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11Аудит ИСПДн рекомендуется проводить группой аудиторов в соответствии с разработанной методикой, содержащей рекомендуемый перечень и порядок работ.
Методика аудита информационной безопасности ИСПДн некоммерческой организации разрабатывалась на основе анализа требований законодательства Российской Федерации в области защиты персональных данных. Перед проведением аудита должны быть определены сроки, и условия проведения необходимых мероприятий. Методика аудита может уточняться и корректироваться в процессе проведения обследования.
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РЕАЛИЗАЦИЯ ИМПУЛЬСНО-КОДОВОГО УПРАВЛЕНИЯ В ПАРАМЕТРИЧЕСКИХ МОДЕЛЯХ ИНДУКЦИОННЫХ УСТРОЙСТВ
Кинев Е. С.
К.т.н., директор,
ООО Тепловые электрические системы, г. Красноярск
Тяпин А.А. аспирант,
Сибирский федеральный университет, г. Красноярск
Пантелеев В.И. Д.т.н, профессор, Сибирский федеральный университет, г. Красноярск
Первухин М.В. Д.т.н, профессор, Сибирский федеральный университет, г. Красноярск
IMPLEMENTATION OF PULSE-CODE CONTROL IN PARAMETRIC MODELS OF INDUCTION
DEVISES
Kinev E.
Ph.D., director of Thermal Electrical Systems LLC
Tyapin A.
Postgraduate student, Siberian Federal University
Panteleev V.
Professor, Siberian Federal University Pervukhin M.
Professor, Siberian Federal University
Аннотация
Предложен подход к построению импульсных регуляторов при моделировании индукционных устройств. В схемах замещения индукторов для нагрева алюминия перед экструзией есть составляющие, обусловленные наличием загрузки. Свойства металла при нагреве меняются и, при создании моделей для численного эксперимента следует учитывать изменение импеданса. В качестве средства управления режимом эквивалентных двухполюсников предложено кодовое импульсное воздействие на ключи, в динамике изменяющее проводимость. Управление периодом переключения модели при последовательном и параллельном соединении элементов обеспечивает плавный закон регулирования. Исследование типовых схем
параметрических звеньев выполнено с применением симулятора, при этом получены примеры регулировочных характеристик токов и напряжений. При моделировании построены переключаемые модели разной разрядности, имеющие свойства аналого-цифровых элементов. В статье получены решения для режимных параметров индукционного устройства, отраженные веерной векторной диаграммой.
Abstract
An approach to the construction of pulse controllers for modeling induction devices is proposed. In the equivalent circuits of inductors for heating aluminum before extrusion, there are components due to the presence of the load. The properties of the metal change during heating, and when creating models for a numerical experiment, one should take into account the change in impedance. As a means of controlling the mode of equivalent two-terminal networks, a code impulse action on the switches is proposed, which changes conductivity in dynamics. Controlling the switching period of the model with serial and parallel connection of elements provides a smooth regulation law. The study of typical circuits of parametric links was carried out using a simulator, while examples of regulation characteristics of currents and voltages were obtained. In the simulation, switchable models of different bit depths have been built, which have the properties of analog-digital elements. The article provides solutions for the operating parameters of an induction device, reflected by a fan vector diagram.
Ключевые слова: Индукционное устройство, индукционный нагрев, математическое моделирование, параметрическая модель, импульсное кодовое управление.
Keywords: Induction device, induction heating, mathematical modeling, parametric model, pulse code control.
Introduction. Induction electric heating is considered the most effective means of heating aluminum before pressing [1]. Heating inductors are made of a copper tube using liquid cooling [2]. Heating of aluminum ingots is carried out until a temperature of 530 °C is reached. To compensate for reactive power and a local increase in the voltage of individual sections of inductors, capacitor banks are widely used [3]. The value of the capacitance of the capacitor banks is changed by connecting capacitors in parallel. The capacitors are switched by power switches. Control of switching elements is performed automatically, using a microcontroller or relay-contactor control system [4, 5]. When the ingot is heated, the electrophysical parameters of
the heating complex change smoothly [6]. The equivalent load impedance contains resistive components, the change of which is not fully taken into account in the control modes of the regulator [7].
General view of methodical and periodic electromagnetic inductors for heating aluminum ingots is shown in Figure 1. The designs of the inductors are quite diverse, and the sections can be connected to a three-phase or single-phase network. In each specific case, the problem of optimal power supply of the induction complex is solved. This task depends on the technological and technical requirements, as well as the circuitry of the windings.
An example of an equivalent circuit for a singlephase induction unit with parametric elements is shown in Figure 2. The circuit implements a balancing device for a three-phase inductor. The balancing device consists of a capacitor bank and a power choke. This is a typical solution for a powerful single-phase load in the form of an ID inductor designed for heating aluminum poles (Figure 1, a), weighing up to 1 ton [8]. The power capacitors are connected to the voltage Uab, and the
electromagnetic choke with taps is connected to the voltage Ubc. Parallel to the load, an additional adjustable capacitor bank is installed, at line voltage Uca. Such a capacitors battery is designed to maintain the resistive resistance of the power branch by creating a resonance of currents [9]. In the course of balancing to the initial parameters of the inductor, the impedance drift is not taken into account.
Figure 2. Schematic of an induction installation with parametric models
In the simulated device, standard regulators of the capacitance of the capacitor banks and the inductance of the choke are used. Switching is performed with gate keys operating under the control of the controller [5, 10]. Traditional discrete controllers are usually built using thyristors or triacs. Modeling such elements in an arbitrary simulator, as a rule, does not cause difficulties.
Problem Statement. Judging by the diagram (Figure 2), the Rid element is a resistive two-port element with variable parameters. Modeling power induction devices with adjustable resistive elements contains certain difficulties. Analog control of two-pole elements in a numerical experiment is not possible. Therefore, to simulate a parametric two-port element, discrete control with the use of idealized keys should be used. Discrete control characteristics can be different. In the simplest case, you can use binary code.
Dynamic control of two-terminal elements has a number of features that are fully manifested in the time domain. Certain difficulties arise when optimizing the switching intervals, since the simulation uses computational methods that are critical to the choice of the iteration step. In addition to simulating dynamic modes, the use of discretely controlled elements makes it possible to automate a numerical experiment in the field of steady-state modes. Using the functions of impulse control of switched models, it is possible to program multivariate studies of a set of quasi-stationary states of a model of a power supply system, a rather complex induction complex.
Solution. In a numerical experiment, the dependence of resistance (conductivity) on temperature must be taken into account. At the same time, the element temperature changes much more slowly than the transient mode lasts. This feature makes it possible to overcome the difficulties with the selection of switching intervals. Nevertheless, it is the parametric nature of the two-terminal element that allows us to talk about impulse control, since in fact the impedance changes over time. Thus, at the stage of modeling in the simulator, the two-terminal element must be replaced by a parametric model.
The degree of complexity of the structure of the parametric model is determined by the level of correspondence of the synthesized control characteristic to the conditions for regulating the curve of changing the operating parameters [6, 11]. The characteristics of the change in the impedance of a parametric two-terminal network in time are monotonous. The impedance variation range does not exceed 20 % of the nominal value. When modeling the power circuits of induction complexes, models created from elements with lumped parameters are used. Thus, the studied circuitry becomes digital-analog.
To change the parameters of two-pole elements, you can use a code pulse control [11, 12]. The state of the electric key of each switched element of the model is determined by a binary code. At the same time, in pulsed parametric models, you can apply different schemes for connecting elements, with a number of ideal keys. Usually, the number of keys corresponds to the number of bits of the regulated model [11, 13].
Depending on the selected switching time intervals At = tk+1 - tk, the model can be dynamic, or go to the region of stationary modes. Low switching frequency provides a set of quasi-stationary modes of inductive load. For the simulation of transient modes, it provides a choice of small time intervals between commutations [4, 14]. This problem is solved when overcoming conflicts, between the time step and the key switching intervals. In the software used, this problem is solved automatically, at the algorithmic level. This increases the complexity of the program code, but excludes crashes during the numerical experiment.
An example of circuitry of the simplest switching resistive regulators of a serial and parallel structure is shown in Figure 3, a, b. Regulated elements can be identified in the Z-region as resistors R (Ohm), and also in the Y-region as conductivity G (S). It should be noted that in most practical circuit solutions, especially taking into account the use of computational algorithms for nodal analysis, the conductivity representation is preferable.
R
b
Figure 3. Fragments of switching regulators circuitry
a
In the figures, the following designations are adopted: Ri is the base value of the resistor, Si is an ideal controlled switch, then kf = tp/T is the duty cycle of the pulses, for the control sequence shown in Figure 3, c. On the basis of linear resistive two-terminal networks, more complex circuit models of controlled elements are created. With the help of impulse action, it is possible to realize both linear and non-linear transient characteristics. The undoubted advantage of such models can be considered the linearity of their parameters and the relatively low order of the matrix equations obtained in the nodal basis. The use of such models is preferable in conjunction with typical multipoles elements of circuit theory, called controlled voltage and current sources [15, 16].
The dynamic state of a branch with pulse-controlled conductivity can be described by the expression:
g(t, kf) =
G, if: nT < t < [T + tp]; 0, if: [nT + tp] < (n + 1)T
(1)
where n = 1, 2, 3, ...,
Applying an expansion in a trigonometric series, for a function g(t, k), that is symmetric with respect to the middle of the switching interval, it is possible to rewrite the expression for the dynamic conductivity of a resistive link as a sum of constant and variable components:
g(t, kf) = g(kf) + ~(t, kf) = Gkf + 2GI
K n=1
sin n k k
f 2n k 1 cos——— t .
(2)
In the case of using a binary control code, it is convenient to use a weighting factor for an adjustable resistance matrix, according to Figure 4, a, b, equal to two k = R
n+1
/ Rn = 2.
An example of pulse-controlled resistive elements of a more complex, parallel and serial structure is shown in Figure 4, a, b.
a b
Figure 4. Variants of circuit models ofparallel (a) and serial (b) regulator
n
In the notation adopted in the figure, Rn - are the values of the adjustable resistors of the matrix, taken with a given weighting factor. An averaging capacitance can be installed in parallel to each switched element [11, 14]. At the same time, the modulating effect of the step process decreases and, accordingly, the intensity of the higher harmonics of voltage and current, caused by switching, decreases. The value of the averaging capacitance is selected from the condition of the minimum possible inertia of the impulse link. Characteristics of binary code control of resistive switches of a five-bit parametric model are shown in Figure 5. In the general case, the number of bits can be increased.
However, it should be understood that when constructing models of 8, 16 or 24-bit controlled elements, it may be necessary to increase the bit depth of the mathematical kernel used by the calculator [16, 17]. This is due not so much to the condition of expanding the bandwidth of the simulated induction device, with pulse-controlled elements, as to the provision of appropriate conditions for the convergence of the iterative computational process. By the way, it can be noted that, according to an approximate estimate, to expand the signal bandwidth above 10 Hz, the frequency of the control pulses of the transient mode should be selected with a value greater than 10 kHz [11]. Therefore, to control elements in industrial installations, the model
operates at a frequency of more than 50 kHz. In this case, the error in setting the resistance values during pulse regulation of a five-bit resistive matrix is determined by the ratio of the value of the least significant digit to the senior one: Sr = Ry lR5 = 6,25 %.
To achieve greater accuracy in resistive analogdigital models, it is preferable to operate with eight-bit matrix constructions, for which the equality is fulfilled:
sR = Ry l R8 = 21256 = 0,78 %. (3)
Characteristics with pulse sequences of control keys Si - S5, without delay at zero time, are shown in Figure 5, a. The characteristics of key management, with a delay at the zero point in time, are shown in Figure 5, b. In this context, the quality of electronic switches, for which MOSFET components are usually used, is not discussed here. Keys are considered perfect. Moments of switching on the graphs are designated by the corresponding letters [ti, t2, t3, t4, t5, t6], switching occurs instantly [16, 18].
The pulse graphical patterns presented in Figure 5 determine the fundamental difference between characteristics 1 and 2 shown in Figure 6, a.
a b
Figure 5. Control characteristics of the switches of the parametric model
The tuning of parametric models is performed using the circuitry of standard current sources J and EMF E. An example of circuit designs for diagnosing adjustment parameters in the field of currents and voltages is shown in Figure 6.
The simplest circuit with a constant current source J, shown in Figure 6, a, is designed to diagnose the in-
stantaneous voltage on a pulsed resistive model, relative to a node with zero potential. When applying control pulses according to Figure 5, a, to the switches S„, inside the model R(t), the instantaneous current i(t) of the model takes on values that change over time, according to Figure 7, a (curve 1).
a b
Figure 6. Test circuits for tuning parametric models
The following designations are adopted in the diagrams: J, E - direct current and EMF sources, R(t) -time-controlled resistive model, Out - instantaneous voltage sensor in the circuit node, EI - current controlled voltage source (CCSV). In the diagram of Figure 6, b, the current change in time is already controlled. The controlled source EI converts the instantaneous current of the primary short-circuited branch into an output voltage measured by the Out sensor.
Since the transfer coefficient EI-source is equal to unity, the output voltage actually reflects the characteristic of the change in the current of the primary branch [18 - 20].
Methods and materials. Calculation of circuits with parametric elements and controlled sources according to Kirchhoff's laws is difficult, therefore, it is preferable to use calculations in a software simulation environment using a typical description of all elements [16, 20, 21]. In fact, the construction of circuit models corresponds to a numerical experiment. The model is created in a certain sequence, in accordance with a previously thought out program of the experiment. The description of the model is formed using a modeling language similar to some versions of the Ansys software environment.
Fragments of the matrix description of EMF and current sources are shown below. The current of the EMF source is directed from node m to node n, the voltage is directed towards. m n /g
Vm(t )
Vn(t )
h(t )
Ek = Vn(t)- Vm(/) = U.
m n *E
0 0 1 0 0 -1 -1 1 0
0
= 0
Ek
The current of the current source is directed from node m to node n, the voltage is directed towards. When forming a system of modified nodal equations, for
small circuits, use the stamp of the current source given below, obtained from the component equation of the Z-branch.
J = I,
J
m 0 0 1 Vm(t ) 0
n 0 0 -1 Vn(t ) = 0
J 0 0 1 ik(t ) Jk
(5)
m n
Let us consider the description of mathematical models used to construct an algorithm for analyzing circuits with a controlled source of EMF [17, 18, 22]. The input current is directed from node i to node j, the input voltage is zero, the output voltage is directed from node m to node n against the source, the output current and EMF source are directed from node n to node m.
The matrix description of the controlled CCSV source is formed on the basis of component equations, which have the form:
u2(t) = kR • h(t),
Vn(t) - Vm(t) = kR ■ il(t),
Vm(t) - Vn(t) + kR ■ il(t) = 0 , ) - Vi(t) = 0,
where: u2(t) - is the output voltage of the source, i\(t) - is the input current of the source, k = RT - is the transfer coefficient of the source (transition resistance), V(t) - are the potentials of the nodes.
The system of extended nodal equations for a controlled source presented below is compiled taking into account the control and controlled branches.
i j n m »1 »2
i 0 0 0 0 1 0 Vi(t ) 0
j 0 0 0 0 -1 0 V(t ) 0
n 0 0 0 0 0 -1 Vn(t ) 0
m 0 0 0 0 0 1 Vm(t ) 0
»1 -1 1 0 0 0 0 »1(t ) 0
»2 0 0 -1 1 kR 0 »2 (t) 0
(6)
The above relations are automatically integrated into the expression of the main computational method. In the software environment for mathematical modeling of induction devices, a modified nodal analysis is programmed [16 - 18].
S11
g kk
a11
a kk
b
kk+1
rkk+1
The generalized expression of the computational method, converted to the time domain, is shown below:
Vf (t )
vi (t )
1 (t ) irn (t )
I j (t )
I ern (t )
(7)
where [gkk] - is the matrix of nodal admittances of the regular part of the circuit, [r„„] - is the resistance matrix, [akk], [bBB], - are matrices with unit and zero coefficients taking into account the controlled elements, [E/k] - is the matrix of nodal currents, [Ee„] - matrix array of EMF sources.
The characteristics of the controlled mode parameters corresponding to the code binary control of the
five-bit resistive model are shown in Figure 7. Judging by the characteristics of Figure 7, a, b, the stepwise change in the mode parameters is modulated by the switching frequency.
The smallest step size is typical for the S5 key of the least significant bit. The set of commutations of all switches at each moment of time is determined by the instantaneous value of the controlled function without averaging [\\, 23].
a b
Figure 7. Dynamics of changes in the operating parameters of the resistive model
b
nn
r
nn
Graphs with nonlinear dependences of parameters (1) and (2) (Figure 7, a) correspond to voltage. Graphs with linear characteristics (1) and (2) (Figure 7, b) correspond to the current. Both voltages and currents are determined by the same pulse control sequences (Figure 5, a, b).
Depending on the task of modeling, it is possible to recommend the use of the combined inclusion of models according to Figure 4, a, b. Moreover, to simulate nonlinear curves, it is convenient to use inversion of characteristics using voltage controlled voltage sources (CVSV) and current controlled current sources (CCSC). Such sources in a relatively simple way provide a mode of galvanic isolation of different parts of the circuit [11, 14, 24].
Results and discussion. Taking into account the possibilities of using parametric models, one can proceed to the analysis of transient modes of induction complexes, taking into account the switching of capacitor banks and relatively simple resistive models of the inductor. The shown features of the control characteristics (Figure 7) require a separate study for the stage of constructing more complex, serial-parallel models. In
addition, additional study requires the issue of choosing the control ranges of parametric models, as well as the construction of methods for the synthesis of controlled elements. An example of a vector diagram of an induction unit obtained using switched models is shown in Figure 8. Taking into account the depth of load change, the control characteristics take on a more complex form [25, 26].
The diagram shows that balancing the electromagnetic mode of the ID by the Steinmetz circuit is effective only if the resistive nature of the load is maintained. The degradation of the power factor of the inductor with the exit from the resonance mode immediately leads to a distortion of symmetry, accompanied by a divergence of the current vectors. That is why, in practice, it is necessary to have precise measuring equipment and a microcontroller control device that automatically regulates the electromagnetic state of the ID. A very significant change in the position of the vectors on the diagram is characteristic of a possible uncoordinated change in the parameters of balancing devices, with the admissibility of a simultaneous drift of the electrophysical parameters of the loaded inductor.
A
!+Re
Figure 8. Vector diagram of an induction unit with switchable models
When constructing a vector diagram, the results of modeling modes for a depth of regulation of an inductive load of 15 % were used. In addition, in the program of the numerical experiment, the range of regulation of each of the balancing elements, extended to ± 25 % with respect to the symmetric mode, is specified. It can be noted that practical coincidence of the given conditions is unlikely. However, the diagram clearly shows the application of inductor currents (3 -4 kA). Naturally, the currents of consumption from the network with such a deep mismatch go beyond the permissible limits, limited by the resonant characteristics of the parallel circuit of the inductor.
The capabilities of the impulse regulation of the models can be used in the calculation of the stationary
regime. To do this, it is necessary to draw up a program for a numerical experiment and describe the simulation sequence in the format of a program code. In this way, a control command file is formed, which makes it possible to carry out multivariate calculations according to the global description of the induction device.
As a result of obtaining a set of operating characteristics, when changing the load parameters, presented in the form of "fan" vector diagrams. The problem of modeling the dynamics of induction heaters with the construction of phase trajectories and portraits for the mode of characteristics [27] is programmed similarly to the problem of analyzing vector diagrams [28]. In view of the large volume of calculations and the cumber-someness of the problem, the described fragments of
the numerical experiment are separated into separate projects and will be considered separately.
Conclusion. The models of resistive pole networks proposed in two parameters can be used when setting up induction installations with variable functions. Pulse control of a resistive unit subsystem, as part of complex RLC models in a numerical experiment, allows the use of a matrix mathematical apparatus and algorithms for iterative analysis of analog systems. When constructing models, the elemental basis of controlled voltage and current sources is widely used, as applied to the theory of circuits. The use of the simulator makes it possible to exclude the formation and solution of complex systems of equations, passing directly to the understandable and obvious circuitry of the modeled system. In this case, the synthesized models turn out to be analog-digital, and the structure of the obtained control characteristics can become nonlinear. With an appropriate choice of control intervals, the control problem can be both parametric and stationary.
Additional conveniences of the proposed approach are manifested in the form of the possibility of obtaining an evolutionary set of vector diagrams for several steady-state modes of the modeled system during the tuning of the models.
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ПОЖАРНАЯ ОПАСНОСТЬ И МЕРЫ ЗАЩИТЫ ОТ СТАТИЧЕСКОГО ЭЛЕКТРИЧЕСТВА
Сафронова И.Г.
Уральский институт ГПС МЧС России, начальник кафедры пожарной безопасности технологических процессов и производств, к.п.н., доцент Шнайдер Н.В. Уральский институт ГПС МЧС России, начальник кафедры автоматизированных систем противопожарной защиты, к.т.н., доцент
Шнайдер А.В. Уральский институт ГПС МЧС России, начальник кафедры пожарной безопасности технологических процессов и производств, к.п.н., доцент
Леменков М.Д.
Уральский институт ГПС МЧС России, курсант факультета пожарной и техносферной безопасности
Казаченко А.И. Уральский институт ГПС МЧС России, курсант факультета пожарной и техносферной безопасности
FIRE HAZARD AND PROTECTION AGAINST STATIC ELECTRICITY
Safronova I.
Ural Institute of State Fire Service of the Ministry of Emergencies ofRussia, Head of the Department of Fire Safety of Technological Processes and
industries, Ph.D., associate professor Schneider N.
Ural Institute of State Fire Service of the Ministry of Emergencies ofRussia, Associate Professor of the Department of Fire Safety of Technological Processes and industries, Ph.D., associate professor
Schneider А.
Ural Institute of State Fire Service of the Ministry of Emergencies ofRussia, Head of Automated Fire Protection System Department, Candidate of Technical Sciences, associate professor
Lemenkov M.
Ural Institute of State Fire Service of the Ministry of Emergencies ofRussia, cadet of the Fire and Technosphere Safety Faculty
Kazachenko A.
Ural Institute of State Fire Service of the Ministry of Emergencies ofRussia, cadet of the Fire and Technosphere Safety Faculty
