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Articles 241 - 270 of 424
Full-Text Articles in Operations Research, Systems Engineering and Industrial Engineering
The Optimization Of Failure Risk Estimation On The Uniform Corrosion Rate With A Non-Linear Function, Fernanda Hartoyo, Jaka Fajar Fatriansyah, Imam Abdillah Mas'ud, Farhan Rama Digita, Hanna Ovelia, D. Rizal Asral
The Optimization Of Failure Risk Estimation On The Uniform Corrosion Rate With A Non-Linear Function, Fernanda Hartoyo, Jaka Fajar Fatriansyah, Imam Abdillah Mas'ud, Farhan Rama Digita, Hanna Ovelia, D. Rizal Asral
Journal of Materials Exploration and Findings
Failures in the oil and gas pipeline system are conditions that must be avoided and anticipated because the losses due to the failures can occur at a very high level. Internal corrosion is one of the significant causes of the failures in pipeline systems. In addition, this type of corrosion is due to the high content of carbon dioxide and other corrosive substances in crude oil and natural gas. Therefore, an optimal inspection scheduling system is required to prevent the possibility of pipeline failures due to corrosion and to avoid any overspending on the budget due to excessive inspection scheduling. …
Effect Of Temperature, Catalyst Concentration And Time, On Polylactic Acid Production From Sisal Boles Juice By Ring Open Polymerization, Neema O. Msuya
Effect Of Temperature, Catalyst Concentration And Time, On Polylactic Acid Production From Sisal Boles Juice By Ring Open Polymerization, Neema O. Msuya
Tanzania Journal of Engineering and Technology (TJET)
Polylactic acid (PLA) is a biodegradable and renewable alternative to non-biodegradable petrochemical-based polymers that is environmentally friendly and green. PLA can be made from a variety of agricultural wastes that contain sugars, such as sisal boles. This study aimed at analysing the possibility of producing PLA from lactic acid (LA) produced from sisal bole. A 2n factorial design was used to analyse the effects of temperature (160-180ºC), time (1-2 hrs) and tin octoate catalyst concentration (0.025-0.05%) on the PLA yield during polymerization. Minitab Version 20.2.0 was used to design the experiment and analyse the effects on the responses through ANOVA. …
The Effective Strategies For Mitigation The Impact Of Covid-19 On Construction Projects In Egypt, Nora Magdy Essa, Ibrahim Mahdi, Hassan Mohamed Ibrahim
The Effective Strategies For Mitigation The Impact Of Covid-19 On Construction Projects In Egypt, Nora Magdy Essa, Ibrahim Mahdi, Hassan Mohamed Ibrahim
Future Engineering Journal
From the time when the first narrated infections in Wuhan China, in late 2019, COVID-19 has had a substantial peal on human life and health. By the early of 2020, the World Health Organization (WHO) announced the eruption of COVID-19, a public health crisis of international concern. On 11 March 2020, the World Health Organization officially announced COVID-19 a pandemic. The first case was infected in Egypt of covid-19 on Feb 14, 2020 (Gilbert et al., 2020). On 16 March 2020, the Egyptian Government began issuing decisions as preventative courses as part of the country's inclusive plan to cope with …
Estimating The Weights Of Latticed Power Transmission Towers Using Genetic Programming, Ahmed M. Ebid Dr.
Estimating The Weights Of Latticed Power Transmission Towers Using Genetic Programming, Ahmed M. Ebid Dr.
Future Engineering Journal
The recent booming in the power network industry inspired a lot of researchers to develop models to estimate the optimum cost of transmission towers. Unlike previous researches which depended on design the tower from scratch, this research depends on collecting actual database from several projects around the globe and applying the well-known (GP) technique to develop a model to predict the tower weight. The accuracy of the developed formula was about 84%. The developed model could be used in early tender stage or to check design economy.
On-Line Process Physics Tests Via Lyapunov-Based Economic Model Predictive Control And Simulation-Based Testing Of Image-Based Process Control, Henrique Oyama, Akkarakaran Francis Leonard, Minhazur Rahman, Govanni Gjonaj, Michael Williamson, Helen Durand
On-Line Process Physics Tests Via Lyapunov-Based Economic Model Predictive Control And Simulation-Based Testing Of Image-Based Process Control, Henrique Oyama, Akkarakaran Francis Leonard, Minhazur Rahman, Govanni Gjonaj, Michael Williamson, Helen Durand
Chemical Engineering and Materials Science Faculty Research Publications
Next-generation manufacturing involves increas- ing use of automation and data to enhance process efficiency. An important question for the chemical process industries, as new process systems (e.g., intensified processes) and new data modalities (e.g., images) are integrated with traditional plant automation concepts, will be how to best evaluate alternative strategies for data-driven modeling and synthesizing process data. Two methods which could be used to aid in this are those which aid in testing data-based techniques on-line, and those which enable various data-based techniques to be assessed in simulation. In this work, we discuss two techniques in this domain which can …
Lyapunov-Based Economic Model Predictive Control For Online Model Discrimination, Henrique Oyama, Helen Durand
Lyapunov-Based Economic Model Predictive Control For Online Model Discrimination, Henrique Oyama, Helen Durand
Chemical Engineering and Materials Science Faculty Research Publications
Economic model predictive control (EMPC) is a flexible control design strategy that can be modified to achieve many operating goals while also ensuring safe operation (e.g., by adding Lyapunov-based stability constraints to form Lyapunov-based EMPC, or LEMPC). Prior works have investigated LEMPC capabilities for achieving goals online beyond optimizing process economics, including aiding in model structure selection to benefit model-based control system design since the accuracy and quality of the process model are important for achieving an expected performance from such systems. This work further probes the capabilities of LEMPC to accomplish multiple objectives during process operation, including aiding in …
Data Driven Bayesian Network To Predict Critical Alarm, Joseph Mietkiewicz, Anders Madsen
Data Driven Bayesian Network To Predict Critical Alarm, Joseph Mietkiewicz, Anders Madsen
Articles
Modern industrial plants rely on alarm systems to ensure their safe and effective functioning. Alarms give the operator knowledge about the current state of the industrial plants. Trip alarms indicating a trip event indicate the shutdown of systems. Trip events in power plants can be costly and critical for the running of the operation.This paper demonstrates how trips events based on an alarm log from an offshore gas production can be reliably predicted using a Bayesian network. If a trip event is reliably predicted and the main cause of it is identified, it will allow the operator to prevent it. …
Efficient Removal Of Lead Ions From Aqueous Media Using Sustainable Sources On Marine Algae, Hannah Namkoong, Erik Biehler, Gon Namkoong, Tarek M. Abdel-Fattah
Efficient Removal Of Lead Ions From Aqueous Media Using Sustainable Sources On Marine Algae, Hannah Namkoong, Erik Biehler, Gon Namkoong, Tarek M. Abdel-Fattah
Electrical & Computer Engineering Faculty Publications
The goal of this project is to explore a new method to efficiently remove Pb(II) ions from water by processing Undaria pinnatifida into immobilized beads using sodium alginate and calcium chloride. The resulting biosorbent was characterized by Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy (SEM-EDS). Using immobilized U. pinnatifida, we investigated the effect of various factors on Pb(II) ion removal efficiency such as temperature, pH, ionic strength, time, and underlying biosorption mechanisms. For Pb(II) ion biosorption studies, Pb(II) ion biosorption data were obtained and analyzed using Langmuir and Freundlich adsorption models. It …
Predictive Analysis And Synthesis, Modeling And Control Of Complex Technological Processes And Systems, Zhahongir Sherboyevich Bekqulov
Predictive Analysis And Synthesis, Modeling And Control Of Complex Technological Processes And Systems, Zhahongir Sherboyevich Bekqulov
Chemical Technology, Control and Management
Consider the theoretical underpinnings of practically predictive analysis and synthesis, modeling and automatic control of complex chemical technological processes and systems, and the evolution of advanced (or advanced) APC (Advanced Process Control) control of technological processes and industries. The current state of industrial automation systems and the characteristics of their deployment are highlighted. The features of each stage of the analysis and synthesis of APC - advanced process control for complex dynamic objects are disclosed. The real situation and features of the implementation of industrial automation systems of industrial enterprises are reflected.
Virtual Analyzers For Increasing The Intelligence Of Industrial Process Control Systems, Umidjon Abdimajotovich Ruziev Phd, Marufjon Kobuljanovich Shodiev
Virtual Analyzers For Increasing The Intelligence Of Industrial Process Control Systems, Umidjon Abdimajotovich Ruziev Phd, Marufjon Kobuljanovich Shodiev
Chemical Technology, Control and Management
It is shown that the development and implementation of virtual analyzers of the quality of the final industrial products is an effective tool for increasing the efficiency of industrial production. The methodology and stages of development of virtual analyzers for predicting the quality of products, monitoring non-measurable or difficult-to-measure parameters of continuous and periodic technological processes are considered, and issues of supporting and adapting a virtual analyzer during its operation without restructuring are also considered.
Algorithm For Calculating The Parameters Of A Multi-Position Electromagnetic Linear Mechatronic Module, Nazarov Khayriddin Nuritdinovich, Matyokubov Nurbek Rustamovich, Temurbek Omonboyevich Rakhimov
Algorithm For Calculating The Parameters Of A Multi-Position Electromagnetic Linear Mechatronic Module, Nazarov Khayriddin Nuritdinovich, Matyokubov Nurbek Rustamovich, Temurbek Omonboyevich Rakhimov
Chemical Technology, Control and Management
Currently, in the world in the field of science, engineering and technology, including in mechatronics and robotics, the creation of multi-coordinate mechatronic systems that perform power and control functions is becoming of paramount importance, this is due to a number of important positive qualities of the systems, such as simplicity and compactness of the design, the possibility of obtaining significant efforts, high accuracy and stability of the establishment of fixed positions, ease of control and high reliability. This article presents the calculation of the parameters of multi-position mechatronic modules based on linear execution elements. In the construction of this model, …
New Transformer Changer Static Characteristics Measuring Angle Silences Difference, Sultan Faizullayevich Аmirov, Nurulla Raxmatullayevich Yuldashev
New Transformer Changer Static Characteristics Measuring Angle Silences Difference, Sultan Faizullayevich Аmirov, Nurulla Raxmatullayevich Yuldashev
Chemical Technology, Control and Management
Presented the specific features of the new transformer converter, which measures the difference in angular displacement, and examines the nonlinearity levels of static characteristics, sensitivity and static characteristics. Studies have shown that in a new measuring device, where one of the two moving parts consists of a magnetic conductor made in the form of an Archimedean spiral made of ferromagnetic material, the balance of the magnetic bridge changes not only depending on the angle of rotation of it’s shoulder resistances. the current is disturbed by the change in the magnitude of the combined air gap depending on the angle of …
Design Lifecycle Management Of Technological Processes, Yusuf Shodiyevich Avazov
Design Lifecycle Management Of Technological Processes, Yusuf Shodiyevich Avazov
Chemical Technology, Control and Management
The issues of life cycle management of design processes of complex technological processes are considered. An analysis of works devoted to the automated design of technological processes and industries, product life cycle management, and the use of predominant modeling in design is presented. A structure for the implementation of the design of technological processes is proposed and it’s components are described. An algorithm is proposed to reduce the life cycle of the design of a technological process. The sequence of selection of the most optimal project options with the help of the proposed algorithm is described. It is shown that …
Developing Advanced Process Control System For Manufacturing Processes Using Virtual Analyzer, Elyor Erkinovich Samadov
Developing Advanced Process Control System For Manufacturing Processes Using Virtual Analyzer, Elyor Erkinovich Samadov
Chemical Technology, Control and Management
This research reflects outlines the main potential features of Advanced Process Control (APC) systems for improved control of technological processes and production. It is shown developing APC systems using a virtualized analyzer (VA) is a very effective technique to increase the efficiency of industrial production. This research reflects the main steps of generating VA as part of the APC system and also describes the key features of each step-in terms of analyzer synthesis.
Mathematical Modeling Of Processes Of Diagnostics Of Technical And Technological Objects, Azizbek Nodirbekovich Yusupbekov, Khurshid Salim Ugli Turayev
Mathematical Modeling Of Processes Of Diagnostics Of Technical And Technological Objects, Azizbek Nodirbekovich Yusupbekov, Khurshid Salim Ugli Turayev
Chemical Technology, Control and Management
The work is an introduction to the technical diagnostics of technical (or technological) objects. It discloses the basic concepts and definitions of the reliability of dynamic systems as objects of diagnostic reference knowledge and their diagnosis. Structural schemes of diagnosing objects with individual and combined channels of influence are analyzed. Questions of rational construction of base of reference knowledge are stated.
Uncertainty Of The Ultrasonic Method For Determining The Strength Of Concrete, Ortagoli Sharipovich Hakimov, Zamira Khudoyberdiyevna Ernazarova
Uncertainty Of The Ultrasonic Method For Determining The Strength Of Concrete, Ortagoli Sharipovich Hakimov, Zamira Khudoyberdiyevna Ernazarova
Chemical Technology, Control and Management
The issues of measuring the strength of concrete by the method of surface sounding by ultrasound are considered. A measurement model and formulas for estimating the total standard measurement uncertainty, information about the standards used, measurement tools and methods, and environmental parameters are given. Information about the estimation of uncertainty in the form of "eight steps", such as: measurement task; mathematical model of measurement; analysis of input values; observation results; correlations; uncertainty budget; expanded uncertainty; measurement result. It has been established that the uncertainty of type B of the ultrasonic method for determining the strength of concrete is much less …
Quality Control Of Combustion Of Gaseous Fuel In Furnaces, Azamat Toirovich Rajabov
Quality Control Of Combustion Of Gaseous Fuel In Furnaces, Azamat Toirovich Rajabov
Chemical Technology, Control and Management
The issues of research and development of systems for monitoring the availability and quality of the process of fuel combustion in industrial furnaces are interpreted. The perspective of using new elements in control systems - communication sensors for the presence and quality in gas-burning installations and furnaces are shown. A method has been developed to control the optimal aeration coefficient based on the extreme of the total integral amplitude-frequency characteristic of the flame conductivity pulsations, which makes it possible to control the quality characteristics of gas-burner devices and control the ratio of the components of the combustible mixture with high …
Regular Algorithms For Adaptive Identification Of Linear Non-Stationary Systems, H.Z. Igamberdiyev, H.I. Sotvoldiev, U.F Mamirov
Regular Algorithms For Adaptive Identification Of Linear Non-Stationary Systems, H.Z. Igamberdiyev, H.I. Sotvoldiev, U.F Mamirov
Chemical Technology, Control and Management
The article deals with the formation of regular algorithms for adaptive parametric spline identification of linear non-stationary systems. Analyzed the issues of constructing adaptive identification of continuous linear non-stationary systems with monotonic and sign-constant parameters. In this case, in a non-stationary system, the entire observation interval is in some way divided into sub-intervals. Identification is carried out at each of the parameter constancy intervals, while the parameter matrix is re-evaluated for the next interval. The input data of the system are determined with an error depending on the error of approximating the state of the system by splines and approximating …
Control Of The Facial Design Process Of Innovative Developments, Yusuf Shodiyevich Avazov
Control Of The Facial Design Process Of Innovative Developments, Yusuf Shodiyevich Avazov
Chemical Technology, Control and Management
The role and place of visual design in the process of creating an innovative development have been stated. It is shown that the tasks of the face stage of the product life cycle are devoted to systemic issues, in the center of which is the resolution of the contradiction between the desired and the achievable. The first is determined by the need to create a new system of a higher level, and the achievable is determined by the level of development of science, technology and production technology, as well as by the conditions of operation and repair. The work is …
Information Software And Devices For Energy Efficiency Management And Control, Narzullo Nuriddinovich Mirzoyev
Information Software And Devices For Energy Efficiency Management And Control, Narzullo Nuriddinovich Mirzoyev
Chemical Technology, Control and Management
The article provides information on modern methods of management and control of energy efficiency at industrial enterprises. This includes the software needed to manage and monitor energy efficiency, as well as the formation of a database. In addition, a structural diagram of an intelligent power monitoring system has been developed and its elements have been selected. Describes the principle of operation of an intelligent measuring device, its connection to the network, conversion of analog signals to digital, channels and ranges of signal transmission, metrological characteristics. The article details the capabilities and benefits of smart meters.
Control System Synthesis With Self-Adapting Regulator By Interactive Adaptation Method, Isamiddin Xakimovich Siddikov, Renata Nikolayevna Izmaylova
Control System Synthesis With Self-Adapting Regulator By Interactive Adaptation Method, Isamiddin Xakimovich Siddikov, Renata Nikolayevna Izmaylova
Chemical Technology, Control and Management
The research results on the creation of a self-adapting control system for a nonlinear dynamic object based on the theory of intelligent control using interactive adaptation methods have been presented. The lack of an accurate description and the nonlinearity of the dynamic properties of the object under study, the presence of mutual influence of cross communication channels in the control circuits, as well as the influence of various types of uncertainties associated with the lack of a priori information about the process, significantly complicate the solution of the problem of synthesis of highly efficient control systems for dynamic objects, which …
Analysis Of Water Treatment Methods For Circulating Water Supply In Industrial Plants, Djalolitdin Paxritdinovich Mukhitdinov, Nilufar Abdusomi Kizi Yunusova
Analysis Of Water Treatment Methods For Circulating Water Supply In Industrial Plants, Djalolitdin Paxritdinovich Mukhitdinov, Nilufar Abdusomi Kizi Yunusova
Chemical Technology, Control and Management
This scientific paper deals with the problem of extracting Ca2+ and Md2+ salts from water in order to prevent the formation of scale on the heating surfaces of heat exchange equipment. The features, advantages and disadvantages of chemical, membrane and ion exchange methods of water treatment have been evaluated. It has been shown that the chemical method of water purification can be used only for the preparation of industrial water at large stations (at the same time, high residual hardness prevails in the water, the equipment has low productivity), and the membrane method requires pretreatment of water, creation of overpressure …
Ultrasonic Extraction Of Instant Forms Of Plant Substrates In Industrial Production, Shakhnoza Abduvaxitovna Sultanova, Jasur Safarov, Azamat Bakir O'G'Li Usenov, Doston Ishmuhammat Ogli Samandarov, Qobil Akmal Ogli Mukhiddinov
Ultrasonic Extraction Of Instant Forms Of Plant Substrates In Industrial Production, Shakhnoza Abduvaxitovna Sultanova, Jasur Safarov, Azamat Bakir O'G'Li Usenov, Doston Ishmuhammat Ogli Samandarov, Qobil Akmal Ogli Mukhiddinov
Chemical Technology, Control and Management
In recent years, both in our country and abroad, ultrasonic extraction methods have been increasingly used in industrial production, which is associated with the extraction of various substances and compounds from natural plant substrates. Domestic and foreign experience shows that this method has significant advantages over traditional methods and can significantly increase the efficiency and profitability of industrial enterprises, producing complete and functional food products.
This article discusses a brief theory of ultrasonic cavitation and the experience of extracting substrates from plants. Different results have been compared and analyzed.
Analysis Of Grain Product Drying Methods, Azizbek Nodirbekovich Yusupbekov, Dilmurod Egamberganov
Analysis Of Grain Product Drying Methods, Azizbek Nodirbekovich Yusupbekov, Dilmurod Egamberganov
Chemical Technology, Control and Management
Various drying methods and grain characteristics have been studied. The advantages and disadvantages of various grain drying methods were obtained. The use of the following methods of drying grain products is very useful for speeding up the drying process, reducing waste, achieving more flexible process management and delivering all the nutrients of dried grain and grain products to the subsequent production process. The technological approaches that increase the efficiency of high-quality production after drying grain products, the requirements for modern grain dryers have analyzed. The ways of overcoming the problem of high energy consumption in the process of drying grain …
Implementation Of Distance Learning At Universities Using The Experience Of The Honeywell Process Control Laboratory At Tashkent State Technical University, Nodirbek Rustambekovich Yusupbekov, Adilov Tulkunovich Farukh, Isakova Ismailovna Sitora
Implementation Of Distance Learning At Universities Using The Experience Of The Honeywell Process Control Laboratory At Tashkent State Technical University, Nodirbek Rustambekovich Yusupbekov, Adilov Tulkunovich Farukh, Isakova Ismailovna Sitora
Chemical Technology, Control and Management
The experience of modernization of the Honeywell Process Control Laboratory at Tashkent State Technical University has been considered (which is equipped with upgraded equipment (simulators for simulating various technological processes, distance learning tools). As a result, the quality of the demonstration of process control mechanisms increased the availability of theoretical and practical knowledge in the field of automated control systems. They also considered the teaching methods necessary for a modern student – remote access in real time, when students pass a knowledge test, consult with teachers, etc.
Error Of Contactless Converters Of High Currents Of Monitoring And Control Systems From The Influence Of Currents Of Neighboring Buses, A.M. Plakhtiev, Gayratjon Gaziev, Y.A. Meliboev, O. Doniyorov
Error Of Contactless Converters Of High Currents Of Monitoring And Control Systems From The Influence Of Currents Of Neighboring Buses, A.M. Plakhtiev, Gayratjon Gaziev, Y.A. Meliboev, O. Doniyorov
Chemical Technology, Control and Management
The article presents the general principles of construction of contactless ferromagnetic converters of large direct currents, the main requirements for them, and the results of the development of one of the developed wide-range magnetomodulation contactless converters of control and control systems concerning large electric power facilities. The developed converter, unlike the known ones, have a wide range of controlled currents, increased accuracy and sensitivity, a technological design, and small weight and dimensions at low material consumption and cost. The errors of contactless wide-range magnetomodulation converters from the influence of currents of neighboring buses connected by and the opposite direction are …
Implementation Of The Pid Control Law Of A Multidimensional Dynamic System, Khurshid Salim Ugli Turayev
Implementation Of The Pid Control Law Of A Multidimensional Dynamic System, Khurshid Salim Ugli Turayev
Chemical Technology, Control and Management
Most industrial automation facilities are multi-circuit with a significant influence of cross-links between the goals. The paper develops a system for automatic parameter adjustment of a programmable logic controller that implements the proportional-integral-differential control law of a multidimensional dynamic object. The issues of decentralized management of multidimensional dynamic objects are discussed. The control system is based on the method of independent synthesis with static compensation of the impact of cross-links. Additional software has been developed to determine the parameters of the control system. After setting the necessary parameters, the process of automatic adjustment of the controller parameters starts. Self-tuning procedures …
Optimization In The Application Of Varnishes Barrier On Cartonboard Packaging, Andre Ramalheiro De Andrade, Maria Isabel Rodrigues Phd, Eduardo Luiz Machado Phd
Optimization In The Application Of Varnishes Barrier On Cartonboard Packaging, Andre Ramalheiro De Andrade, Maria Isabel Rodrigues Phd, Eduardo Luiz Machado Phd
Journal of Applied Packaging Research
In this work adjustments in the rotogravure printing process are proposed to the varnish water vapor transmission rate (WVTR) aiming to obtain results smaller than 20g/m²/24h. One case study was used for the propositions for improvements, where focused on varnish application process in a gravure printer for an eight-printing unit cartonboard packaging, maximum printing speed of 175 m/min and a 285 g/m² weight cartonboard. The possible variables that influenced the WVTR result were selected from the technical expertise of the people involved in the project, the analysis in the printing process with the application of directed trials using experimental designs …
Problems Of Modeling And Control Of The Technological Process Of Ore Grinding, Djalolitdin Pakhritdinovich Mukhitdinov, Sanjar Boybutayev
Problems Of Modeling And Control Of The Technological Process Of Ore Grinding, Djalolitdin Pakhritdinovich Mukhitdinov, Sanjar Boybutayev
Chemical Technology, Control and Management
The article analyzes the methods of mathematical modeling of the closed-loop process of fine grinding of ore in order to predict the composition of the crushed raw material. Analyzed modeling methods that consider the control of classification of crushed raw materials and finished products by the size of the recirculating load, simulation modeling methods, methods that use neuro-phase netthe research apparatus, in which the fuzzy logic apparatus serves as a fundamental component for the formation of conclusions. The materials presented in the article reflect the theoretical substantiation and generalization of the accumulated practical experience in modeling and control of the …
Structural-Parametric Analysis And Synthesis Of Control Systems With Two Degrees Of Freedom, Azizbek Nodirbekovich Yusupbekov, Khurshid Salim Ugli Turayev
Structural-Parametric Analysis And Synthesis Of Control Systems With Two Degrees Of Freedom, Azizbek Nodirbekovich Yusupbekov, Khurshid Salim Ugli Turayev
Chemical Technology, Control and Management
Automatic tuning of the parameters of PID - regulators is proposed by means of a modified experiment that takes into account the influence of elements and circuits in the form of additive uncertainty. The use of a multiply connected control scheme with two degrees of freedom for decoupling is proposed in order to facilitate the implementation of a mechanism for combating the phenomenon of integral saturation. Equations are derived for the transition from a circuit with one degree of freedom to a circuit with two degrees of freedom for the general and special cases of a two-dimensional system, which makes …