Solution Of Synthesis Problem Research Articles

Нагруженные уравнения, возникающие при синтезе управления нагревом стержня движущимися источниками

The article proposes an approach to solving the problem of synthesis of motion and power control of lumped sources. For concreteness, the problem of linear feedback control of moving heat sources during heating of the rod is considered. The powers and motion of point sources, participating in the right-hand side of the differential equation of parabolic type, are determined depending on the measured values of the process state at the points of measurement. As a result, the right-hand side of the differential equation linearly depends on the values of the process state at the given points of the bar. Formulas for the components of the gradient of the functional with respect to the parameters of linear feedback are obtained, which make it possible to use first-order optimization methods for the numerical solution of synthesis problems.

ACTIVE SHIELDING OF EXTERNAL MAGNETIC FIELD OF BUILT-IN TRANSFORMER SUBSTATIONS

This paper deals with the mitigation of low-frequency magnetic field of build-in transformer substations down to the reference level 0.5 μT in nearby living spaces. To meet the reference level, we substantiate the actuality of the usage of active shielding methods having higher efficiency, comparably to metal consuming passive shielding. We show that the optimization of parameters and localization of compensation coils is the main goal of the synthesis of the active shielding system. The solution of synthesis problem is based on the developed 3D numerical model by using particles multiswarm optimization algorithms from Pareto-optimal solutions set taking into account binary preference relations. This allows justifying the usage of simple active shielding system for magnetic field mitigation down to the reference level in living spaces, located near build-in transformer substations (2×400 kVA, 6/0.4 kV). The synthesized active shielding system has two plane compensation coils installed near the ceiling (wall) of the substation room. The area of each coil is less than 10 m2 and the number of ampere-turns is less than 30. We show that the efficiency of the active shielding system is 6 when it electric power consumption is less than 100 W. This allows mitigating the magnetic field down to 0.5 μT in 40 m2 living space located on top or side from the substation. The application of synthesized active shielding system (subject to the positive results of experimental studies of their full-scale physical models) allows solving the actual and socially significant problem of the health protection of tenants of residential buildings with build-in transformer substations from the negative effects of power frequency magnetic field.

Active Shielding of External Magnetic Field of Built-In Transformer Substations

This paper deals with the mitigation of low-frequency magnetic field of build-in transformer substations down to the reference level 0.5 μT in nearby living spaces. To meet the reference level, we substantiate the actuality of the usage of active shielding methods having higher efficiency, comparably to metal consuming passive shielding. We show that the optimization of parameters and localization of compensation coils is the main goal of the synthesis of the active shielding system. The solution of synthesis problem is based on the developed 3D numerical model by using particles multiswarm optimization algorithms from Pareto-optimal solutions set taking into account binary preference relations. This allows justifying the usage of simple active shielding system for magnetic field mitigation down to the reference level in living spaces, located near build-in transformer substations (2×400 kVA, 6/0.4 kV). The synthesized active shielding system has two plane compensation coils installed near the ceiling (wall) of the substation room. The area of each coil is less than 10 m2 and the number of ampere-turns is less than 30. We show that the efficiency of the active shielding system is 6 when it electric power consumption is less than 100 W. This allows mitigating the magnetic field down to 0.5 μT in 40 m2 living space located on top or side from the substation. The application of synthesized active shielding system (subject to the positive results of experimental studies of their full-scale physical models) allows solving the actual and socially significant problem of the health protection of tenants of residential buildings with build-in transformer substations from the negative effects of power frequency magnetic field.

A suboptimal algorithm for synthesis of a movable object control

In this paper a suboptimal algorithm for synthesis of a movable object control, based on the known approach, according to which a control is formed depending on a control error – the difference between current and required values of a regulated variables vector is considered. The distinctive peculiarity of the algorithm was based on the vector of regulated parameters estimation approach. This vector is proposed to be estimated by solving a mobile left endpoint problem derived from the original one. It is shown by examples that the proposed approach allows to simplify the control synthesis problem solution and obtain effective control algorithms, providing a suboptimal control and, in some cases, presented in this paper, an optimal control. The suggested algorithm can be used to determine continuous and pulse controls of aircrafts (including spacecrafts) in problems of their approaching (guidance) and spacecraft docking, carrying out of correcting maneuvers, descent and soft landing of spacecrafts at al.

Geometrical synthesis of four-bar gear train with related gears

The method of optimal geometric synthesis of four-bar cylindrical gear with related gears with one external and one internal gearing is proposed. The method is based on a new calculation system that increases the number of synthesis output parameters to six, which makes it possible to considerably expand the domain of existence of the synthesis problem solution with the simultaneous synthesis of two gearing. The software implementing the proposed technique is described. To solve the problem of nonlinear mathematical programming the library of Optimization Toolbox functions included in Matlab is used. Examples of calculations are given.

Solution of Nanomaterial Problems by Processing and Promotion of Industry-Academia-Government Collaboration

For practice application of nanomaterial, it need solution of synthesis problems. These nanomaterial problems were solved by new concept fabrication system. Metal oxide used as ecometal source in new concept processing. Solid-liquid system will be high concentration, high yield and high throughput processing. Ultrasound and microwave reactor were enhanced chemical reaction and created novel chemical reaction. Realization of innovative nanomaterial fabrication were enabled joining environment, low cost and high throughput by combining these concepts. This commentary was explained nanomaterial problems and introduced the example of some metal nanoparticle related material processing by synergistic effects of solid-liquid system and ultrasound, microwave reactor, and promotion of industry-academia-government collaboration.

АНАЛИТИЧЕСКОЕ КОНСТРУИРОВАНИЕ РАЗОМКНУТЫХ СИСТЕМ СТОХАСТИЧЕСКОГО УПРАВЛЕНИЯ МНОГОМЕРНЫМ НЕЛИНЕЙНЫМ ОБЪЕКТОМ

This article is devoted to the development of a new method of synthesis a regulators’ transfer functions matrix of an optimal multivariable open-loop control system. The regulator is designed to maximize an accuracy of a nonlinear multivariable control object transition from one steady state to another. It is assumed that disturbances act on the control object and sensors measuring data has inertia and noise. Both disturbances and noises are an additive combination of regular and random components. Random components belong to a class of interconnected stationary processes with rational spectral density matrices. A substantiated method differs from the known one by the fact that during formulation and solution of the problem somebody uses a new block diagram of the control system, which takes into account the results of metrological certification of a sensor dynamics. Synthesis of the regulator is carried out in the frequency domain by the Wiener-Kolmogorov method. A new algorithm, which is obtained as a result of synthesis problem solution, allows you to find the matrix of regulator transfer functions , which provides a minimum of corresponding quadratic quality criteria’s. The first of them is equal to the sum of certain way weighted squared deviations regular repetition errors of the object path and control signals. The second criterion is equal to the sum of the weighted variance of the random error components and the control signals. To execute the proposed algorithm it is necessary to perform the operations of Wiener factorization and separation of rational matrices. The corresponding functions are contained in the freely distributed software package SciLab.

The Controllability Prefix for Supervisory Control under Partial Observation with an Application to Fault-Tolerant Control

The controllability prefix is known as a useful concept for the discussion and solution of synthesis problems in supervisory control of ω-languages, i.e., formal languages of infinite-length words. There, the controllability prefix is defined as the set of all finite-length prefixes that can be controlled to satisfy prescribed liveness and safety properties. In this paper, we discuss a variation of the controllability prefix to address supervisory control under partial observation for regular *-languages, i.e., formal languages of finite-length words. We derive algebraic properties that are useful for a quantitative analysis on how an upper-bound language-inclusion specification affects achievable lower-bound specifications. Our study is motivated by the synthesis of fault-tolerant supervisory controllers, where the possible occurrence of a fault may restrict the achievable pre-fault behaviour so severe, that a relaxation of the upper-bound specification becomes a practical option. As our study shows, such a relaxation can be systematically constructed in terms of the controllability prefix.

Synthesis of anisotropic suboptimal control for linear time-varying systems on finite time horizon

This paper presents the statement and solution to the problem of synthesis of the anisotropic control that guarantees some prescribed level of attenuation of the uncertain stochastic disturbances affecting the linear discrete time-varying system on finite time horizon. The anisotropy of a random vector is considered as a measure of the statistical uncertainty of the disturbance. The closed-loop system capabilities to attenuate the external disturbances are characterized by its anisotropic norm. The synthesis problem solution is formulated in form of sufficient conditions of existence of a controller that guarantees the anisotropic norm of the closed-loop system to be bounded by some given threshold level. The controller synthesis algorithm is based on solving the system of matrix inequalities recursively.

Input electrical impedance and efficiency of ultrasonic transducers with phased excitation of two piezoelectric plates

The type of changes in the total input conduction and its active and reactive components has been analyzed for an ultrasonic transducer with two independent piezoelectric plates separated by a dielectric layer as compared with the case of in-phase excitation of the transducer. Results of calculating the efficiency are considered for different transducer designs in accordance with a synthesisproblem solution that ensures a uniform amplitude-frequency response and a linear phase-frequency characteristic of emission.

A generic methodology for processing route synthesis and design based on superstructure optimization

In this paper, a systematic framework for novel and sustainable synthesis-design of processing routes is presented along with the associated computer-aided methods and tools. In Stage 1, superstructure optimization is used to determine the optimal processing route(s). In Stage 2, the design issues are resolved and targets for improvement are identified through the use of integrated tools. In Stage 3, new alternatives are generated using the selected route and the previously identified targets. In addition to the various computer-aided tools, two special tools are presented: (1) a database employing a specially developed knowledge representation system, and (2) Super-O, a software interface that guides users through the formulation and solution of synthesis problems. Super-O transfers data between the different tools, including a library of generic models, representing a wide range of processing options. Application of the synthesis and design stages is highlighted through two case studies (biorefinery and carbon capture-utilization).

СИНТЕЗ БИНАРНЫХ R-КОДОВ

Purpose: The increase in efficiency of modern systems is impossible without improving binary codes and signals on their basis. Widely used N-element binary codes do not provide the desirable low level of the lateral peaks of the autocorrelated function if N varies in a rather wide range. Additional requirements can be imposed on binary codes for various systems, concerning alternation of the coefficient signs and the existence of an analytical numbering system. It is important for constructing and generating a set of volume ensemble codes, storing not the code coefficients but their numbers in a certain numeral system. The purpose of this work is analytical synthesis of N-element binary codes with a preset level R of lateral peaks of the autocorrelation function (R-codes) under certain requirements to the alternation of the code coefficients, as well as the development of a system for their accounting. Results: A technique for the restricted synthesis problem solution is outlined, and its features are specified (for example, the possibility to transform a set of inequalities into a system of equations, its first half used for finding possibly appropriate codes, and its second half for choosing truly appropriate ones). Ratios are given which help to find the values of the code sequences. A way of numbering the synthesized codes based on a system of full codes is proposed. The concept of an author's code is introduced, to determine the rule of sign alternation for some R-code coefficients. A technique is given for finding lists of codes with these properties in the offered numbering system. Examples are given of synthesizing author's codes with R = 3, N = 32, 33. Practical relevance: The proposed technique and the results of the synthesis can find a use in building binary codes and signals on their basis for control systems, communication systems, radiolocation, computer systems and networks.

Invariance for Systems with Separated Motions

The paper presents the methods of synthesis of invariant dynamic systems on the basis of the theory of systems with separated motions with usage of deep feedback and discontinuous controls. Usage of this class of feedback with padding hierarchical structure of synthesized controls allows: to expand the class of invariant systems as contrasted to by known approaches; to provide a solution of the posed problem in conditions of parametric indeterminacy of a control plant model to divide the solution of synthesis problem into a separately solved subproblems of smaller dimension at the expense of creation motions with different temps in a closed-loop system.

On the existence of solutions of synthesis problems for radiating systems in terms of a prescribed amplitude directional pattern

We study two variational formulations for nonlinear inverse problems applied to the synthesis of radiating systems, and we derive nonlinear operator equations that follow from the necessary condition for the functional to have a minimum. On the basis of the properties of these functionals we prove theorems and exhibit an existence domain for solutions of this class of problems. Using the example of a linear grid, we exhibit the transition from the variational formulation of a problem to nonlinear integral equations of Hammerstein type.

Symbolic integration of logic in mixed-integer linear programming techniques for process synthesis

This paper deals with the branch and bound solution of synthesis problems that are modeled as mixed-integer linear programming (MILP) problems. Logic relations between potential units in a superstructure are considered through symbolic integration within the numerical based branch and bound scheme. The objective of this integration is to reduce the number of nodes that must be enumerated by using the logic to decide on the branching of variables, and to determine by symbolic inference whether additional variables can be fixed at each node. Two different strategies for performing the integration are proposed that use the disjunctive and conductive normal form representations of the logic, respectively. The paper also addresses the question of how to systematically generate the logic for process flowsheet superstructures. Computational results are presented to compare the performance of the proposed methods and a variant that includes violated logic inequalities in the model with the cases when all logic inequalities are included in or excluded from the model.

Control synthesis in equations containing an unbounded operator

A general theorem is proved on the solution of the control synthesis problem for equations with operators, generated by strongly continuous groups. The solution of the synthesis problem of bounded control is given for the wave control process.

Generalized array pattern synthesis by the method of alternating orthogonal projections

A geometric formulation of the null-steering array antenna pattern synthesis problems for arbitrary array geometries is proposed. The formulation allows the use of some simple intuitive techniques for the construction of the array weights. In particular it is shown that the optimum vector can be obtained in an appropriately selected weight vector subspace via a recursive projection algorithm starting from its known projection on the vector lying in the constrained look direction. The algorithm is computationally very simple and can be used for on-line solution of synthesis problems for complex array geometries.

Investigation of a certain stray process applied to the optimum synthesis problems

A new method is proposed for the random checking of the region of admissible solutions of synthesis problems by means of digital computers. This method is characterized by increasing efficiency of random checking and by preference of the boundary and its neighbourhood to the interior of the region. The algorithm of the stray process is described. The paper contains also the test results of the influence of various parameters on the process. The application of the method is illustrated by examples. The results obtained by different methods are confronted. The computers used were the GIER and ZAM-2 computers.