Pub Date : 2021-06-01DOI: 10.21638/11701/spbu10.2021.209
Аlexander M. Kamachkin, Dmitriy K. Рotaрov, V. V. Yevstafyeva
The article considers a class of automatic control systems that is described by a multi- dimensional system of ordinary dil'erential equations. The right hand-side of the system additively contains a linear part and the product of a control matrix by a vector that is the sum of a control vector and an external perturbation vector. The control vector is defined by a nonlinear function dependent on the product of a feedback matrix by a vector of current coordinates. The authors solve the problem of constructing a matrix of a nonsingular transformation, which leads the matrix of the linear part of the system to the Jordan normal form or the first natural normal form. The variables included in this transformation allow us to vary the system settings, which are the parameters of both the control matrix and the feedback matrix, as well as to convert the system to an integrable form. Integrable form is understood as a form in which the system can be integrated in a final form or reduced to a set of subsystems of lower orders. Furthermore, the sum of the subsystem orders is equal to the order of the original system. In the article, particular attention is paid to cases when the matrix of the linear part has complex conjugate eigenvalues, including multiple ones.
{"title":"Method for the transformation of complex automatic control systems to integrable form","authors":"Аlexander M. Kamachkin, Dmitriy K. Рotaрov, V. V. Yevstafyeva","doi":"10.21638/11701/spbu10.2021.209","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.209","url":null,"abstract":"The article considers a class of automatic control systems that is described by a multi- dimensional system of ordinary dil'erential equations. The right hand-side of the system additively contains a linear part and the product of a control matrix by a vector that is the sum of a control vector and an external perturbation vector. The control vector is defined by a nonlinear function dependent on the product of a feedback matrix by a vector of current coordinates. The authors solve the problem of constructing a matrix of a nonsingular transformation, which leads the matrix of the linear part of the system to the Jordan normal form or the first natural normal form. The variables included in this transformation allow us to vary the system settings, which are the parameters of both the control matrix and the feedback matrix, as well as to convert the system to an integrable form. Integrable form is understood as a form in which the system can be integrated in a final form or reduced to a set of subsystems of lower orders. Furthermore, the sum of the subsystem orders is equal to the order of the original system. In the article, particular attention is paid to cases when the matrix of the linear part has complex conjugate eigenvalues, including multiple ones.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88169253","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 : 2021-06-01DOI: 10.21638/11701/spbu10.2021.202
Dmitry Р. Goloskokov, Аlexander V. Matrosov
The article considers the problem of a rectangular plate, supported by a cross system of stiffening ribs, bending. In addition to the transverse load, the plate is subjected to forces in its plane, transmitted through the ribs. Аn analytical solution to the boundary value problem for the resolving differential equation with respect to the normal deflection of the plate, describing the deformation of a rectangular plate supported by stiffeners, is obtained. The solution is presented in the form of series in combinations of regular and special discontinuous functions, which converge quickly and lead to a simple computational algorithm. The influence of the ribs is taken into account in the equation in the form of additional terms containing factors with a delta function. This approach allows us to get rid of a number of assumptions regarding the interaction of the plate with its reinforcing elements. The use of the apparatus of generalized functions when modeling objects of this type simplifies the boundary conditions (there are no conditions for conjugation of various structural elements), but at the same time the differential equations become more complicated. The problem is reduced to the so-called partially degenerate equations. Development of analytical methods that allow obtaining exact solutions of differential equations of this type, and their introduction into computational practice, is one of the urgent tasks of the mechanics of objects with disturbed regularity.
{"title":"Bending of a ribbed plate under complex loading","authors":"Dmitry Р. Goloskokov, Аlexander V. Matrosov","doi":"10.21638/11701/spbu10.2021.202","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.202","url":null,"abstract":"The article considers the problem of a rectangular plate, supported by a cross system of stiffening ribs, bending. In addition to the transverse load, the plate is subjected to forces in its plane, transmitted through the ribs. Аn analytical solution to the boundary value problem for the resolving differential equation with respect to the normal deflection of the plate, describing the deformation of a rectangular plate supported by stiffeners, is obtained. The solution is presented in the form of series in combinations of regular and special discontinuous functions, which converge quickly and lead to a simple computational algorithm. The influence of the ribs is taken into account in the equation in the form of additional terms containing factors with a delta function. This approach allows us to get rid of a number of assumptions regarding the interaction of the plate with its reinforcing elements. The use of the apparatus of generalized functions when modeling objects of this type simplifies the boundary conditions (there are no conditions for conjugation of various structural elements), but at the same time the differential equations become more complicated. The problem is reduced to the so-called partially degenerate equations. Development of analytical methods that allow obtaining exact solutions of differential equations of this type, and their introduction into computational practice, is one of the urgent tasks of the mechanics of objects with disturbed regularity.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85729130","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 : 2021-06-01DOI: 10.21638/11701/spbu10.2021.203
N. V. Egorov, E. Vinogradova
In this paper the mathematical modeling of the triode emission axially symmetric system on the basis of field emitter is considered. Emitter is an ellipsoid of revolution, anode is a confocal ellipsoidal surface of revolution. Modulator is a part of the ellipsoidal surface of revolution, confocal with the cathode and anode surfaces. The boundary-value problem for the Laplace's equation in the prolate spheroidal coordinates with the boundary conditions of the first kind is solved. The variable separation method is applied to calculate the axisymmetrical electrostatic potential distribution. The potential distribution is represented as the Legendre functions expansion. The expansion coefficients are the solution of the system of linear equations. All geometrical dimensions of the system are the parameters of the problem.
{"title":"Mathematical modeling of triode system on the basis of field emitter with ellipsoid shape","authors":"N. V. Egorov, E. Vinogradova","doi":"10.21638/11701/spbu10.2021.203","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.203","url":null,"abstract":"In this paper the mathematical modeling of the triode emission axially symmetric system on the basis of field emitter is considered. Emitter is an ellipsoid of revolution, anode is a confocal ellipsoidal surface of revolution. Modulator is a part of the ellipsoidal surface of revolution, confocal with the cathode and anode surfaces. The boundary-value problem for the Laplace's equation in the prolate spheroidal coordinates with the boundary conditions of the first kind is solved. The variable separation method is applied to calculate the axisymmetrical electrostatic potential distribution. The potential distribution is represented as the Legendre functions expansion. The expansion coefficients are the solution of the system of linear equations. All geometrical dimensions of the system are the parameters of the problem.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77939289","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 : 2021-06-01DOI: 10.21638/11701/spbu10.2021.201
O. Baskov
The article examines the infimum and supremum of an infinite number of fuzzy numbers. It is shown that familiar properties of these operations, which are valid for real numbers, may apply to fuzzy numbers only under certain conditions. А formula for computing the infimum and supremum of any set of fuzzy numbers is provided. Since the union and meet of type-2 fuzzy sets are defined via the infimum and supremum of fuzzy numbers, all the results obtained are applicable to these operations as well.
{"title":"Union and meet of an infinite number of type-2 fuzzy sets","authors":"O. Baskov","doi":"10.21638/11701/spbu10.2021.201","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.201","url":null,"abstract":"The article examines the infimum and supremum of an infinite number of fuzzy numbers. It is shown that familiar properties of these operations, which are valid for real numbers, may apply to fuzzy numbers only under certain conditions. А formula for computing the infimum and supremum of any set of fuzzy numbers is provided. Since the union and meet of type-2 fuzzy sets are defined via the infimum and supremum of fuzzy numbers, all the results obtained are applicable to these operations as well.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87058311","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 : 2021-03-01DOI: 10.21638/11701/SPBU10.2021.102
A. Aleksandrov, A. Tikhonov
The article analyzes a linear mechanical system with a large parameter at the vector of velocity forces and a distributed delay in positional forces. With the aid of the decomposition method, conditions are obtained under which the problem of stability analysis of the original system of the second-order differential equations can be reduced to studying the stability of two auxiliary first-order subsystems. It should be noted that one of the auxiliary subsystems does not contain a delay, whereas for the second subsystem containing a distributed delay, the stability conditions are formulated in terms of the feasibility of systems of linear matrix inequalities. To substantiate this decomposition, the Lyapunov direct method is used. Special constructions of Lyapunov—Krasovskii functionals are proposed. The developed approach is applied to the problem of monoaxial stabilization of a rigid body. The results of a numerical simulation are presented confirming the conclusions obtained analytically.
{"title":"Stability analysis of mechanical systems with distributed delay via decomposition","authors":"A. Aleksandrov, A. Tikhonov","doi":"10.21638/11701/SPBU10.2021.102","DOIUrl":"https://doi.org/10.21638/11701/SPBU10.2021.102","url":null,"abstract":"The article analyzes a linear mechanical system with a large parameter at the vector of velocity forces and a distributed delay in positional forces. With the aid of the decomposition method, conditions are obtained under which the problem of stability analysis of the original system of the second-order differential equations can be reduced to studying the stability of two auxiliary first-order subsystems. It should be noted that one of the auxiliary subsystems does not contain a delay, whereas for the second subsystem containing a distributed delay, the stability conditions are formulated in terms of the feasibility of systems of linear matrix inequalities. To substantiate this decomposition, the Lyapunov direct method is used. Special constructions of Lyapunov—Krasovskii functionals are proposed. The developed approach is applied to the problem of monoaxial stabilization of a rigid body. The results of a numerical simulation are presented confirming the conclusions obtained analytically.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79750531","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.402
D. P. Goloskokov, A. Matrosov
In this paper, the method of initial functions (MIF) is used to solve the problem of bending an orthotropic plate clamped along all four sides, under the influence of a normal load uni- formly distributed over its surface. The solution is obtained in the form of an exponential series with unknown coefficients. The algorithm of the method is such that on two opposite sides the boundary conditions (equality to zero of displacements and angles of rotation) are satisfied exactly, while on a pair of two other opposite sides the boundary conditions are satisfied with an arbitrary degree of accuracy by the collocation method. All studies were carried out using the Maple analytical computing system. This system allows you to perform calculations with an arbitrary mantissa in the representation of real numbers. Calculations with a long mantissa overcome one of the main disadvantages of the MIF: the computational instability of its algorithm, which arises under certain parameters of the problem. The com- putational stability of the obtained solution is investigated, as well as the stress-strain state in the neighbourhood of the corner points of the plate. It is shown that the moments and shear forces tend to zero when approaching the corners of the plate with a single change in sign.
{"title":"Method of initial functions in analyses of the bending of a thin orthotropic plate clamped along the contour","authors":"D. P. Goloskokov, A. Matrosov","doi":"10.21638/11701/spbu10.2021.402","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.402","url":null,"abstract":"In this paper, the method of initial functions (MIF) is used to solve the problem of bending an orthotropic plate clamped along all four sides, under the influence of a normal load uni- formly distributed over its surface. The solution is obtained in the form of an exponential series with unknown coefficients. The algorithm of the method is such that on two opposite sides the boundary conditions (equality to zero of displacements and angles of rotation) are satisfied exactly, while on a pair of two other opposite sides the boundary conditions are satisfied with an arbitrary degree of accuracy by the collocation method. All studies were carried out using the Maple analytical computing system. This system allows you to perform calculations with an arbitrary mantissa in the representation of real numbers. Calculations with a long mantissa overcome one of the main disadvantages of the MIF: the computational instability of its algorithm, which arises under certain parameters of the problem. The com- putational stability of the obtained solution is investigated, as well as the stress-strain state in the neighbourhood of the corner points of the plate. It is shown that the moments and shear forces tend to zero when approaching the corners of the plate with a single change in sign.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76117225","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.405
V. Pavlovsky, S. A. Kabrits
The calculation of the turbulent boundary layer is performed when a steady flow of a viscous fluid flows around a flat plate. The calculation is based on a system of equations of turbulent fluid motion, obtained by generalizing Newton’s formula for the tangential stress in a fluid by giving it a power-law form followed by writing the corresponding rheological relationship in tensor form and substituting it into the equation of motion of a continuous medium in stresses. The use of this system for the problem of longitudinal flow around a flat plate after estimates of the boundary layer form made it possible to write a system of equations describing a two-dimensional fluid flow in the boundary layer of a flat plate. This system is reduced to one ordinary third-order equation, similarly to how Blasius performed it for a laminar boundary layer. When solving this equation, the method of direct reduction of the boundary value problem to the Cauchy problem was used. The results of this solution made it possible to determine expressions for the thickness of the boundary layer, displacement and loss of momentum. These values are compared with the available experimental data.
{"title":"Calculation of the turbulent boundary layer of a flat plate","authors":"V. Pavlovsky, S. A. Kabrits","doi":"10.21638/11701/spbu10.2021.405","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.405","url":null,"abstract":"The calculation of the turbulent boundary layer is performed when a steady flow of a viscous fluid flows around a flat plate. The calculation is based on a system of equations of turbulent fluid motion, obtained by generalizing Newton’s formula for the tangential stress in a fluid by giving it a power-law form followed by writing the corresponding rheological relationship in tensor form and substituting it into the equation of motion of a continuous medium in stresses. The use of this system for the problem of longitudinal flow around a flat plate after estimates of the boundary layer form made it possible to write a system of equations describing a two-dimensional fluid flow in the boundary layer of a flat plate. This system is reduced to one ordinary third-order equation, similarly to how Blasius performed it for a laminar boundary layer. When solving this equation, the method of direct reduction of the boundary value problem to the Cauchy problem was used. The results of this solution made it possible to determine expressions for the thickness of the boundary layer, displacement and loss of momentum. These values are compared with the available experimental data.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72896373","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.306
R. Ospanov, Y. Seitkulov, N. Sissenov, Banu B. Yergalieva
The article discusses a new version of the internal function underlying the perspective modern scheme for constructing cryptographic hash functions Sponge (cryptographic sponge). The considered example of an internal function is similar to the Keccak permutation, but it has a number of main differences. The inner function operates on a 2048-bit state S, which can be viewed as a three-dimensional bit array of 4 x 8 x 64 size. The structure of the internal function is made up of 5 transformations similar to Keccak. However, firstly, in this example, instead of a 5-bit S-box, an 8-bit one is used. In this regard, the parameters of the three-dimensional representation of the state have been changed. Secondly, instead of a linear feedback shift register, a dictionary shift register with ring carry feedback is used to generate round constants. The properties of these transformations are analyzed in the work.
本文讨论了构建加密哈希函数海绵(cryptosponge)的透视现代方案的一个新版本的内部函数。所考虑的内部函数示例与Keccak排列类似，但它有许多主要区别。内部函数对2048位的状态S进行操作，可以将其视为4 x 8 x 64大小的三维位数组。内部函数的结构由5个类似于Keccak的变换组成。然而，首先，在这个例子中，使用的不是5位的S-box，而是8位的S-box。对此，对状态的三维表示参数进行了改变。其次，用带环进位反馈的字典移位寄存器代替线性反馈移位寄存器来生成整数常数。文中对这些变换的性质进行了分析。
{"title":"An example of an internal function for the SPONGE scheme","authors":"R. Ospanov, Y. Seitkulov, N. Sissenov, Banu B. Yergalieva","doi":"10.21638/11701/spbu10.2021.306","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.306","url":null,"abstract":"The article discusses a new version of the internal function underlying the perspective modern scheme for constructing cryptographic hash functions Sponge (cryptographic sponge). The considered example of an internal function is similar to the Keccak permutation, but it has a number of main differences. The inner function operates on a 2048-bit state S, which can be viewed as a three-dimensional bit array of 4 x 8 x 64 size. The structure of the internal function is made up of 5 transformations similar to Keccak. However, firstly, in this example, instead of a 5-bit S-box, an 8-bit one is used. In this regard, the parameters of the three-dimensional representation of the state have been changed. Secondly, instead of a linear feedback shift register, a dictionary shift register with ring carry feedback is used to generate round constants. The properties of these transformations are analyzed in the work.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86761948","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.407
R. Abramov, K. Kulakov, A. Lebedev, N. Moskin, A. Rogov
The paper is devoted to the study of the publicity style of F. M. Dostoevsky on the basis of publications in the journals “Time” and “Epoch” (1861-1865). For this, fragments of texts (including other authors: M. M. Dostoevsky, N. N. Strakhov, A. A. Golovachev, etc.) were selected in sizes of 500, 700 and 1000 words, on which the occurrence of bigrams and trigrams (encoded sequences of parts of speech) were counted. Decision trees were built on their basis and an analysis of the accuracy of text recognition was performed. If we consider the class cation at the rest level of the tree (fragment size 1000), then the accuracy was on average 87 resulting decision trees.
{"title":"Research of features of Dostoevsky’s publicistic style by using m-grams based on the materials of the “Time” and “Epoch” magazines","authors":"R. Abramov, K. Kulakov, A. Lebedev, N. Moskin, A. Rogov","doi":"10.21638/11701/spbu10.2021.407","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.407","url":null,"abstract":"The paper is devoted to the study of the publicity style of F. M. Dostoevsky on the basis of publications in the journals “Time” and “Epoch” (1861-1865). For this, fragments of texts (including other authors: M. M. Dostoevsky, N. N. Strakhov, A. A. Golovachev, etc.) were selected in sizes of 500, 700 and 1000 words, on which the occurrence of bigrams and trigrams (encoded sequences of parts of speech) were counted. Decision trees were built on their basis and an analysis of the accuracy of text recognition was performed. If we consider the class cation at the rest level of the tree (fragment size 1000), then the accuracy was on average 87 resulting decision trees.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91374270","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 : 2021-01-01DOI: 10.21638/11701/spbu10.2021.412
M. Sotnikova, R. Sevostyanov
The article is devoted to the control of a dynamic object with the retention of controlled variables in the required range, taking into account the high dimension of input and output, time delay, constraints and external disturbances. The formalized statement of the problem of digital control synthesis is considered. An approach based on the use of predictive models is proposed. Its key feature is the introduction of a specialized quality functional that reflects the specifics of the problem, the error functional. This functional plays the role of a penalty for the output of controlled variables that go beyond the specified range. It is shown that the implementation of the control law is reduced to solving the problem of quadratic program- ming at each instant of discrete time. The results obtained are illustrated by an example of controlling the oil refining process in a distillation column.
{"title":"Digital control of output variables in a given range considering delay","authors":"M. Sotnikova, R. Sevostyanov","doi":"10.21638/11701/spbu10.2021.412","DOIUrl":"https://doi.org/10.21638/11701/spbu10.2021.412","url":null,"abstract":"The article is devoted to the control of a dynamic object with the retention of controlled variables in the required range, taking into account the high dimension of input and output, time delay, constraints and external disturbances. The formalized statement of the problem of digital control synthesis is considered. An approach based on the use of predictive models is proposed. Its key feature is the introduction of a specialized quality functional that reflects the specifics of the problem, the error functional. This functional plays the role of a penalty for the output of controlled variables that go beyond the specified range. It is shown that the implementation of the control law is reduced to solving the problem of quadratic program- ming at each instant of discrete time. The results obtained are illustrated by an example of controlling the oil refining process in a distillation column.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87418913","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：