Pub Date : 2021-06-30DOI: 10.25728/ASSA.2021.21.2.1077
D. V. Tunitsky
The article concerns a piecewise linear modeling of a vast range of color printing devices: various printers of different kind and nature, presses, etc. The central purpose is not a presentation of ready to use computational algorithms, or, moreover, accomplished software solutions. The point is to reveal some aspects of mathematical modeling, which could serve as both a guideline for creation of practical and robust engineer solutions and an example of nontrivial application of piecewise linear topology.
{"title":"Mathematical Modeling of Color Printing Devices: Color Gamut Visualization and Colorimetric Measurements Regularization","authors":"D. V. Tunitsky","doi":"10.25728/ASSA.2021.21.2.1077","DOIUrl":"https://doi.org/10.25728/ASSA.2021.21.2.1077","url":null,"abstract":"The article concerns a piecewise linear modeling of a vast range of color printing devices: various printers of different kind and nature, presses, etc. The central purpose is not a presentation of ready to use computational algorithms, or, moreover, accomplished software solutions. The point is to reveal some aspects of mathematical modeling, which could serve as both a guideline for creation of practical and robust engineer solutions and an example of nontrivial application of piecewise linear topology.","PeriodicalId":39095,"journal":{"name":"Advances in Systems Science and Applications","volume":"21 1","pages":"117-132"},"PeriodicalIF":0.0,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49129360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-31DOI: 10.25728/ASSA.2021.21.1.1037
M. Morozov
The paper considers a periodic differential inclusion with an asymptotically stable set. The uniform character of convergence of solutions to an asymptotically stable set is established. An exponential estimate is obtained for solutions of a periodic differential inclusion homogeneous in state vector. Examples of control systems leading to consideration of periodic differential inclusions are given. These results can find applications in the stability analysis of control systems with periodic parameters, in particular, servomechanisms whose elements operate on AC, control systems with pulse amplitude modulation, and systems used to solve problems related to investigating vibrations of milling machines.
{"title":"On Uniform Convergence Property of Solutions for Periodic Differential Inclusions with Asymptotically Stable Sets","authors":"M. Morozov","doi":"10.25728/ASSA.2021.21.1.1037","DOIUrl":"https://doi.org/10.25728/ASSA.2021.21.1.1037","url":null,"abstract":"The paper considers a periodic differential inclusion with an asymptotically stable set. The uniform character of convergence of solutions to an asymptotically stable set is established. An exponential estimate is obtained for solutions of a periodic differential inclusion homogeneous in state vector. Examples of control systems leading to consideration of periodic differential inclusions are given. These results can find applications in the stability analysis of control systems with periodic parameters, in particular, servomechanisms whose elements operate on AC, control systems with pulse amplitude modulation, and systems used to solve problems related to investigating vibrations of milling machines.","PeriodicalId":39095,"journal":{"name":"Advances in Systems Science and Applications","volume":"21 1","pages":"76-85"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41347348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-31DOI: 10.25728/ASSA.2021.21.1.1052
V. S. Viktorova, A. S. Stepanyants
This paper describes models, methods and software tool for testability analysis of aviation systems. It comprises analytical and programing aspects of calculations of main testability, reliability and availability indices. It presents general description of the software, XML schema of input data and technique of their mapping to the database structure. The procedure for generating the initial data for testability analysis based on the line replaceable units failure modes report is described. Fault tree model for analysis of the built-in test conformity is suggested. Markov models have been created for analyzing reliability and availability, taking into account the features of the built-in test and the specifics of the aircraft operation. An approach to the construction of trends in the operative availability of aviation systems in the inter-maintenance interval is proposed.
{"title":"Software for Testability Analysis of Aviation Systems","authors":"V. S. Viktorova, A. S. Stepanyants","doi":"10.25728/ASSA.2021.21.1.1052","DOIUrl":"https://doi.org/10.25728/ASSA.2021.21.1.1052","url":null,"abstract":"This paper describes models, methods and software tool for testability analysis of aviation systems. It comprises analytical and programing aspects of calculations of main testability, reliability and availability indices. It presents general description of the software, XML schema of input data and technique of their mapping to the database structure. The procedure for generating the initial data for testability analysis based on the line replaceable units failure modes report is described. Fault tree model for analysis of the built-in test conformity is suggested. Markov models have been created for analyzing reliability and availability, taking into account the features of the built-in test and the specifics of the aircraft operation. An approach to the construction of trends in the operative availability of aviation systems in the inter-maintenance interval is proposed.","PeriodicalId":39095,"journal":{"name":"Advances in Systems Science and Applications","volume":"21 1","pages":"113-138"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43873307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-31DOI: 10.25728/ASSA.2021.21.1.808
V. Kramar, V. Alchakov, A. Osadchenko
An optimal algorithm for linear control of the unmanned vessel dynamic positioning system with provision for vessel characteristics, equipment, and the process has been developed. A block diagram for the automatic dynamic positioning system has been suggested which allows presenting a necessary set of devices for its technical implementation.
{"title":"The Optimal Control of the Vessel’s Automatic Dynamic Positioning System Under Deviation","authors":"V. Kramar, V. Alchakov, A. Osadchenko","doi":"10.25728/ASSA.2021.21.1.808","DOIUrl":"https://doi.org/10.25728/ASSA.2021.21.1.808","url":null,"abstract":"An optimal algorithm for linear control of the unmanned vessel dynamic positioning system with provision for vessel characteristics, equipment, and the process has been developed. A block diagram for the automatic dynamic positioning system has been suggested which allows presenting a necessary set of devices for its technical implementation.","PeriodicalId":39095,"journal":{"name":"Advances in Systems Science and Applications","volume":"21 1","pages":"1-10"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48832023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-31DOI: 10.25728/ASSA.2021.21.1.942
Y. Mitrishkin, E. Pavlova, M. Patrov
The article aims to present an approach to design and compare cascade Hinf loop shaping and essentially new cascade RGA-Hinf double decoupling magnetic control systems for a multivariable dynamical plant, specifically plasma in a vertically elongated tokamak. Identification of the present control closed-loops containing a plasma linear model of a relatively high order for the spherical Globus-M tokamak (Ioffe Institute, St Petersburg, Russia) to derive a low order linear model (without the application of reduction algorithms) as a plant under control is undertaken. A robust H¥ loop shaping method was applied to the identified model to design a plasma position, current, and shape (6 gaps between the first wall and plasma separatrix) multivariable controller. A structural analysis was done to get the most effective structure of the square plant with the 3rd gap eliminated in the feedback and a separate loop for the plasma current control. The methodology of the relative gain array (RGA) was applied to this structure to choose the proper correspondences between inputs and outputs (pairing), which brought the plant model closer to a decoupling plant (first decoupling in the open plant model). Further, the Hinf adjustment of the control system with the pairing plant and an additional feedback decoupling matrix (second decoupling of the plant model in the feedback) and PI controllers in the feedback gave increased control system accuracy while tracking references. Comparison of the two control systems designed has shown that double decoupling gives higher performance accuracy and a less robust stability margin, while the robust loop shaping method allows the stability margin to be increased but gave less accurate control of the gaps.
{"title":"Design and Comparison of Plasma H∞ Loop Shaping and RGA-H∞ Double Decoupling Multivariable Cascade Magnetic Control Systems for a Spherical Tokamak","authors":"Y. Mitrishkin, E. Pavlova, M. Patrov","doi":"10.25728/ASSA.2021.21.1.942","DOIUrl":"https://doi.org/10.25728/ASSA.2021.21.1.942","url":null,"abstract":"The article aims to present an approach to design and compare cascade Hinf loop shaping and essentially new cascade RGA-Hinf double decoupling magnetic control systems for a multivariable dynamical plant, specifically plasma in a vertically elongated tokamak. Identification of the present control closed-loops containing a plasma linear model of a relatively high order for the spherical Globus-M tokamak (Ioffe Institute, St Petersburg, Russia) to derive a low order linear model (without the application of reduction algorithms) as a plant under control is undertaken. A robust H¥ loop shaping method was applied to the identified model to design a plasma position, current, and shape (6 gaps between the first wall and plasma separatrix) multivariable controller. A structural analysis was done to get the most effective structure of the square plant with the 3rd gap eliminated in the feedback and a separate loop for the plasma current control. The methodology of the relative gain array (RGA) was applied to this structure to choose the proper correspondences between inputs and outputs (pairing), which brought the plant model closer to a decoupling plant (first decoupling in the open plant model). Further, the Hinf adjustment of the control system with the pairing plant and an additional feedback decoupling matrix (second decoupling of the plant model in the feedback) and PI controllers in the feedback gave increased control system accuracy while tracking references. Comparison of the two control systems designed has shown that double decoupling gives higher performance accuracy and a less robust stability margin, while the robust loop shaping method allows the stability margin to be increased but gave less accurate control of the gaps.","PeriodicalId":39095,"journal":{"name":"Advances in Systems Science and Applications","volume":"533 ","pages":"22-45"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41282292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-31DOI: 10.25728/ASSA.2021.21.1.1012
H. Shibly, Orwah H. Shibly
Break points, break-away and break-in points, are an essential part in root locus technique for single input single output linear invariant control systems. The importance of Break points comes from the fact that at the Break points at least two roots of the characteristic equation of the closed loop control system change their type from real to a complex at the break away point, and from complex to real at break-in point. This change affects the response of the system which can be crucial for some of systems’ applications. The conditions for being a Break point are analysed and a new formulated systematic method for finding the Break points and their corresponding gains is presented. An efficient algorithm was developed and can be solved analytically. There is no mathematical differentiation during calculation, and the algorithm can be programmed easily. The developed algorithm is applicable for any order of transfer function of a linear invariant control system. This method is compared with other common methods to show its merits and effectiveness.
{"title":"Formularization Method for Calculating the Breakaway and Break-in Points and the Corresponding Gain of Root Locus Graphs","authors":"H. Shibly, Orwah H. Shibly","doi":"10.25728/ASSA.2021.21.1.1012","DOIUrl":"https://doi.org/10.25728/ASSA.2021.21.1.1012","url":null,"abstract":"Break points, break-away and break-in points, are an essential part in root locus technique for single input single output linear invariant control systems. The importance of Break points comes from the fact that at the Break points at least two roots of the characteristic equation of the closed loop control system change their type from real to a complex at the break away point, and from complex to real at break-in point. This change affects the response of the system which can be crucial for some of systems’ applications. The conditions for being a Break point are analysed and a new formulated systematic method for finding the Break points and their corresponding gains is presented. An efficient algorithm was developed and can be solved analytically. There is no mathematical differentiation during calculation, and the algorithm can be programmed easily. The developed algorithm is applicable for any order of transfer function of a linear invariant control system. This method is compared with other common methods to show its merits and effectiveness.","PeriodicalId":39095,"journal":{"name":"Advances in Systems Science and Applications","volume":"21 1","pages":"60-75"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49098130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-31DOI: 10.25728/ASSA.2021.21.1.1044
Jeetendra Rajagopal, Jeevanandan Balamurugan
This paper investigates the matter of stability criteria for linear time delay systems with distributed delay. Firstly, a relaxed double integral inequality is established to estimate the double integral terms appearing within the derivative of Lyapunov-Krasovskii functionals (LKFs) with a triple integral term. Unlike the recently introduced Jensen's inequalities, Wirtinger based integral inequalities, refined Jensen's inequalities and therefore the auxiliary function based integral inequalities the proposed relaxed integral inequality provides large feasible solution region and fewer conservative results. Secondly, by constructing an augmented Lyapunov-Krasovskii functional with a triple integral term, the robust stability criteria for linear time delay systems with distributed delay are given in terms of linear matrix inequalities (LMIs), which may be easily computed by the LMI toolbox of MATLAB. Finally, two numerical examples are performed to indicate the effectiveness of the proposed criterion.
{"title":"Enhanced Results on Stability Criteria for Linear Time Delay Systems with Distributed Delay via Relaxed Double Integral Inequality","authors":"Jeetendra Rajagopal, Jeevanandan Balamurugan","doi":"10.25728/ASSA.2021.21.1.1044","DOIUrl":"https://doi.org/10.25728/ASSA.2021.21.1.1044","url":null,"abstract":"This paper investigates the matter of stability criteria for linear time delay systems with distributed delay. Firstly, a relaxed double integral inequality is established to estimate the double integral terms appearing within the derivative of Lyapunov-Krasovskii functionals (LKFs) with a triple integral term. Unlike the recently introduced Jensen's inequalities, Wirtinger based integral inequalities, refined Jensen's inequalities and therefore the auxiliary function based integral inequalities the proposed relaxed integral inequality provides large feasible solution region and fewer conservative results. Secondly, by constructing an augmented Lyapunov-Krasovskii functional with a triple integral term, the robust stability criteria for linear time delay systems with distributed delay are given in terms of linear matrix inequalities (LMIs), which may be easily computed by the LMI toolbox of MATLAB. Finally, two numerical examples are performed to indicate the effectiveness of the proposed criterion.","PeriodicalId":39095,"journal":{"name":"Advances in Systems Science and Applications","volume":"21 1","pages":"86-94"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45553006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-31DOI: 10.25728/ASSA.2021.21.1.963
S. Yordanova
The control of room temperature and humidity is important for ensuring of the necessary indoor human comfort for optimal work capacity and effective rest. The plant nonlinearity and the variables coupling require intelligent control techniques in order to satisfy the high performance demands. The present paper suggests a procedure for the design of a simple for industrial implementation fuzzy logic controller on the principle of parallel distributed compensation (PDC) that consists of linear local decoupling two-variable controllers. It is based on a Takagi-Sugeno-Kang (TSK) plant model, derived from experimentally obtained plant step responses using expert knowledge and parameter optimisation via genetic algorithms. The design is applied for the control of the temperature and the relative humidity of a laboratory air-conditioning system. The PDC system outperforms an existing Mamdani two-variable control system with adaptive properties in shorter settling time, higher robustness and reduced overshoot, estimated from simulations.
{"title":"Decoupling Model-Based Fuzzy Logic Control of Room Temperature and Humidity","authors":"S. Yordanova","doi":"10.25728/ASSA.2021.21.1.963","DOIUrl":"https://doi.org/10.25728/ASSA.2021.21.1.963","url":null,"abstract":"The control of room temperature and humidity is important for ensuring of the necessary indoor human comfort for optimal work capacity and effective rest. The plant nonlinearity and the variables coupling require intelligent control techniques in order to satisfy the high performance demands. The present paper suggests a procedure for the design of a simple for industrial implementation fuzzy logic controller on the principle of parallel distributed compensation (PDC) that consists of linear local decoupling two-variable controllers. It is based on a Takagi-Sugeno-Kang (TSK) plant model, derived from experimentally obtained plant step responses using expert knowledge and parameter optimisation via genetic algorithms. The design is applied for the control of the temperature and the relative humidity of a laboratory air-conditioning system. The PDC system outperforms an existing Mamdani two-variable control system with adaptive properties in shorter settling time, higher robustness and reduced overshoot, estimated from simulations.","PeriodicalId":39095,"journal":{"name":"Advances in Systems Science and Applications","volume":"21 1","pages":"46-59"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46500245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-31DOI: 10.25728/ASSA.2021.21.1.1055
E. Laneev, N. Chernikova, O. Baaj
The paper considers a method for correcting thermographic images. Mathematical processing of thermograms is based on the analytical continuation of the stationary temperature distribution as a harmonic function from the surface of the object under study to the heat sources. The continuation is performed by solving an ill posed mixed problem for the Laplace equation in a cylindrical region of rectangular cross-section. The cylindrical area is bounded by an arbitrary surface and plane. The Cauchy conditions are set on the surface-the boundary values of the desired function and its normal derivative. Inhomogeneous conditions of the first kind are set on the side faces of the cylinder. The problem is the inverse of the corresponding mixed problem for the Poisson equation. In this paper, an approximate solution of the problem is obtained that is stable with respect to the error in the Cauchy data and inhomogeneity in the boundary conditions. In the course of constructing an approximate solution, the problem is reduced to the Fredholm integral equation of the first kind, which is solved using the minimum smoothing functional principle. The convergence of the approximate solution of the problem is proved when the regularization parameter is matched to the error in the data.
{"title":"Application of the Minimum Principle of a Tikhonov Smoothing Functional in the Problem of Processing Thermographic Data","authors":"E. Laneev, N. Chernikova, O. Baaj","doi":"10.25728/ASSA.2021.21.1.1055","DOIUrl":"https://doi.org/10.25728/ASSA.2021.21.1.1055","url":null,"abstract":"The paper considers a method for correcting thermographic images. Mathematical processing of thermograms is based on the analytical continuation of the stationary temperature distribution as a harmonic function from the surface of the object under study to the heat sources. The continuation is performed by solving an ill posed mixed problem for the Laplace equation in a cylindrical region of rectangular cross-section. The cylindrical area is bounded by an arbitrary surface and plane. The Cauchy conditions are set on the surface-the boundary values of the desired function and its normal derivative. Inhomogeneous conditions of the first kind are set on the side faces of the cylinder. The problem is the inverse of the corresponding mixed problem for the Poisson equation. In this paper, an approximate solution of the problem is obtained that is stable with respect to the error in the Cauchy data and inhomogeneity in the boundary conditions. In the course of constructing an approximate solution, the problem is reduced to the Fredholm integral equation of the first kind, which is solved using the minimum smoothing functional principle. The convergence of the approximate solution of the problem is proved when the regularization parameter is matched to the error in the data.","PeriodicalId":39095,"journal":{"name":"Advances in Systems Science and Applications","volume":"21 1","pages":"139-149"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46265746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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