. Most centrifugal pump manufacturers/providers traditionally assume that pump efficiency remains constant across various operating frequencies, often equating the efficiency at various frequencies to that at the standard frequency (50/60 Hz). In contrast, this paper introduces a new formula for estimating pump efficiency, crucial to precise power consumption determination, particularly in variable-frequency scenarios. The formula parameters are identified by using experimental data acquired from an existing pumping system. The tests and results presented in this paper demonstrate that the proposed formula outperforms the formulas of the current industry standards in accuracy. Practically, the new relation assures enhanced accuracy in estimating pump efficiency and absorbed power, allowing for the design of a more precise model used for control systems synthesis required for operating centrifugal pumps at variable frequency. This research offers a new way of calculating pump efficiency, which could be very useful for industry practitioners seeking to optimize energy consumption in pumping systems.

Синтез параметрически грубых систем управления с регуляторами и наблюдателями состояния на основе грамианных технологий

Automatic control systems based on regulators with state observers are effective means to control linear and linearized objects of a high degree of complexity. One of the key problems in the synthesis of modal systems is the development of parametrically rough (robust) systems that retain their performance, as well as the main quality indicators with possible variations of the parameters of both the control object and the controller itself. The synthesis of a robust system with a state observer is carried out by the modal control method based on the matrix model of the controlled object. To ensure the parametric robustness of the system, the authors have proposed a technique which based on the mathematical apparatus of Gramians of controllability and observability as well as on the similarity transformation of observer matrices. Computer simulation of the system with state controller and observer is carried out by means of the MatLab software. The authors have proposed a method to form an observer state structure that is optimal in the sense of parametric roughness of the system, which is based on the procedure of transforming the similarity of the object model. And the transformation matrix is formed by varying the singular numbers of the controllability and observability gramians. The proposed method allows us to obtain an observer structure with a certain ratio of controllability and observability that ensures the fulfillment of the condition of parametric roughness i.e., the absence of positive feedback in the control device. The results obtained make it possible to clearly demonstrate the high efficiency of using the Gramian method for the synthesis of control systems with state observers with low sensitivity to variations of the controller own parameters.

Synthesis of resilient fallback control system under cyber-attacks via supervisory control

Industrial control systems (ICS) require system design and operation under cyber-attacks. This study aims to design a fallback control system that can switch from normal control to fallback control and verify its superiority. The target system is a factory automation (FA) system consisting of a normal programmable logic controller (PLC) and a fallback PLC. In this system, we design a fallback logic that takes over control in the case of cyber-attacks. The design of this logic requires a system model that manages smooth state transitions between normal control and fallback control in an integrated manner under cyber-attacks. In response, we model a control program in the framework of discrete event systems (DESs) and apply supervisory control to derive a supervisor model that can manage the system in an integrated manner. To ensure the controllability of the FA system during cyber-attacks, we design a control specification that includes a detection function to enable rapid switching of the control state. As a result, we generate the fallback logic from the supervisor model with guaranteed controllability under cyber-attacks and implement it in a fallback PLC to verify the effectiveness of the proposed logic.

Optimal control model as an approach to the synthesis of a supersonic transport control system

Optimal control model as an approach to the synthesis of a supersonic transport control system

Design of Optimal Control Systems in the Frequency Domain by the Functional of the Generalized Work

The paper considers the problem of analytical design of optimal controllers (ADOC) for one-dimensional linear stationary objects according to the functional of generalized work (FGW) A. A. Krasovsky. The use of FGW in comparison with the quadratic performance functional greatly simplifies the calculation of the optimal controller — the calculation of its matrix of coefficients mainly consists in solving the linear matrix Lyapunov equation, which, in contrast to the nonlinear matrix Riccati equation, fundamentally reduces the amount of calculations. In addition, the use of FGW provides the best stability margins of the designed system in terms of amplitude and phase. This work is devoted to the development of a method for solving the ADOC problem A. A. Krasovsky in the frequency (complex) domain, which reduces the determination of the transfer function coefficients of the optimal controller for an object of order n to the solution of the corresponding system of n linear algebraic equations. In this regard, the proposed method for solving the ADOC problem by A. A. Krasovsky differs by a much smaller amount of calculations in comparison with the standard method, in which the Lyapunov equation is solved with the desired matrix of dimensions n * n. The proposed method for the synthesis of optimal control systems, which has an analytical nature, became the basis for solving the inverse problem ADOC A. A. Krasovsky, which consists in determining the values of the weight coefficients of the FGW, which provide the given primary quality indicators of the synthesized control system. Using its relations, a relatively simple method for calculating the FGW coefficients based on the given values of the error coefficients for the designed dynamic system has been developed.

Using the State Space Method for Calculating Electromechanical Transients

The state space method is widely used for the analysis and synthesis of automatic control systems in a wide variety of industries. It was revealed that the analysis of electromechanical processes in electrical systems is associated with the solution of a system of nonlinear differential equations by very laborious mathematical methods. It is shown how to represent a system of differential equations describing electromechanical transients in synchronous machines in d, q, 0 – coordinates, in matrix form. An algorithm for calculating electromechanical transients by the state space method is considered. The transit matrix of states is represented by a decomposition formula, the terms of which are determined by matrices with constant elements. Comparison with known numerical calculation methods allows us to conclude that the state space method is a fairly effective way to analyze electromechanical transients in synchronous machines.

Simulation model of a flat plate air solar collector

Simulation model of a flat plate air solar collector

Filtr Kalmana jako alternatywa dla rozszerzonego obserwatora stanu w algorytmie regulacji ADRC

The article presents a modified Active Disturbance Rejection Control (ADRC) algorithm that uses the Kalman Filter (KF) for the estimation of extended state vector. The Kalman filter replaced the Extended State Observer (ESO) used in its basic form. The purpose of this modification was to improve the system robustness under conditions of stochastic measurement disturbances. The method of the control system synthesis and the Kalman filter gains selection, ensuring control efficiency, as well as their impact on the system operation, were presented. The experiments were carried out on a laboratory setup – the Ball Balancing Table (BBT). Control quality was assessed based on time plots of signals and integral performance indices for various algorithm gains configurations and different noise levels. As a result of the conducted research, the advantage of using the Kalman filter over the ESO in terms of sensitivity to measurement noises was demonstrated. Implementation of the Kalman filter as the ESO determined a positive impact on control quality and the ability to reject internal disturbance also in a deterministic system.

ADAPTIVE IDENTIFICATION OF NON-STATIONARY AIRCRAFT, ASSESSMENT OF THEIR STABILITY

For the most part, various processes are multi-link inertial systems that have a certain non-stationarity to one degree or another. The presence of inertia leads to the fact that it is customary to consider processes as dynamic objects. Such dynamic non-stationary objects can be described by models, both in continuous time (for example, differential equations) and in discrete time (for example, difference equations). Ultimately, the choice of a discrete or continuous form of representation of a non-stationary object is determined by which mathematical apparatus is considered more appropriate by the researcher.
 In some cases, it is possible to consider the process as a static object, which allows to significantly simplify the analysis of such a non-stationary object. However, replacing a dynamic object with a static model is not always possible and leads to an uncontrolled error at the output.
 Non-stationarity is an important characteristic of the process as an object of management and is caused primarily by changes in process properties, under the influence of changes in environmental conditions, aging and wear of equipment, etc. Non-stationarity of the process significantly complicates the analysis and synthesis of control systems of this kind of objects, since the theory for control systems stationary in time is not applicable for non- stationary systems.
 Depending on the set goal and management tasks, process models can have different forms of presentation.
 The article examines various forms of presentation and research of non-stationary dynamic objects and their parameters from the standpoint of synthesis of the circuit of assessment and management of various processes, in particular the flight of an aircraft.
 The results of the analysis of the accuracy of identification of non-stationary objects, the adaptation of systems when combining or distributing in time the stages of "learning" and "management" in conditions of stochastic uncertainty are presented. The conditions for obtaining reliable estimates of the current values of object parameters during their measurement, processing and transmission in communication channels in real time are determined.