Schemes of control and management of technological process parameters. Control and management of machine tools and automatic lines. Single-circuit and multi-circuit regulation systems
Despite not a huge variety of technological processes in the chemical industry, all of them consist of separate technological operations, each of which, as mentioned above, can be attributed to one of the following groups of typical processes: mechanical, hydrodynamic, thermal, mass transfer, chemical (reactor), and thermodynamic. The processes of each group are based on general physicochemical laws, which determines the significant similarity of their properties as objects of automation.
Thanks to this, it is possible to develop standard automation schemes for the objects of each group. However, one technological feature is not enough for typing automation objects, because the processes of one group can have different hardware design (for example, drying in a drum dryer or in a fluidized bed dryer) and, as automation objects, vary significantly in their properties. Therefore, only a combination of two features - the type of technological process and the type of apparatus in which this process is carried out, completely determines the typical object of automatic regulation in chemical production.
For each typical object, one or several variants of automation systems can be developed.
ACP flow . Most often, the problem arises of regulating the flow of gas, liquid or steam transported through the pipeline. Flow control in such a system is performed by throttling the flow, which depends on the degree of opening of the control valve (see Figure 7.2):
Figure 7.2 - The simplest ASR flow
The object of regulation is actually a section of the pipeline between the flow sensor and the control valve, which can be considered as inertialess amplification unit. Therefore, the dynamic characteristic of a given part of the ASR is determined only by the dynamic properties of the flow sensor and the regulatory body. To maintain a given flow rate without a residual deviation in the flow rate control system, PI controllers are usually used.
In flow control systems, one of three methods for changing the flow is used:
- throttlingsubstance flow through the regulating body installed on the pipeline (valve, gate, damper);
Changing the pressure in the pipeline using an adjustable energy source (for example, by changing the number of revolutions of the pump motor or the angle of rotation of the fan blades);
- bypass , i.e., the excess of substance has grown from the main pipeline to the bypass line.
Flow control after the centrifugal pump is carried out by a control valve installed on the discharge pipe (Figure 7.3, a). When using a piston pump, the use of such an ACP is unacceptable, since during the operation of the regulator the valve may close completely, which will lead to rupture of the pipeline (or surge if the valve is installed on the pump inlet). In this case, flow bypass is used to control the flow (Figure 7.3, b).
1 - flow meter; 2 - control valve; 3 - regulator; 4 - pump.
Figure 7.3 - Flow control schemes after centrifugal (a) and piston (b) pumps.
Flow control by flow throttling in a bypass pipe. When using reciprocating pumps, regulators cannot be installed on the pressure pipe, as a change in the degree of opening of such an organ leads only to a change in pressure in the discharge line, while the flow rate remains constant. Complete closure of the regulator may result in damage to the pump. In this case, the regulatory body is installed on the bypass line connecting the suction and discharge pipelines (Figure 7.3, 6).
The disadvantage of this method of regulation is low efficiency. More economical is the method of regulation by changing the performance of the pump: the number of revolutions of the shaft, the stroke of the piston, the angle of inclination of the blades.
The shaft speed can be changed:
1. By switching the stator winding to a different number of pole pairs,
2. The introduction of a rheostat in the rotor circuit of the engine,
3. By changing the frequency of the supply current,
4. Using adjustable slip couplings between the pump and the induction motor.
Regulation of the flow rate of bulk solids is carried out by changing the degree of opening of the control flap at the outlet of the hopper (Fig. 7.4, a), or by changing the speed of the conveyor belt. The flow meter with this option is a weighing device that determines the mass of material on the conveyor belt (Fig. 7.4, b).
1 - hopper. 2 - conveyor; 3 - regulator; 4 - the regulating gate; 5 - electric motor
Figure 7.4. Bulk substance flow control schemes:
Regulation of the ratio of the costs of two substances can be carried out in three ways:
With undefined total productivity, the flow rate of one substance (Figure 7.5, a) G1, called the “lead”, can vary arbitrarily; the second substance is supplied at a constant ratio of γ with the first, so that the “driven” flow is equal to JG1. Sometimes, instead of the ratio regulator, a ratio relay and a conventional regulator for one variable are used (Figure 7.5, b). The output signal of the relay 6, which sets the specified ratio coefficient γ, is supplied in the form of a task to the regulator 5, which ensures the maintenance of the “slave” flow.
For a given “leading” flow rate, in addition to the ACP ratio, the ACP of the “leading” flow rate is also used (Figure 7.5, c). With such a scheme, in the event of a change in the task for the flow rate G1, the flow rate G2 will also automatically change (in the given ratio with G1).
For a given total load and correction factor for the third parameter. The ASR of the expense ratio is the internal circuit in the cascade control system of the third technological parameter (for example, the temperature in the apparatus). In this case, the specified ratio coefficient is set by an external regulator depending on this parameter, so G2 \u003d JfyJG1 (Figure 7.5, d). A feature of tuning cascading ASRs is that a restriction of HRN is set on the task of the internal regulator< хр < хрв. Для АСР соотношения расходов это соответствует ограниче-нию ун < γ < ув. Если выходной сигнал внешнего регулятора выходит за пределы [хрн,хрв], то задание регулятору соотношения остается на предельно допустимом значе-нии γ (т. е. Ji1 или J6).
1, 2 - flow meters, 3 - ratio regulator, 4, 7 - control valves; 5 - flow regulator, 6 - ratio relay, 8 - Temperature regulator, 9 - device restrictions.
Figure 7.5. Schemes of regulation of the ratio of costs.
Mixing liquids.When developing a typical solution, the control object will be understood as a container with a mechanical mixer, in which two liquids are mixed. The purpose of control is to obtain a liquid (mixture) with a certain concentration of any component. The flow rates of liquids A and B and their concentrations may vary in case of violation of the technological regime of previous processes. The flow rate of the mixture is determined by the subsequent process.
Required during the mixing process:
1. Maintain the material balance of the mixer, ie. F A + F B \u003d F mixture.
2. Maintain a constant concentration of the mixture, ie Q mixture \u003d const.
To maintain material balance, you should choose the level of the mixture in the tank as an adjustable quantity. The constancy of the level is achieved by changing the flow rate F B. The constancy of the concentration Q of the mixture can be ensured by changing the flow rate F A (Figure 7.6)
Figure 7.6 - Example of an ACP level
If the flow rate of liquid B varies greatly with level control, to improve the quality of concentration control, use the regulator for the ratio of flow rates of liquids with a correction for concentration. This regulator helps to reduce concentration disturbances that occur during the initial change in fluid flow. Upon receipt of other disturbing influences, for example, with a change in the concentration of components in liquids, the task of the flow ratio will change (Figure 7.7).
Figure 7.7 - An example of an ACP level ratio
Regulation of the mixing process in the pipeline.If the mixing process is carried out directly in the pipeline, then there is no need for a level stabilization unit; it is enough to set the concentration regulator of the component in the mixture or the flow ratio regulator (with or without correction, Figure 7.8).
Figure 7.8 - Regulation of the mixing process in the pipeline
ACP level. The level is an indirect indicator of the hydrodynamic equilibrium in the apparatus. The constancy of the level indicates the observance of the material balance, when the flow of fluid is equal to the drain, and the rate of change of the level is zero.
In general, a level change is described by an equation of the form:
where S - the area of \u200b\u200bthe horizontal (free) section of the apparatus; G ex, G ex - fluid flow at the inlet and outlet of the apparatus; G o6 - the amount of fluid generated (or consumed) in the apparatus per unit time. Depending on the required accuracy of maintaining the level, one of the following two control methods is used:
Depending on the required accuracy of maintaining the level, one of the following two control methods is used:
Positional regulation, in which the level in the device is maintained within a given, fairly wide range: Lfs< L < L^ Такие системы регулирования устанавливают на сборниках жидкости или промежуточных емкостях (рисунок 7.9). При достижении предельного значения уровня происходит автоматическое переключение потока на запасную емкость;
Continuous regulation, which ensures stabilization of the level at a given value, i.e., L \u003d L.
1 - pump; 2 - apparatus; 3 - level indicator; 4 - level control; 5,6 - control valves.
Figure 7.9 - Scheme of positional level control
Particularly high requirements are placed on the accuracy of level control in heat exchangers, in which the liquid level significantly affects thermal processes. For example, in steam heat exchangers, the condensate level determines the actual heat exchange surface. In such ASRs, to control the level without static error, they use PI controllers . P-controllers are used only in cases where a high quality of regulation is not required and disturbances in the system do not have a constant component, which can lead to the accumulation of static error.
In the absence of phase transformations in the apparatus, the level in it is regulated in one of three ways:
A change in the flow rate of the liquid at the inlet to the apparatus (regulation "on the influx", Figure 7.10, a);
A change in the fluid flow rate at the outlet of the apparatus (regulation "on the drain", Figure 7.10, b);
By adjusting the ratio of fluid flow rates at the inlet and outlet of the apparatus with level correction (cascading ASR, Figure 7.10, c); turning off the correction loop can lead to an accumulation of error during level control, because due to inevitable errors in the adjustment of the ratio controller, the liquid flow rates at the input and output of the device will not be exactly equal to each other, and due to the integrating properties of the object, the level in the device will continuously increase (or decrease) )
a - regulation "on the inflow"; b - regulation "on the drain", c - cascade ASR (1 - level control, 2 - control valve, 3, 4 - flow meters, 5 - ratio controller).
Figure 7.10 - Schemes of continuous level control:
1 - evaporator; 2 - level control, 3 - control valve
Figure 7.11 - The scheme of level control in the evaporator
In the case when the hydrodynamic processes in the apparatus are accompanied by phase transformations, you can adjust the level by changing the flow of coolant (or refrigerant). In such devices, the level is interconnected with other parameters (for example, pressure), therefore, the choice of the level control method in each particular case should be made taking into account the rest of the control loops. A special place in the level control systems is occupied by the ASR level in devices with a fluidized (fluidized) layer of granular material (Figure 7.12).
Stable maintaining the level of the fluidized bed is possible in a fairly narrow range of the ratio of gas flow and mass of the layer. With significant fluctuations in gas flow (or flow rate of granular material), the mode of entrainment of the layer or its subsidence occurs. Therefore, particularly high demands are placed on the accuracy of fluid level control. As regulatory actions, use the flow rate of granular material at the inlet or outlet of the apparatus (Figure 7.12, a) or the flow rate of gas to liquefy the bed (Figure 7.12, b).
a - removal of granular material, 6 - a change in gas flow (1 - apparatus with a fluidized bed, 2 - level control, 3 - regulatory body).
Figure 7.12 - Fluidized bed level control:
ASR pressure.Pressure is an indicator of the ratio of the gas phase flow rate at the inlet and outlet of the apparatus. The constancy of pressure indicates compliance with the material balance in the gas phase. Typically, the pressure (or vacuum) in a process unit is stabilized in any one device, and throughout the system it is set in accordance with the hydraulic resistance of the line and devices. For example, in a multi-case evaporator (see Figure 7.13, a), the vacuum in the last evaporator is stabilized. In other devices, in the absence of disturbances, a vacuum is established, which is determined from the conditions of material and thermal balances, taking into account the hydraulic resistance of the production line.
In those cases when the pressure significantly affects the kinetics of the process (for example, during the rectification process), a pressure stabilization system is provided for individual equipment (Figure 7.13, b). In addition, when regulating the process of binary distillation, its boiling point is often used as an indirect indicator of the composition of the mixture, which is uniquely related to the composition only at constant pressure. Therefore, special pressure stabilization systems are usually provided in product distillation columns.
1, 2 - evaporators; 3 - barometric capacitor; 4 - rarefaction regulator;
5 - control valve.
Figure 7.13a - Regulation of vacuum in a multi-case evaporator
1 - column; 2 - reflux condenser; 3 - reflux capacity; 4 - pressure regulator;
5 - control valve
Figure 7.13B - pressure ASR in the distillation column
Regulation of discharge in a multi-case evaporator. In this system, the regulating effect is the flow of cooling water into the barometric condenser, which affects the rate of condensation of the secondary steam.
Differential pressure control. In such devices, the differential pressure is regulated, which characterizes the hydrodynamic regime, which affects the course of the process (Figure 7.14).
a - in a column apparatus with a nozzle; b - in a fluidized-bed apparatus (1 - apparatus; 2 - differential pressure regulator; 3 - control valve).
Figure 7.14 - Pressure differential control circuit
Generally ASR pressureliquid, gas or steam transported through the pipeline has a lot in common with ASR flow, because regulatory objects have the same properties. Sometimes, to control the pressure in the pipelines of steam or compressed air, P-regulators direct action.
In the absence of sharp and significant perturbations in amplitude, they provide good quality control due to the minimum inertia of the control loop.
ACP temperature control.Temperature is an indicator of the thermodynamic state of the system and is used as the output coordinate for regulating thermal processes. The dynamic characteristics of objects in temperature control systems depend on the physicochemical process parameters and apparatus design. Therefore, it is impossible to formulate general recommendations on choosing an ACP temperature, and analysis of each specific process is required.
The common features of temperature ACP include the significant inertia of thermal processes and industrial temperature sensors. Therefore, one of the main tasks in the design of temperature ASR is to reduce the inertia of the sensors.
Consider, for example, the dynamic characteristics of a thermometer in a protective case (Figure 7.15).
1 - a protective cover; 2 - air gap; 3 - wall of the thermometer; 4 - working fluid.
Figure 7.15. The principal (a) and structural (b) diagrams of the thermometer
The structural diagram of a thermometer can be represented as a series connection of four thermal capacities (Figure 7.15, b): a protective cover 1, an air gap 2, a wall of a thermometer 3, and the actual working fluid 4. If we neglect the thermal resistance of each layer, then all the elements can be approximated by aperiodic links of the first order, the equations of which are of the form:
M j - the mass of the cover, air gap, wall and liquid, respectively; c pj - specific heat; α j1, α j2 - heat transfer coefficients; Fj1, Fj2 - heat transfer surfaces.
As can be seen from the last equations, the main directions of reducing the inertia of temperature sensors are:
Increased heat transfer coefficients from the medium to the cover as a result of the correct choice of the sensor installation location; while the velocity of the medium should be maximum; ceteris paribus, it is more preferable to install thermometers in the liquid phase (compared with the gaseous), in a condensing pair (compared with the condensate), etc .;
Reduction of thermal resistance and thermal capacity of the protective cover as a result of the choice of its material and thickness;
Reducing the time constant of the air gap due to the use of fillers (liquid, metal chips); for thermoelectric converters (thermocouples), the working junction is soldered to a protective cover;
Choice of type of primary converter; For example, when choosing a resistance thermometer, thermocouple or gauge thermometer, it is necessary to take into account that the thermocouple in the low-inertia version has the lowest inertia, and the gauge thermometer is the largest.
ACP pH. PH control systems can be divided into two types, depending on the required control accuracy. If the rate of change of pH is small, and the permissible limits of its fluctuations are wide enough, apply positional control systems that maintain pH within the specified limits: pHn ≤ pH ≤ pHv. The second type includes systems that provide control of processes in which accurate pH maintenance at a given value is required (for example, in neutralization processes). For their regulation using continuous PI or PID controllers.
A common feature of objects in the regulation of pH is the non-linearity of their static characteristics associated with the non-linear dependence of pH on the costs of reagents. Figure 7.16 shows a titration curve characterizing the dependence of pH on acid consumption G 1. For various preset pH values \u200b\u200bon this curve, three characteristic sections can be distinguished: the first (middle), which relates to almost neutral media, is close to linear and is characterized by a very large gain; the second and third sections, related to strongly alkaline or acidic media, have the greatest curvature.
In the first section, the object, by its static characteristic, approaches a relay element. In practice, this means that when calculating a linear ASR, the gain of the regulator is so small that it goes beyond the working settings of industrial regulators. Since the neutralization reaction itself proceeds almost instantly, the dynamic characteristics of the apparatuses are determined by the mixing process and in apparatuses with mixing devices are fairly accurately described by differential equations of the first order with delay. Moreover, the smaller the time constant of the apparatus, the more difficult it is to ensure stable regulation of the process, since the inertia of the devices and the regulator and the delay in the impulse lines begin to affect.
Figure 7.16 - The dependence of pH on the consumption of reagent
To ensure stable pH control, special systems are used. Figure 7.17a shows an example of a pH control system with two control valves.
a is a functional diagram; b - static characteristics of valves (1, 2 - control valve 3 - pH regulator).
Figure 7.17 - Example of a pH control system
Valve 1, having a large nominal diameter, is used for coarse flow control and is set to the maximum range of the regulator output signal [x ph, x pb] (Figure 7.17, b, curve 1). Valve 2, which is used for precise control, is designed for lower throughput and is configured in such a way that when x p \u003d x 0 p + Δ it is completely open, and when x p \u003d x 0 p - Δ it is completely closed (curve 2). Thus, with a slight deviation of pH from pH 0, when x 0 p - Δ< х р < х 0 р + Δ, степень открытия клапана 1 практически не изменяется, и регулирование ведется клапаном 2. Если |х р - х 0 р |, клапан 2 остается в крайнем положении, и регулирование осуществляется клапаном 1.
In the second and third sections of the static characteristic (Figure 3.12, b), its linear approximation is valid only in a very narrow range of pH changes, and in real conditions the control error due to linearization can be unacceptably large. In this case, a piecewise-linear approximation gives more accurate results (Figure 7.18), in which the linearized object has a variable gain.
Figure 7.18 - Piecewise linear approximation of the static characteristics of the object when adjusting pH
Figure 7.19 shows the structural diagram of such an ASR. Depending on the mismatch in pH, one of the regulators tuned to the corresponding gain of the object is included in the operation.
Figure 7.19 - Block diagram of a pH control system with two regulators.
ACP composition and quality parameters.In the processes of chemical technology, an important role is played by the exact maintenance of the qualitative parameters of the products (concentration of a certain substance in the stream, etc.). These parameters are difficult to measure. In some cases, chromatographs are used to measure the composition, which give the measurement results at discrete time points (by the length of the chromatograph’s cycle of operation).
The measurement discreteness can lead to significant additional delays and a decrease in the dynamic accuracy of regulation. To reduce the undesirable effects of measurement delays, a model is used to relate product quality to variables that measure continuously. This model can be quite simple; the coefficients of the model are specified by comparing the value of the qualitative parameter calculated from it and found as a result of the next analysis.
Thus, one of the rational ways of regulating quality is regulation by an indirectly calculated indicator with a refinement of the algorithm for its calculation by direct analysis. In the intervals between measurements, the product quality indicator can be calculated by extrapolating the previously measured values. The block diagram of the product quality parameter regulation system is shown in Figure 7.20. In the general case, the computing device continuously calculates an estimate of the quality index ~ (t) by the formula:
in which the first term reflects the dependence on continuously measured process variables or quantities dynamically associated with them, such as derivatives, and the second on the output of the extrapolating filter.
To increase the accuracy of regulation of composition and quality, instruments with an automatic calibration device are used. In this case, the control system periodically calibrates the composition analyzers, adjusting their characteristics.
1 - object; 2 - quality analyzer; 3 - computing device; 4 - regulator
Figure 7.20 -. Block diagram of ACP product quality parameter:
As an example, consider decision making process in automation one of the common type processes.
Automation of the mixing process. General characteristics of mixing processes in liquid media. Mixing is a hydromechanical process of mutual movement of particles in a liquid medium with the aim of their uniform distribution in the entire volume under the influence of a pulse transmitted to the medium by a mixer, a stream of liquid or gas.
Transcript
1 Ministry of General and Professional Education of the Russian Federation Tver State Technical University V.F. Komissarchik Automatic process control Tutorial Tver
2 UDC 6.5 Automatic control of technological processes: Textbook Second edition, extended / V.F. Commissar; Tver State Technical University, Tver, 48c. The methods of calculating automatic control systems for technological processes of various types are considered. Designed for specialty students. “Automation of technological processes and production” when they study the discipline of the same name. Prepared at the Department of Automation of Technological Processes, Tver State Technical University.
3 3 Introduction One of the most important tasks of automation of technological processes is automatic regulation, with the aim of maintaining constant stabilization of the set value of the controlled variables or changing them according to the law set in time, program regulation with the required accuracy, which ensures the production of the right quality, as well as safe and economical work of technological equipment. As controlled variables, the usually used are the level, temperature, pressure, flow rate, or qualitative humidity, density, viscosity, composition, etc. performance indicators of technological processes characterizing the material or energy balance in the apparatus and product properties. The task of automatic regulation is realized through automatic systems of regulation of ASR. The block diagram of the closed ASR is shown in Fig. F RO x OR S P - back Fig.
4 4 In fig. designated: OR object of regulation of the technological process or apparatus; have an adjustable variable; x regulatory impact through which the regulatory process is carried out. Regulatory effects are usually the costs of liquid, gaseous, bulk solids; RO is a regulating working body, with the help of which the energy consumption of a substance changes. To change the flow rates of liquid and gaseous bodies, throttling-type working bodies with a variable flow area are widely used; S the position of the working body is usually measured in% of the stroke RO, for example, the movement of the valve stem or rotation of the valve. Since the regulatory action x, as a rule, is not measured, S is usually taken as the regulatory action, thereby referring to the object of regulation; F- disturbing effects that affect the value of the controlled variable; P - automatic controller, a set of elements designed to solve the regulatory problem; ass - the set value of the controlled variable, which should be supported by the controller; - a comparator generating an error error signal: ass. As an example, in fig. shows the temperature control scheme of the product θ ol at the heat exchanger outlet by changing the flow of heat carrier G.
5 5 G pr θ pr R G Fig. One of the main disturbances in this system is the consumption of the heated product G pr. The reason for regulation in a closed ASR is the occurrence of an error. When it appears, the regulator changes the regulatory influence x until the error is completely eliminated in an ideal system. Thus, ASR is designed to maintain a controlled variable at a given level with fluctuations in the disturbance within a certain range. In other words, the main task of the regulator is to eliminate the mismatch by changing the regulatory effect. The most important advantage of a closed ASR is that it responds to any disturbance leading to a mismatch. At the same time, such systems are fundamentally characterized by a regulatory error, since the occurrence
6 6 mismatch always precedes its elimination and, in addition, a closed ASR under certain conditions can become unstable. The main tasks arising in the calculation of ASR are :. The mathematical description of the object of regulation ;. Justification of the structural diagram of the RSA, type of regulator and the formation of requirements for the quality of regulation; 3. Calculation of controller settings; 4. Analysis of the quality of regulation in the system. The purpose of the calculation of closed ASR is to ensure the required quality of regulation. By the quality of regulation, we mean the values \u200b\u200bof indicators characterizing the shape of the curve of the transition process in a closed ASR with a stepwise effect at its input. An approximate form of the transient characteristics of a closed ASR through the channels of the master and the disturbing in the particular case of regulatory actions is shown in Fig. 3. Transient response of a closed system along the channel of the driving action line y fact in fig. 3a reflects the nature of the transition of the controlled variable from one steady-state value to another. x and y ass b y id y fact u fact u id Fig. 3.
7 7 It would be ideal if this transition were abrupt, the line y id Transitional characteristic along the channel of the regulatory influence line y fact in fig. 3b reflects the process of suppressing disturbance by the system. It would be ideal if the system did not react at all to the disturbance of the line at id. This manual discusses methods for solving typical problems that arise in the calculation of various types of automated process control systems that are used in the practice of automation of technological processes .. Mathematical description of regulatory objects [4] .. Main characteristics and properties of regulatory objects A regulatory object can be in one of two states: statics or dynamics. Static is a steady state in which the input and output values \u200b\u200bof an object are constant in time. This definition is valid for stable static objects. Dynamics is the change in time of the output variable of an object due to a change in the input variable or nonzero initial conditions. Static characteristics of regulating objects The behavior of the regulating object in statics is characterized by a static “input-output” characteristic, which represents the relationship between the steady-state values \u200b\u200bof the output and input variables: f set By the type of static characteristics, linear and nonlinear objects are distinguished. The static characteristic of a linear object represents a line passing through the origin with the equation
8 8 K The characteristic with the equation K b that does not pass through the origin can be reduced to a linear one, denoting b ". Objects whose static characteristics differ from the straight line are nonlinear. The tangent of the slope of the static characteristic α, equal to the derivative of the output variable with respect to the input, is called the static transfer coefficient of the object: K lim gα The coefficient K has the dimension: units of the output variable per unit of input impact Physical meaning: change of the controlled variable by unit of input ie, the transmission coefficient characterizes the steepness of the static characteristic. function x. For linear objects, Ku / constant, for non-linear K is. When calculating ASR, non-linear characteristics are usually linearized. Linearization by the tangent linear approximation of expansion in a Taylor series is widely used. Let x, y is a point in the vicinity of which the function f is linearized. Assuming ddd we find d When using the linearized equation, it should be taken into account that the linearization accuracy decreases with increasing increment, tangent nonarization is valid only in
9 9 a sufficiently small neighborhood of the point x. In addition, since the derivative of the function f is included in the expression, this linearization method is suitable only for differentiable functions. Dynamic characteristics of regulatory objects. Differential equation The main dynamic characteristic of regulatory objects is the differential equation. Objects can be described by two types of differential equations: ordinary differential equations and partial differential equations. Ordinary differential equations describe objects with lumped parameters, which can conditionally be considered containers with ideal instantaneous mixing. Variables in such objects depend only on time and do not depend on the coordinates of the measuring point of the variable. Partial differential equations describe objects with distributed parameters. Physically, these are usually devices in which one of the coordinates is much larger than the others, for example, a pipe-in-pipe heat exchanger, column-type devices, etc. In such objects, the values \u200b\u200bof the variables depend not only on time, but also the coordinates of the measuring point of the variables, therefore, differential equations include not only time derivatives, but also coordinates. In calculations, partial differential equations are usually approximated by a system of ordinary differential equations. In the future, we will consider objects described by ordinary differential equations of the form: d d n n n n< n n n d d m d d L bm L b ; m, m d d
10 where n is the order of the left side and the entire equation as a whole, m is the order of the right side. Since real objects of regulation represent inertial links, always m 11 Basic properties of the Laplace transform. The delay of the argument by τ corresponds to the multiplication of the image by τ e the original bias theorem, i.e. L e τ (τ) 4 This property allows one to find images of differential equations with a delayed argument. Differentiation of the original under zero initial conditions corresponds to multiplication of the image by p: d L d, therefore formally the variable p can be considered a symbol of differentiation. In the static river. In the general case, d L d 5 Since integration is the opposite of differentiation, integrating the original corresponds to dividing the image by p: (d) L / Property 5 allows you to write the Laplace image of the differential equation: nnnnm L bm L b Thus, the Laplace image of the differential equation represents an algebraic expression that can be resolved relative to the image of the output variable ur, and then again go from the image to the original. This operation is called the inverse Laplace transform and is denoted by the operator L () L: 12 The inverse Laplace transform is determined by the integral α j π e d j α j To facilitate finding the image in the original and the original in the image, tables of correspondence between the originals and their images for simple functions are compiled. These tables are provided in Laplace transform manuals and in management theory textbooks. To find the originals of complex images, use the formula for decomposing the image into simple fractions. see p The ratio of the Laplace image of the output variable to the image of the input variable under zero initial conditions is called the transfer function W bm nmn L b L, of the form: or, since b, the transfer function can be written in b WLL mmnn B, A where Ap and Bp are polynomials from p orders n and m, respectively. What is the relationship between the transfer function and the static transfer coefficient? The transfer function is a dynamic characteristic, transmission coefficient is a static characteristic. Static peace is a special case of motion dynamics. Therefore, K is a special case of W in statics. Since p is static, then K W 6 13 3 Temporal characteristics The temporal characteristic of an object is its response to a typical aperiodic signal. The most commonly used input signals are a step function or its derivative - δ - function. The reaction of an object or any dynamic link to a step function of unit amplitude, a unit step function is called a transition characteristic of an object of link h. The reaction of an object to a step of arbitrary amplitude x is called the acceleration curve of the object in Fig. 4. To obtain the transient response from the acceleration curve, y, each ordinate of the acceleration curve should be divided by the step amplitude: h / Fig. 4. Fig. 5. The reaction of an object to a δ function in real conditions on an impulse of finite duration and amplitude, for example, a rectangular one is called the impulse response, the weight function of the control object, Fig. 5. 14 4 Frequency characteristics Determine the behavior of an object in the frequency domain when a harmonic signal is applied to its input: m sin, where πf π / is the circular frequency of the signal, f is the frequency, is the signal repetition period, x m is the signal amplitude. At the output of a linear object, harmonic oscillations of the same frequency also occur, but with a different amplitude and phase (Fig. 6: ϕ m ϕ; 36, j m m ϕ j Fig. 6. Fig. 7. The values \u200b\u200bof m and ϕ depend on the frequency of the input signal. Since we are interested in a change in two amplitude and phase quantities at once, it is convenient to consider the frequency characteristics in the complex plane. The harmonic input signal is depicted on the complex plane by the vector j, the module length of which is equal to the amplitude x m, and the argument angle is equal to the oscillation phase of Fig. 7: j m e j The symbol in this case means "portrayed." 15 5 Similarly, the object output signal is represented in the complex plane by the vector j: m e j ϕ j Images j and j are called Fourier images by the Fourier spectra of harmonic signals and. The ratio of the Fourier images of the output harmonic signal to the input is called the frequency transfer function of the PFD or the complex frequency response W j: jm jϕ W jejm A e jϕ The frequency transfer function module A at the frequency determines the transmission coefficient of the object at a given frequency, ϕ is the phase shift between the output and frequency input signals. The transfer function is a function of the complex variable α j. The frequency transfer function is a function of the imaginary variable j. Therefore, the frequency transfer function is a special case of the transfer function when the variable p takes on a purely imaginary value j. Therefore, formally, the expression for the frequency transfer can be found by replacing the variable p by j in the transfer function W, i.e. setting j: bm W j j n m j n LL b LL What is the difference between the transfer function and the frequency transfer function? The transfer function reflects the behavior of the regulatory object or any dynamic link in the dynamics with an arbitrary form of input impact. The frequency transfer function reflects 16 6 the behavior of the link object only in the steady state harmonic oscillations. Thus, the frequency transfer function is a special case of the transfer function in the same way as the imaginary variable is a special case of the complex variable p. j is The frequency transfer function is written in the algebraic form of the Cartesian coordinates: W j P jq, [W j]; Q Jm [W j], P Re or in exponential form polar coordinates: W j W j A e jϕ [W j] A W j; ϕ rg Hodograph of the vector W j the graph described by the end of the vector when the frequency changes from about to is called the amplitude-phase characteristic of the AFC. The AFC shows how the amplitude ratios and the phase shift between the output and input signals change when the frequency of the input signal changes. 8. The dependences of the ratio of the amplitudes of the output and input signals A and the phase shift between the output and input signals ϕ on the frequency are called the amplitude-frequency response and phase-frequency response characteristics, respectively, Fig. 9. The AFC contains the same information about the object link as the frequency response and phase response combined. j A ϕ ϕ A Fig. 8. Fig. 9. 17 7 Basic properties of regulatory objects. Load The load is the amount of a substance or energy taken during operation from the regulatory object. Changing the load, as a rule, is the main disturbing effect in the regulatory system, because leads to an imbalance between the influx and drain of energy substance in the object, which causes a change in the controlled variable, for example, the liquid level in the tank Fig. Q pr H Q article Fig. In addition, a change in load leads to a change in the dynamic characteristics of the object. For example, in containers with perfect mixing, fig. the time constant is equal to the ratio of the volume of liquid stored in the tank to the load, i.e. the time constant of this object is inversely proportional to the load. Capacity Capacity is the amount of energy substance that an object can accumulate. Capacity characterizes the inertia of the regulatory object. Objects of regulation can be single and multi-capacitance. Multi-capacity objects consist of two or more capacities separated 18 8 transition resistance. The number of capacities determines the order of the differential equation of the object. For example, the container with liquid in fig. refers to single capacitance objects. An example of a three-capacity object is a shell-and-tube heat exchanger in Fig., In which the heated liquid receives heat through the walls of the tubes from the coolant. The first tank is the amount of heat in the heated fluid in the annulus. The second tank is the amount of heat in the coolant inside the tubes. The third tank is the amount of heat in the walls of the pipes, this tank is usually small compared to the others, and it is neglected. Self-alignment Self-alignment is the ability of an object to restore equilibrium between the influx and drain of an energy substance due to a change in the controlled variable due to internal negative feedback in the control object. For example, in a tank with a free drain fig. with an increase in the inflow, the level increases and due to this, the drain increases until the equilibrium between the inflow and the drain is restored. The larger the self-leveling value, the less the controlled variable deviates due to disturbances. Thus, self-leveling facilitates the operation of the automatic controller. Depending on the level of self-leveling, the objects of regulation can be divided into objects with positive, zero and negative self-leveling. From a dynamic point of view, objects with positive self-alignment are stable inertial links. Their transient characteristics end in steady state 19 9 the section in which the controlled variable comes to rest and the fig. Curve stops changing. 3 Fig. Quantitatively, the self-alignment value is characterized by the self-alignment coefficient ρ, which is the modulus of the reciprocal of the static transfer coefficient of the object: ρ K The self-alignment coefficient shows how much the input variable of the object should change in order for the output to change by one. Linear objects have constant self-alignment ρ cons, non-linear variables ρ Vr. Objects that do not have self-leveling objects with zero self-leveling include the so-called neutral or astatic objects, which represent integrating links from a dynamic point of view. Changes in the controlled variable in such objects can be arbitrarily large. An example of a neutral 20 of the object is a tank with forced discharge of rice. Here, with Qpr Qst, the level rises to overflow the tank or drops to zero. Q pr N Q article Fig. With equality between the inflow and the drain, such an object can be in equilibrium for any value of the controlled variable, therefore it is called neutral or astatic. The steady-state section of the transition characteristic of an astatic object represents a straight line, on which the adjustable variable changes with constant speed, the curve in Fig. The equation of the ideal integrating link K d, whence d / d K The parameter K a characterizing objects with zero self-alignment is called the reduced acceleration speed of the neutral object and it makes sense the rate of change of the controlled variable per unit of input exposure. There are objects in which under certain conditions an uncontrollable process arises. In these objects, the rate of change of the controlled variable in the transient tends to 21 self-growth curve 3 in Fig. Such objects are called objects with negative self-alignment. From a dynamic point of view, they are unstable links. For neutral and unstable objects ρ. Delay Delay is the period of time from the moment of disturbance application to the beginning of the change of the controlled variable. Distinguish between pure and capacitive retardation. Pure transport delay τ is the time that the flow of energy substance spends on traveling the distance from the point of perturbation to the point of measurement of the controlled variable in a single-capacitance object. An example of a link with pure delay is the belt feeder conveyor fig. 3. The time of pure delay is equal to the ratio of the length of the active section of the conveyor belt l to the linear speed of the belt V: τ l V Q n n V l Q П τ l nm Fig. 3. Fig. 4. 22 In multi-capacitance objects, several capacitances are connected in series, which causes a slowdown in the flow of energy substance from one container to another and leads to the appearance of capacitive delay. Figure 4 shows the transient characteristics of one n, two n, and multi-capacitance nm objects. With the number of capacities n\u003e in the transient response, the inflection point of P. appears. With increasing n, the initial portion of the transient response tends more and more to the abscissa axis, as a result of which a capacitive delay τ e is formed. There is a fundamental difference between pure and capacitive delays. With pure lag, the adjustable variable is zero throughout the entire lag time. With capacitive delay, it changes, although very little. In the time domain, the transport and capacitive delays appear approximately the same, and in the frequency domain the behavior of these links varies significantly. Real objects usually contain both types of delay, as a result of which the total delay τ is equal to their sum: τ τ τ e It is almost impossible to separate capacitive delay from pure on the experimental characteristic. Therefore, if the net delay is determined by the experimental acceleration curve, its value is always subjective, i.e. Depends on the researcher. Delay sharply worsens the quality of regulation in the ASR ... Methods of mathematical description of regulatory objects Methods of mathematical description of regulatory objects can be divided into analytical ones i.e. not requiring an experiment 23 3 at an industrial facility and experimental i.e. based on experiment results. Analytical methods are methods for obtaining mathematical models of objects, based on the analysis of the physicochemical processes occurring in the object, taking into account its design and characteristics of the processed substances. Advantages of analytical models of objects. No industrial experimentation is required at the facility. Therefore, these methods are suitable for finding models of objects at the stage of their design or when it is impossible to experimentally study the characteristics of regulatory objects. Analytical models include constructive characteristics of objects and indicators of the technological mode of their functioning. Therefore, such models can be used to select the optimal design of the apparatus and optimize its technological mode. 3. Analytical models can be used for such objects. At the same time, analytical models are rather complicated. In real objects, three types of processes can occur simultaneously: chemical transformations, heat and mass transfer. Simultaneous accounting of all these processes is a rather difficult task. Experimental methods for obtaining models include obtaining time or frequency characteristics as a result of an industrial experiment and their approximation, i.e. selection of an analytical relationship that describes the experimental data with the required accuracy. When taking the time characteristics, the object is in transition from one steady state to another. When removing the frequency characteristics of the object is introduced into the steady state harmonic oscillations. Therefore getting frequency 24 4 characteristics, in principle, allows you to get more representative information about the object, to a much lesser extent dependent on random disturbances acting on the object. But the experiment on taking the frequency characteristics is more time-consuming in comparison with the experiment on taking the time characteristics and requires special equipment. Therefore, the most affordable in real conditions is to obtain temporal characteristics. However, it should be noted that experimental models of objects can be used only for those objects and those conditions of their functioning for which the experiment was conducted. 3. Obtaining and approximating the temporal characteristics of regulatory objects Preparation and conduct of the experiment When developing an experimental design for taking the temporal characteristics of regulatory objects, issues related to measuring and recording the test effect and the controlled variable are solved. The design of the experiment is reduced to the choice of the type of test effect, the magnitude of its amplitude and the number of experiments. To obtain an acceleration curve, a step function is used as a test action. If a stepwise effect is unacceptable for the regulation object without self-leveling or a long-term deviation of the controlled variable from the nominal value is unacceptable, a rectangular pulse type action is used. The impulse response characteristic thus obtained in accordance with the principle of superposition for linear objects can be converted into an acceleration curve. 25 5 When choosing the amplitude of the test effect, a compromise is sought between the following conflicting requirements. On the one hand, the amplitude of the input action should be large enough to reliably highlight a useful signal against the background of measurement noise. On the other hand, too large deviations of the controlled variable can lead to violations of the operation mode of the facility, leading to a decrease in product quality or the emergence of an emergency mode. In addition, with large perturbations, the nonlinearity of the static characteristics of the object is affected. When determining the number of experiments, it is useful to take into account the following factors: linearity of the static characteristics of the object, the degree of noise of the characteristics, the magnitude of the load fluctuations, the non-stationary characteristics in time. Before the experiment, the object must be stabilized in the vicinity of the nominal mode of its operation. The experiment on taking the time characteristic continues until a new value of the controlled variable is established. When the object is noisy, the experimental characteristics are smoothed in time with high-frequency noise or in a multitude with low-frequency noise. Approximation of transient characteristics of regulatory objects. The approximation problem includes three stages. The choice of the approximating transfer function. The transient characteristics of objects with self-alignment and lumped parameters are approximated by a rational transfer function in the general case with a pure delay of the form: 26 6 W about K about b m n m n LL e LL For objects without self-alignment, in the denominator of the transfer function 7, the Laplace transform variable p sign of the integrating link is added by the factor. As practice shows, a satisfactory approximation accuracy is achieved using models for which n, 3, and n-m in the absence of an inflection point in the acceleration curve and n-m in its presence .. Determination of the coefficients of the approximating transfer function. See below 3. Estimation of approximation accuracy. To assess the accuracy of the approximation, it is necessary to construct the calculated characteristic and determine the maximum approximation error. The expressions for the transient characteristics corresponding to some approximating transfer functions are given in Table. When calculating on a computer in the expressions for the transient characteristics, go to the discrete time τ 7 i the sampling interval, and if model 7 has a pure delay, the argument for ii for i \u003e τ k Approximation of the transient characteristics of objects with self-leveling by an inertial link of the first order with delay a Graphic method tangent method The transfer function is sought in the form: 27 7 W To e τ 8 To determine τ and T to the transient response of Fig. 5, a tangent AB is drawn at the inflection point. With the inflection point there corresponds the maximum angle α between the tangent and the abscissa axis of the mouth B C mouth O τ α A D Line segment OA cut off by the tangent on the abscissa axis, is taken as the time of pure delay τ: τ OA The length of the tangent projection of the segment AB on the abscissa axis is taken as T: TAD Fig. 5. The transmission coefficient K is found as the ratio of the increments of the output and input quantities in the steady state: mouth K 9 mouth 28 8 Table. models Transfer function The roots of the characteristic equation The transition characteristic K e K, is the amplitude of the step action K α β ee К β α β α β α β 3 K α j ±, α α α rcg e К sin 4 b К α β ebeb К β α α β β α β α α β 5 b К α j ±, sin α α α α α b bcg ebb К α β γ 3 eee К γ β α γ β γ α γ αβ γ β α β αγ γ α β α βγ K α j ±, γ 3 ercg e γ α α γ α α γ α α α γ γ α α γ sin 3 3 b K α β γ 3 ebebeb K γ β α β γ α γ γ αβ γ β α β β αγ γ α β α α βγ 29 9 3 3 b К α j ±, γ 3 [e b b b rcg e b b К γ α γ α γ α α γ α γ α α α α γ γ α α α γ sin 30 b Interpolation method The acceleration curve is previously normalized from to by the formula ~; ~ Two points A and B are selected on the normalized curve in Fig. 6, the interpolation nodes through which the calculated curve should pass. ~ B ~ B ~ A A A B Fig. 6. The normalized transition characteristic of the link with transfer function 8 is τ ~ e. Writing down the expression for points A and B, we obtain a system of two equations with two unknowns: ~ ~ A B e e Aτ b τ Solving this system with respect to τ and Т, we obtain: 31 3 ~ ~ B ln AA ln B τ ln ~ ln ~ ABA τ B τ ln ~ ln ~ AB Approximation of the transient characteristics of control objects without self-alignment by an integrating link with a delay or a real integrating link The approximating transfer function is sought in the form: W K τ e 3 or W K 4 Parameters of models 3, 4 can be easily determined by drawing the asymptote of the aircraft to the steady-state part of the acceleration curve in Fig. 6 .: C A α B Fig. 6. To d / d mouth gα mouth OB OA mouth 5 τ OA for model 3 32 3 TOA for model 4 Approximation of the transient characteristics of control objects of the n-th order link Since the method considered below is designed to approximate the transition characteristics of objects without pure delay and self-alignment, it is necessary to first exclude from the acceleration curve the components corresponding to the links of pure delay and integrating, if those are available. To eliminate the component due to pure delay, it is necessary to reduce all abscissas of the acceleration curve by the value of the net delay τ i.e. move the origin to the right by τ. Moreover, in the transfer function of an object with a pure delay W about W e "about the Section AB of the transient response without delay Fig. 7 τ" corresponds to the transition function W about. B Y A C τ A Fig. 7. B α Fig. 8. - When approximating the transition characteristic of an object without self-alignment, it is presented in the form of the difference of two characteristics in Fig. 8: 33 33 For this, we draw the asymptote of the aircraft to the steady-state section of the characteristic and the OA beam parallel to the aircraft. Subtracting from, we find. - the transition characteristic of the integrating link with the transfer function W K The coefficient K is still found according to formula 5: K gα mouth the transition characteristic of the object with self-alignment. The transfer function W corresponds to it. Due to the linearity of the Laplace transform, the transfer function of the object corresponding to the characteristic is: W K W W W о Coefficients of the transfer function W can be found by the method described below. Reducing the expression for W about to a common denominator, we obtain the desired transfer function of the object without self-alignment. Determination of the transfer function coefficients of an object by the area method Simuyu The method is designed to determine the coefficients of a fractional rational transfer function of an object of the form m bm L W rev K ob n 6 L n 34 34 In practice, as noted, n, 3; m ,. The transfer coefficient of K, as always, is determined by the formula 9. To simplify the calculations, we normalize the acceleration curve of the object in the range - by the formula. For a normalized curve ~ with a single input action about K. We write the expression for the inverse of the transfer function 6 and expand it in an infinite series in powers of p: mn about SSS b WL 7 Reducing 7 to a common denominator and equating the coefficients for the same powers of p, we find: 8, SS b S bb SS b S bb SS bb S b L LLLLLLLLL in the particular case for m SSS 9 The numerator and denominator of the desired transfer function 6 contain nm of unknown coefficients, therefore, to find them, it is necessary that system 8 or, in the special case 9, contain the same equations. 35 35 So, system 8 or 9 allows determining the coefficients of the transfer function 6 through the expansion coefficients unknown so far S. To determine the latter, we consider the Laplace image of the deviation of the normalized transition characteristic from the steady-state value: L rev (~) L () L (~) [W p] From W we find (L [~]), or taking into account the definition of the Laplace transform 3: W about [~] ed Expanding the function e in a series in powers: e !! 3 3 L L, 3 !! we can represent the integral in the expression as the sum of the integrals: ~ e d ~ d d ~ d! ~! ~ d L! Substituting expansions 7 and in, multiplying the power series of and equating the coefficients in the resulting relation with the same powers of p, we obtain the following expressions for the coefficients S. 36 36 3 !! ~, 6 ~ ~, ~, ~ d i S S d S S S S d d S S d S S d S i i i LLLLLLLLLLLLLLL In practical calculations, the integrals 3 are determined by numerical methods. For example, when using the trapezoidal method, the expressions for the S coefficients take the form: 4.5 6 ~, 5 ~, 5 ~, 5 ~ 3 3 `N ii N ii N ii N ii S ii S i SSSS ii SSSS i SSS where is the interval discreteness of readings of the normalized transient response, N is the number of points of the transient response. From a geometric point of view, the coefficient S is the area bounded by the curve ~ and the line of steady-state values. S - is the area weighted with the weight function S, etc. Thus, 37 37 S coefficients are some weighted areas, which determines the name of the method. If in calculations the ith coefficient S turned out to be negative, it is necessary in model 6 to reduce n by one or increase m i.e. reduce the difference n-m .. Industrial controllers АСР [4] .. Functional diagram of an automatic regulator An automatic regulator is a set of elements used to regulate technological processes. The functional diagram of the closed ASR has the form Fig. 9 rear S x З СУ ФУ ИМ РО ОР ИЭ F Automatic regulator Fig. 9. The object of regulation 9 is indicated: Z - the controller of the adjustable variable is used to set its predetermined desired value; SU - a comparator; it generates an error signal; back FU - forming device, serves to form the regulation law in electrical controllers together with the MI; IM - actuator, actuates the RO; 38 38 RO - regulatory working body, serves to change the regulatory impact x; OR actually the object of regulation; IE measuring element, serves to measure the controlled variable y and convert it into a unified signal. The working body together with the drive, if any, is usually attributed to the object of regulation. The measuring element can be attributed to both the object and the regulator. In those cases when the measuring element is used to take the time characteristic, it is referred to the object. Thus, the automatic controller includes a variable speed controller, a comparator, a forming device and an actuator ... Classification of regulators by the energy consumption of an external source According to this criterion, the regulators are divided into direct and indirect controllers. In direct-acting controllers, the energy of the controlled environment itself is used to rearrange the working body. For example, in a direct-acting fluid level regulator, fluid energy, the level of which is regulated, is used to rearrange the working body. Regulators of direct action are simple, cheap, but do not provide high quality regulation. Their disadvantages are also the difficulty of implementing complex laws of regulation and obtaining great efforts to rearrange the working body. Indirect controllers use external source energy to rearrange the working body, which means 39 39 distinguish electric electronic, pneumatic, hydraulic, combined regulators. Electric regulators have a number of advantages. Their main drawback in the usual version is the inability to use in fire and explosive atmospheres. This lack of pneumatic regulators. The main advantage of hydraulic controllers is the increased power of the actuator with a relatively small size. Combined regulators allow you to combine the advantages of various types of regulators. For example, electro-pneumatic systems combine the advantages of electrical controllers with the ability to operate pneumatic actuators in fire and explosive atmospheres. In recent years, programmable controllers have found widespread use for the implementation of local automation systems. The choice of the type of controller is dictated by various considerations: the nature of the environment, working conditions, special requirements. 3. Classification of regulators according to the law of regulation Under the law of regulation is understood the equation of dynamics of the regulator. Five typical laws of regulation are known: proportional P, integral I, proportional-integral PI, proportionally-differential PD and proportionally-integral-differential PID. Proportional Static Regulators Equation of dynamics of the P-regulator K 5 40 4 where is the mismatch of the controlled variable, rear x is the regulatory action more precisely, the increment of the regulatory action is relative to the constant component, therefore it is more correct to write x - x instead of x in 5, but x is usually omitted, K is the transfer coefficient P of the controller. As we see from 5, the regulatory effect of the P regulator is proportional to the mismatch, i.e. The P controller is an inertialess link with the transfer function W K. Since the P controller does not introduce a negative phase shift of the PFC of the P controller into the system, an ASR with a P controller has ϕ good dynamic properties. The disadvantage of systems with a P controller is the presence of a static error. For a single controller, the magnitude of this error is determined from the controller equation: K When the P controller operates in the system of Fig. F To To about Fig .. the magnitude of the error from the disturbance F is 41 4 FK ЗСF F К о Коб К р where disturbance. К ЗCF - transfer coefficient of a closed system according to As you can see, the static error in a system with a P controller is inversely proportional to its transfer coefficient, the limit value of which is determined by the required value of the stability margin of a closed ASR. Proportional controllers are used in the automation of low-inertia control objects, when the value K can be selected errors. large enough to reduce static Integral astatic regulators Regulation law: K d, 6 i.e. the regulatory action in this case is proportional to the integral of the mismatch. The transfer coefficient of the I-regulator K d / d has the meaning of the rate of change of the regulatory effect per unit of mismatch. Transfer function: K W Frequency transfer function: 42 4 K K W j j e The advantage of a controller is a zero static error. From 6 it follows that this error is equal and vanishes in statics. d / d K At the same time, since the phase response and regulator ϕ π, a system with an AND regulator has very poor dynamic properties, because this regulator introduces a negative phase shift in phase π into the system. Integrated controllers can only be used in the automation of virtually inertia-free objects. ASR with an AND regulator and an object without self-alignment is structurally unstable, π j i.e. unstable at any regulator settings. Proportionally integrated controllers The PI control law can be written in two forms: K K d K d 7 T The regulatory action of the PI controller is the sum of P and I components with proportionality coefficients K and K. From a comparison of the two forms of writing the control law, we obtain: K , K T AND I 43 43 where T And the time of the isodrome. K \u003e\u003e The transfer function and the frequency transfer function: W W K j K K K, K e I K jrcg K From the last expression it is seen that in the low-frequency region at K PI the controller behaves like the And regulator. At large K frequencies K \u003e\u003e, i.e. The PI controller behaves like a P controller. This makes it possible for the PI controller to combine the advantages of both the controller in statics and the P controller in dynamics. The physical meaning of the isodrome time can be explained by the transient response of the PI controller of Fig. As can be seen from this figure, T And this is the doubling time of the P component of the regulatory effect of the PI regulator, or, what is the same, the time by which the regulatory effect of the PI regulator is ahead of the regulatory effect of the And regulator. The value of T And characterizes the speed of integration. The greater the T AND, the lower the integration speed. At T AND PI, the controller turns into a P controller. K x PI I K P I R .. 44 44 So, an ASR with a PI controller has a zero static error due to the presence of an AND component in the regulation law. This is true for all regulators with an AND component. As can be seen from the phase response of the PI regulator in Fig., In the operating region 3 ϕ slave π Fig. .. of frequencies the slave of the PI regulator introduces a negative phase shift of approximately -3 into the system. This is significantly less than the And regulator, but more than the P regulator. Therefore, the dynamic properties of ASR with a PI controller are much better than with an I-controller, but worse than with a P controller. Proportional - differential regulators Law of regulation of an ideal PD regulator: d d К К К П, 8 d d where К, К - proportionality coefficients of П- and Д- components of the regulation law. T P is the time of the advance. Transfer and frequency transfer functions: W W K K j K K K e P, K jrcg K 45 45 From the last expression it can be seen that at low frequencies the PD regulator behaves like a P regulator, and at high frequencies like a differentiator. Since the ideal differentiating link is physically unrealizable, real inertial differentiating link is used in real PD controllers. The transfer function of such a controller has the form W K K The smaller the time constant T, the closer the characteristics of the ideal and real controllers. In statics, the transfer function of the PD controller coincides with the transfer function of the P-controller, therefore, a static error is also inherent in the ACP with the PD controller. As can be seen from the phase response of Fig. 3, ϕ π is an ideal -3 real slave. 3. in the field of operating frequencies, the PD controller introduces a positive phase shift into the system, increasing its stability margin. Therefore, ASR with PD controller has the best dynamic properties. For the same reason, the value of K can be chosen more than in the case of P 46 46 regulators. Therefore, the static error in ACP with PD controller is less than in a system with P controller. Nevertheless, PD regulators are practically not used, because in the presence of high-frequency noise superimposed on the low-frequency useful signal, the differentiation operation sharply worsens the signal-to-noise ratio, as a result of which the amplitude of the noise derivative can significantly exceed the amplitude of the derivative of the useful signal. Regarding the physical meaning of the pre-start time, we can say that T P is the time at which the regulatory action of the PD regulator is ahead of the regulatory effect of the P regulator with a linear input action Fig. 4 x PD P D p Fig. 4. Proportional - integral differential controllers. Equation of dynamics: d d K K d K K d P d 9 d AND Transfer functions of ideal and real PID controllers: 47 47 WW K K K K K K I P, Frequency transfer function of an ideal PID controller: W j K K K e K K jrcg K Systems with PID controllers combine zero static error with good dynamics, as it can be seen from the PFC PID controller .5 in the field of operating frequencies, the PID controller is the same as ϕ π ideal slave real π Fig. 5. and P regulator, does not introduce a negative phase shift into the system. To increase the noise immunity of the PID controller, in practice, the ratio of the lead time / time of the isodrome is limited from above by the inequality / П И<,5, 3 поэтому помехоустойчивость ПИД регулятора выше, чем ПД регулятора. При выборе закона регулирования учитывают следующие соображения. 48 48 If a static error is unacceptable, the controller must contain an AND component. In order of deterioration of dynamic properties, the control laws are arranged in the following order: PD, PID, P, PI, I. Regulators with a D component have poor noise immunity. For this reason, PD regulators are practically not used, and PI regulators are used with a limit of 3. The laws of regulation are most widely used in PI and PID. 3. Calculation of regulator settings in linear continuous systems [4] 3 .. Quality of regulation We will determine the quality of regulation by a set of indicators characterizing the shape of the transition process curve in closed ASR fig. 6. Key indicators of quality. The maximum dynamic deviation of the dyne is the largest deviation of the controlled variable from its given value in the transition process. Indicator dyn m ass. In a stable ASR, the first deviation is maximum. dyne characterizes the dynamic accuracy of regulation .. Residual deviation residual non-uniformity ct - absolute static error of regulation, defined as the difference between the steady-state value of the controlled variable and its predetermined value: 49 49 ct set back Indicator in static mode. m c characterizes the accuracy of regulation in the setpoint 3 δ st Fig. Attenuation degree ψ is the ratio of the difference of two adjacent oscillation amplitudes directed on one side of the steady-state line to the largest of them 3 3 ψ;< ψ < 3 Показатель ψ характеризует колебательность переходных процессов и запас устойчивости системы. Значение ψ соответствует незатухающим колебаниям на границе устойчивости системы. При ψ имеем апериодический переходной процесс. 4. Время регулирования промежуток времени от момента нанесения возмущающего воздействия до момента, начиная с которого отклонение регулируемой переменной от установившегося значения становится и остается меньше наперёд заданного значения δ. Показатель характеризует быстродействие системы. 50 5 The considered quality indicators belong to the group of direct indicators, i.e. indicators to assess quality directly from the transition curve, to obtain which it is necessary to solve the differential equation of the system. In addition to direct ones, there are indirect criteria that make it possible to judge the quality of regulation without having at its disposal a transition curve. Such criteria, in particular, include integral quality criteria representing time integrals from the deviation of the controlled variable from the steady-state value, or from some function of this deviation and its mouth derivatives. The simplest is the linear integral criterion defined by the relation: I lin d mouth From a geometric point of view, the criterion I lin is the area between the curve and the line of mouth. The value of I lin depends on all quality indicators, except for art. Moreover, with a decrease in dyne, i.e. by improving the quality of regulation, the value of I lin decreases, and with an increase in the oscillation of the transient process, I lin also decreases, although the quality of regulation deteriorates. Thus, a decrease in I lin indicates an improvement in the quality of regulation only for well-damped transients. Therefore, criterion I lin is applicable for aperiodic or weakly oscillatory processes. For such processes, the controller settings can be considered the best for which the value of I lin reaches a minimum. Criterion I lin can be calculated through the coefficients of the differential equation of a closed ASR. 51 5 It can be shown that for the regulating object with self-alignment and PI regulator I lin, 3 K i.e. the minimum of I lin is achieved at the maximum of the integral component of the regulatory action, or, what is the same, the best quality of the transition process is achieved at the maximum of K. For vibrational transients, other integral criteria are used, for example, I mode set d, but this criterion cannot be calculated using the differential coefficients equations. The quadratic integral criterion I quarter: I quarter mouth d 3 is deprived of this drawback. Typical optimal processes The requirements for quality indicators are contradictory. For example, a decrease in dynamic error is achieved by increasing the oscillation and duration of transients. On the contrary, processes with a short regulation time can be obtained by increasing the dynamic error. Therefore, a compromise decision has to be made regarding the desired values \u200b\u200bof quality indicators in a closed ASR. Transients with certain quality indicators are recommended when calculating ASR as typical. In the extended frequency method discussed below 52 5 characteristics the main quality indicator is the degree of attenuation ψ, i.e. oscillation of the transition process, since this indicator characterizes the safety margin of the ASR. Processes for which ψ, 75.9, i.e. the third amplitude is 4 times less than the first. In those cases when the task is to select the controller settings that minimize any quality indicator, the corresponding transient process, as well as the values \u200b\u200bof the controller settings, are called optimal in the sense of the specified criterion. For example, in the method of extended frequency characteristics, the task is to select the controller settings so that in addition to the given transient oscillation, the minimum value of the criterion I lin is ensured. Such a process is optimal in the sense of criterion I lin Simplified formulas for calculating the settings of regulators simplified formulas are given for determining the settings of regulators providing a given transient oscillation. The formulas are obtained from the results of simulation of ASR. Static objects are represented by a model of an inertial link with a net delay of 8, astatic objects by a model of an integrating link with a delay of 3 Lecture 3 Mathematical description of control systems In control theory, when analyzing and synthesizing control systems, they deal with their mathematical model. The mathematical model of self-propelled guns is an equation Test 1 in the discipline "Management of technical systems" Option 1 1. What is the functional purpose of the sensor in the control system? 1) adjust the parameters of the process; 2) suppress noise The equations of dynamics and statics. Linearization At a certain stage of development and research of the automatic control system, its mathematical description is obtained, a description of the processes occurring in the system METHODOLOGICAL INSTRUCTIONS for homework on the course of the TCB Study of a nonlinear system of automatic regulation DEFINITION OF THE BACKGROUND Initial data for homework are given Fundamentals of Control Theory Mokrova Natalia Vladislavovna Dynamic characteristics of objects of regulation 1. Time characteristics. Acceleration curve. Pulse transition function. 2. The solution of differential FSBEI HPE “Omsk State Technical University” SECTION II CONTINUOUS LINEAR AUTOMATIC CONTROL SYSTEMS Lecture 4. DYNAMIC LINKS. GENERAL CONCEPTS, TEMPORARY CHARACTERISTICS AND FREQUENCY Practical class TRANSMISSION FUNCTION FREQUENCY CHARACTERISTICS Goals and objectives of the work As a result of mastering the topic, the student should be able to obtain the operator equation using the given differential equation; Lecture 5 Automatic controllers in control systems and their adjustment Automatic controllers with typical relay control algorithms, proportional (P), proportional-integral (PI), Calculation of the dynamic characteristics of linear self-propelled guns Determine the weight function g (t) and the transition function h (t) of a linear self-propelled guns, consisting of a series connection of an aperiodic and ideal integrating Lecture 3. Mathematical description of control objects 1. Control objects In the chemical industry, various processes in the apparatus of technological plants are referred to typical control objects. For Lecture 8 33 ONE-DIMENSIONAL STATIONARY SYSTEMS APPLICATION OF FOURIER TRANSFORM 33 Description of signals and systems Description of signals The Fourier transform is used to describe deterministic signals: it Federal State Budgetary Institution of Higher Professional Education KAZAN NATIONAL RESEARCH TECHNICAL UNIVERSITY A.N. TUPOLEV-KAI Department of Television Lecture 4 Typical dynamic links Automatic control systems are conveniently represented as a combination of elements, each of which is described by an algebraic or differential equation LABORATORY WORK 5 TYPICAL LINKS OF AUTOMATIC SYSTEMS Purpose of the study of the dynamic properties of the typical links of automatic control systems GENERAL INFORMATION In the theory of automatic control Lecture 11,12 Section 2: MATHEMATICAL MODELS OF LINEAR CONTROL SYSTEMS Topic 2.4: TYPICAL DYNAMIC SYSTEM LINKS 1. Typical system links: characteristics and equations; physical models. Lecture Plan: UDC: 62-529 AUTOMATIC REGULATION SYSTEMS WITH SEQUENTIAL CORRECTION Vitaly Anatolyevich Chigarev Senior Lecturer, Belarusian National Technical University, [email protected] Topic 8 LINEAR DISCRETE SYSTEMS The concept of a discrete system. Methods for describing linear discrete systems: difference equation, transfer function, impulse response, frequency transfer function. Continuously Determined Models Continuously determined models are used to analyze and design dynamic systems with continuous time, the functioning of which is described MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION Federal State Autonomous Educational Institution of Higher Education "NATIONAL RESEARCH TOMSK POLYTECHNICAL UNIVERSITY" Topic 3 HARMONIC ANALYSIS OF NON-PERIODIC SIGNALS Direct and inverse Fourier transforms Spectral characteristic of a signal Amplitude-frequency and phase-frequency spectra Spectral characteristics Fall semester of the academic year. Topic 3 HARMONIC ANALYSIS OF NON-PERIODIC SIGNALS Forward and reverse Fourier transforms Spectral characteristic of the signal Amplitude-frequency and phase-frequency spectra 4. TRANSITIONAL CHARACTERISTIC OF MEMBRANE 4.1 Temporal characteristics of a dynamic system In order to evaluate the dynamic properties of a system and individual links, it is customary to study their response to typical input influences, 64 Lecture 6 OPERATIVE METHOD FOR ANALYSIS OF ELECTRIC CIRCUITS Plan Laplace transform Properties of the Laplace transform 3 Operator method for analyzing electrical circuits 4 Definition of the original according to the well-known Workshop 4. ANALYSIS OF SELF-OSCILLATIONS BY THE HARMONIC LINEARIZATION METHOD STATEMENT OF THE PROBLEM A closed system with one nonlinear element is considered. g F (z W (s x Fig. We study the free movement of the system, Federal Agency for Education State Educational Institution of Higher Professional Education Vladimir State University Department of Plastic Processing Technology UDC Fulfilled: Accepted: Umarov D. 1-14 IKSUTP Abdurakhmanova M.I. ACS sustainability analysis The practical suitability of regulatory systems is determined by their stability and acceptable regulatory quality. Under 54 Lecture 5 FOURIER TRANSFORM AND THE SPECTRAL METHOD OF ANALYSIS OF ELECTRIC CHAINS Plan Spectra of aperiodic functions and Fourier transform Some properties of the Fourier transform 3 Spectral method 1. Automatic regulation of the water level in the steam generator The regulation of power in each of the steam generators (GHGs) is reduced to maintaining a material balance between the removal of steam, the purge and the supply Mathematical schemes: D-schemes Continuously determined models are used for analysis and design of dynamic systems with continuous time, the process of functioning of which is described by deterministic 4.1 Control questions for self-control 1 SECTION “Linear continuous models and characteristics of control systems” 1 What does control theory study? 2 Define the concepts of management and the object of management. Lecture 5. 8.3. ANALYSIS OF SELF-OSCILLATIONS BY THE HARMONIC LINEARIZATION METHOD 8.3 .. Statement of the problem A closed system with one nonlinear element is considered. F W s x Fig. Free movement is being studied Institute Direction of training AVTI 70404 Management in technical systems Bank of tasks in the special part of the entrance test to the master's degree Examination ticket 6 (5 points) Topic Theme 8 DISCRETE SPGS Lecture 7 General concepts and definitions of the theory of discrete SPGs. Basic information about the mathematical apparatus of the theory of linear discrete stationary systems. Mathematical description of processes Lecture 4 Frequency characteristics of ACS systems Frequency characteristics of ACS characterize the response of systems to a sinusoidal input in steady state. Frequency characteristics include: STABILITY THEORY OF LINEAR SYSTEMS 1. Basic terms and definitions Any ACS is always affected by external perturbations that may interfere with its normal operation. A properly designed self-propelled gun must Lecture 1 General information about control systems The subject "Theory of automatic control" introduces you to the basic principles of building automatic control systems, methods of formalized description Guidelines for laboratory work on the course "Theory of automatic control" Module "Linear automatic systems" Laboratory work Determination of the parameters of typical dynamic links Robotics RAR1300 Sergei Pavlov TTÜ Virumaa Kolledž Drive control Control of the movement of a working machine or mechanism means controlling the position, speed and acceleration of a system that TAU Practical exercises Tasks for the control work and methodological instructions for its implementation Practical lesson AFC, LAH, transient and weight characteristics of typical dynamic links Most Lecture 6 CHAINS OF PERIODIC NONSINOSOIDAL CURRENT Plan Trigonometric form of the Fourier series Fourier series in complex form Complex frequency spectrum 3 Power in non-sinusoidal current circuits Coefficients, SEMINAR Basic concepts. Drawing up (derivation) of a differential equation. The concept of solving a differential equation. Solution by the method of separable variables. Solution of a linear differential equation Fundamentals of circuitry BASES OF SCHEME TECHNOLOGY ... 1 1. BASIC PROVISIONS ... 1 2. AMPLIFICATION OF WEAK SIGNALS ... 6 3. STRENGTHENING OF STRONG SIGNALS ... 14 4. BASES OF MICROSHEMOTICS OF AMPLIFIERS ... 18 1. General provisions Fundamentals of Control Theory Mokrova Nataliya Vladislavovna Lecture 7 Non-linear systems of automatic control Features of non-linear systems. Typical nonlinearities of automatic control systems. Lecture 4 Frequency functions and characteristics 4 The concept of frequency functions and characteristics An important role in the study of linear stationary systems is played by frequency characteristics They are 70 Lecture 7 OPERATOR FUNCTIONS OF CHAINS Plan Operator input and transfer functions Poles and zeros of chain functions 3 Conclusions Operator input and transfer functions The operator is called a chain function I Study of the dynamics of typical automation links 1 Ideal amplifier (aperiodic link of the zero order - AP-0) and a real amplifier (aperiodic link of the first order - AP-1) Purpose of work: to research Adjustment and adjustment of automatic regulators. 1.Special cycle 1.1. Introduction The main stages and dates in the development of automatic regulation. Until 1600 Float control system Laboratory work 1 1 DYNAMIC CHARACTERISTICS OF TYPICAL LINKS 1. Purpose of work To investigate the dynamic characteristics of typical links of automatic control systems (ACS), as well as to get acquainted Ministry of Education of the Republic of Belarus Education Institution Belarusian State University of Informatics and Radioelectronics Department of Radio Engineering Systems Report on laboratory work “RESEARCH 1. GENERAL INFORMATION ABOUT ANALOGUE ELECTRONIC DEVICES (AEU). PARAMETERS AND CHARACTERISTICS OF AEU 1. 1. General information about analog electronic devices (AEU), principles of their construction Analog signals Laboratory work 1 1 TYPICAL ACCUED LINES 1. Purpose of work To investigate the dynamic characteristics of typical links of automatic control systems (ACS), as well as get acquainted with the basic rules of structural Topic 5 LINEAR STATIONARY SYSTEMS Properties of linear stationary systems: linearity, stationarity, physical realizability Differential equation Transfer function Frequency transfer function Lecture 6 Transformation of mathematical models of systems. Transfer functions. Models in the form of signal graphs. To study the properties of complex physical systems and learn how to manage them, you must have UDC 681.52 ALGORITHMS FOR SOLVING THE PROBLEM OF IDENTIFICATION N.V. Plotnikova, N.S. Kalistratova, O.N. Malyavkin Recently, in connection with the presentation of increasingly higher requirements for management processes in various Topic 2. Basic concepts and definitions in the theory and practice of automatic regulation of life support parameters (2 hours) In order to ensure normal operation of the regulatory object (OR) 54 Lecture 5 FOURIER TRANSFORM AND THE SPECTRAL METHOD OF ANALYSIS OF ELECTRIC CIRCUITS Plan Spectra of aperiodic functions and Fourier transform 2 Some properties of the Fourier transform 3 Spectral method Zaitsev GF Theory of automatic control and regulation Second edition, revised and supplemented Approved by the Ministry of Higher and Secondary Special Education of the USSR as a teaching aid 1.1. Methods for the analysis of the nonlinear inertial properties of analog devices In the literature on the analysis of the nonlinear inertial properties of analog devices, several The set of unit operations forms specific technological processes. In the general case, the technological process is implemented through technological operations that are performed in parallel, sequentially or in combination, when the beginning of the subsequent operation is shifted relative to the beginning of the previous one. Process control is an organizational and technical task, and they solve it today by creating automatic or automated process control systems. Management purpose technological process can be: stabilization of a certain physical quantity, its change according to a given program, or, in more complex cases, optimization of a certain generalizing criterion, the greatest productivity of the process, the lowest cost of the product, etc. Typical technological parameters subject to control and regulation include flow, level, pressure, temperature and a number of quality indicators. Closed systems use current information on output quantities, determine the deviation ε ( t) controlled value Y (t) from its given value Y (o) and take actions to reduce or completely eliminate ε (t). The simplest example of a closed system, called the deviation control system, is the stabilization system for the water level in the tank shown in Figure 1. The system consists of a measuring transducer (sensor) 2 levels, a control device 1 (regulator) and an actuator 3, controlling the position of the regulatory body (valve) 5.
Fig. 1. Functional diagram of the automatic control system: 1 - regulator, 2 - level measuring transducer, 3 - actuator, 5 - regulatory body. Flow control Flow control systems are characterized by low inertia and frequent pulsation of the parameter. Typically, flow control is the throttling of the flow of a substance using a valve or gate, a change in the pressure in the pipeline due to a change in the speed of the pump drive or the degree of bypassing (removal of part of the flow through additional channels). The principles for the implementation of flow controllers for liquid and gaseous media are shown in Figure 2, a, bulk materials - in Figure 2, b.
Fig. 2. Flow control schemes: a - liquid and gaseous media, b - bulk materials, c - media ratios. In the practice of automation of technological processes, there are cases when stabilization of the ratio of the costs of two or more media is required. In the circuit shown in Figure 2, c, the flow to G1 is the lead, and the flow G2 \u003d γ G is the slave, where γ is the coefficient of the flow ratio, which is established during the static adjustment of the controller. When the master stream G1 changes, the controller FF proportionally changes the slave stream G2. The choice of regulation law depends on the required quality of stabilization parameter. Level control Level control systems have the same features as flow control systems. In general, the level behavior is described by the differential equation D (dl / dt) \u003d G in - G out + G arr. where S is the horizontal sectional area of \u200b\u200bthe tank, L is the level, Gin, Gout is the flow rate of the medium at the inlet and outlet, G arr is the amount of medium increasing or decreasing in the tank (it can be 0) per unit time t. The constancy of the level indicates the equality of the amounts of fluid supplied and consumed. This condition can be provided by influencing the supply (Fig. 3, a) or the flow rate (Fig. 3, b) of the liquid. In the version of the regulator shown in Figure 3, c, the results of measurements of the flow and fluid flow are used to stabilize the parameter. The liquid level impulse is corrective, it eliminates the accumulation of errors due to the inevitable errors that occur when the flow and flow rate change. The choice of the regulation law also depends on the required quality of the stabilization parameter. In this case, it is possible to use not only proportional, but also positional regulators.
Fig. 3. Schemes of level control systems: a - with impact on the flow, b and c - with impact on the flow rate of the medium. Pressure regulation The constancy of pressure, as well as the constancy of the level, testifies to the material balance of the object. In the General case, the change in pressure is described by the equation: V (dp / dt) \u003d G in - G out + G arr. where V is the volume of the apparatus, p is the pressure. Pressure control methods are similar to level control methods. Temperature control Temperature is an indicator of the thermodynamic state of the system. The dynamic characteristics of the temperature control system depend on the physicochemical parameters of the process and the design of the apparatus. A feature of such a system is the significant inertia of the object and often the measuring transducer. The principles for the implementation of temperature controllers are similar to the principles for the implementation of level controllers (Fig. 2), taking into account the control of energy consumption in the facility. The choice of the regulation law depends on the inertia of the object: the larger it is, the more complicated the regulation law. The time constant of the measuring transducer can be reduced by increasing the velocity of the coolant, reducing the wall thickness of the protective cover (sleeve), etc. Regulation of the composition and quality of the product When adjusting the composition or quality of a product, it is possible that a parameter (for example, grain moisture) is measured discretely. In this situation, loss of information and a decrease in the accuracy of the dynamic regulatory process are inevitable. The recommended scheme of the regulator stabilizing some intermediate parameter Y (t), the value of which depends on the main adjustable parameter - the product quality indicator Y (ti), is shown in Figure 4.
Fig. 4. Scheme of the product quality control system: 1 - object, 2 - quality analyzer, 3 - extrapolation filter, 4 - computing device, 5 - regulator. Computing device 4, using a mathematical model of the relationship between the parameters Y (t) and Y (ti), continuously evaluates the quality indicator. The extrapolation filter 3 provides an estimated product quality parameter Y (ti) in the intervals between two measurements. On universal machines, process and machine parameters are controlled by the machine tool. He also makes decisions on the restructuring of equipment, equipment shutdown, coolant supply, etc. Maintaining the operating parameters of the GPM equipment (flexible production module) or automatic line is carried out management system (Fig. 12.1), which includes means of monitoring and diagnostics, which allows using GPM to refuse personnel directly involved in the technological process. Two sources of information are used in the GPM control system: a program for monitoring deviations from the normal operation of the GPM and information received from diagnostic devices, for example, feedback sensors, which measure the motion parameters (speed, coordinates) of the machine’s working bodies and its auxiliary mechanisms or automation devices. Fig. 12.1. Additional tools designed to perform the functions of the operator are integrated into a system that includes instrumentation and diagnostic devices and devices (with sensors for determining the magnitude of the monitored parameters), devices for collecting and initial processing of information and decision-making. In the case of replacing the operator, the system should: monitor the operation of the PM mechanisms, the progress of the working process, the quality of finished products, identify deviations from normal gPM functioning, including those that have not yet led to failures and failures, but which in the future may become their cause; record crashes and failures; to formulate the decisions necessary for the automatic continuation of the work of the GPM after a temporary stop for one reason or another; if necessary, interrupt the work of the PMU, call the installer and give him information about the reason for the deviation from normal functioning. The system for maintaining the health of the machine consists of several subsystems that work together or independently, depending on the design decisions or production conditions. These include a subsystem for monitoring the state of the cutting tool, a quality control subsystem, a subsystem for monitoring the functioning of machine tools and a subsystem for diagnosing mechanisms. Devices subsystems for monitoring the state of the cutting tool can carry out periodic or current control (Fig. 12.2, 12.3). A small axial tool (drills, taps, end mills with a diameter of up to 6-8 mm), as well as another tool, if current monitoring of its condition is impossible or impractical, is subjected to periodic control. To implement this procedure, a command to stop the machine should be given. The control device can be located in the working area of \u200b\u200bthe machine, on the node that carries the tool, in the tool magazine. The measurement method is usually direct, using inductive, electromechanical or photoelectric sensors. In fig. 12.2 is a diagram for monitoring the status of tool 2 on a multi-purpose machine 6. After processing the workpiece 1 and removing the tool with a drill, the probe 3 comes into contact. When the tool breaks, the probe position changes, as a result of which the lever 4 rotates and ceases to act on the contact sensor (limit switch) 5. At the signal of the latter, the control system gives the command to stop processing and replace the tool with an understudy or call the installer. As a sensor, a BVK type sensor or a Hall sensor can be used, which significantly increases its service life and uptime. To monitor the condition cutting tool on the lathe use the method of measuring the coordinates of the tip of the cutter. After of the next pass, the cutter moves to the control position, and in the event that there is no electrical contact between the tip of the cutter and a special contact plate, a signal is sent to interrupt the processing process, with the subsequent replacement of the tool or calling the installer. head; 3- tool; 4 - machine spindle Fig. 12.2. Control scheme of a cutting tool on a multi-purpose machine Fig. 12.3. Placement of the measuring head on a multi-purpose machine: 1-table; 2-measuring For control tool in the shop of the multipurpose machine, they use television cameras based on CCD arrays, which, with satisfactory image quality, can significantly reduce the cost of equipment. The image of the instrument is projected onto the screen, and the electronic system sequentially “reads” the image and transfers it to the computer's memory. Due to the low quality of the image, special mathematical methods are used to restore it. To detect a breakdown, the reference image recorded in the computer’s memory after installing a new tool is compared with the image of the same tool, but already working. The time required to transfer the image to the computer's memory is quite small, which allows measurement without stopping. Regardless of the size of the instrument, the camera is always in the same position. Periodic - monitoring is carried out and if necessary, enter correction in the control program in case of replacement of a worn or broken tool with an understudy. For this, by means of a measuring head with a touch sensor on turning machines measure the incidence of cutters, on multi-purpose (see. Fig. 12.3) - the length and diameter of the tool. The measuring head occupies a certain position in the working area of \u200b\u200bthe machine: on the multi-purpose table or on the headstock of the lathe. Such measurements allow you to “snap” the tool to the coordinate system of the machine, to obtain information about the presence of the tool in the spindle, to control its wear and integrity. Subject to current monitoring axial tools with a diameter greater than 8... 12 mm and cutters and milling cutters various kind. Control is carried out during the cutting process; its purpose is to prevent emergencies arising from a sudden breakdown of the tool. The current control method is mainly indirect (in terms of torque, current value of the main drive motor, load, acceleration, etc.). So, when the tool is blunted, the cutting force increases, and therefore, the load (torque) on the motor and the current flowing through its windings. The sensitivity of a torque sensor operating according to this principle depends on the type of engine, its power and the ratio of the kinematic chain between the engine and the spindle assembly. Before each cutting cycle, the idle load should be measured and stored. Measuring axial load on the machine spindle with strain gauge The screw built into the support allows you to monitor the wear of the tool, as well as the change in its mode of operation during processing of a batch of workpieces (for example, a change of 0.2 ... 0.3 mm is recorded on a lathe). The signal of such a sensor is practically free of interference. The sensor is low inertia, i.e. can register rapidly changing loads caused, for example, by uneven rotation of the spindle within one revolution. To measure the load experienced by turrets, spindle boxes and spindle units, strain gauges made in the form of strain bearings are built into them. The rotation of each ball of the bearing under the corresponding load causes local deformation of the outer ring, perceived by the strain gauges located in the groove on the outer surface of the ring. When processing the output signal of the sensor, one should take into account its ripple, the frequency of which is directly related to the spindle speed. To measure the load acting on various nodes, widely used overhead piezosensors (Fig. 12.4). Their sensitivity is higher than that of thermistors, and the bandwidth allows you to record fairly quick changes in the load acting on the tool. Design solutions implemented using such sensors are different. For example, they are embedded in a slab Fig. 12.4. Piezoelectric sensors for measuring cutting force: and measurement concept; b - its constructive implementation; (1 - elastic element; 2 - piezoelectric transducer; 3 - machine part; 4 - contact surfaces, / - measuring base of the sensor; R, - tensile-compression force; R, - clamping force under the turret of a lathe. For creating the preload the piezosensor should protrude above the surface by 10 ... 15 microns. Tool wear can be determined by the magnitude of the acceleration of the elastic wave, which extends from the cutting zone to the sensor installation site (1accelerometer) fixing vibroacoustic emission. If the tool rotates, the sensor set on the table of the machine; if the tool is stationary, and the workpiece rotates - on the tool holder or on the turret body. When using such sensors necessary for tools each type to pre-determine the frequency range, in which to the greatest extent manifests the connection of parameters vibroacoustic emission with wear or breakage of the instrument. The number of joints between the workpiece (or tool) and the sensor should be minimized, since they have a deforming effect (weaken the vibration), which makes measurement difficult. Tool runtime is measured a timer cutting and cutting time - force sensor or acceleration (the moments of the beginning and end of the cutting process are fixed), the magnitude of the cutting forces is pressure sensors in hydrostatic spindle bearings or magnetoelastic sensors measuring cutting torque, EMF - millivoltmeter electrical resistance of the contact of the workpiece with the tool - ohmmeter. Keep in mind that the reliability of automatic monitoring of the state of the cutting tool is relatively small. The reasons may be microcracks in the cutting part, heterogeneity and local fluctuations in the hardness of both the processed and the tool material and other factors that cannot be determined by automatic means. Therefore recommended double controltool life resource for its timely replacement and the real state of the tool according to one of the indirect parameters (current control). When designing equipment, the sensors used to control the instrument are not developed. The designer selects a commercially available or orders a special sensor, the characteristics of which correspond to the task, and embeds it in the corresponding area of \u200b\u200bthe machine. Various devices used in the subsystem for monitoring the state of the cutting tool are described in the literature. One of these devices is the Monitor system used in the GPM. Monitoring system with a contact indicator (see. Fig. 12.5) is based on information received from the feed drive of the machine and sensors that record the movement of the table and spindle assembly. Three data arrays are entered into Monitor: 1) constants that determine the device setting on a particular machine, type of control and signal level from the sensor (for example, current); 2) tool profiles containing constant data on the characteristics of specific tools; 3) a control program drawn up for each workpiece being processed. Data is entered using the keyboard; To display information, use the display screen or digital display. Fig. 12.5. Monitoring scheme with contact indicator: 1 - contact indicator; 2 - blank (part); 3 - control panel; 4 - information input device; 5 - terminals; 6 - head control computer; 7 - counter; 8 - pulse rulers TO quality control subsystem devices (Fig. 12.6) include active control devices (PAC) used in mass and large-scale production, and touch sensors used in mass production. If necessary automatic control sizes, shapes and the accuracy of installation of the workpiece and (or) the machined part on different Fig. 12.6. Typical control schemes for processing accuracy when using PAK (o) and auto-adjusting ( 6)
stages of processing using PAK, which can be located both in the working area of \u200b\u200bthe machine (Fig. 12.6, and), and with automatic cyclic control. Moreover, two information flows are organized in the machine control system. The first provides the processing process for a given program, the second is used to adjust the level of settings. The operator also participates in the management of the processing process, his task is to adjust the level of tuning of machines and means of active control. In the second flow of information, there are two control loops: the loop / refers to the automatic control system by means of a PAK or auto-adjuster (Fig. 12.6, b), contour II - to the system of manual adjustment of the processing process using conventional measuring instrument. The diagrams are conventionally marked: TO - technological operation; IO - the executive body of the machine; MP - machine sub-mechanism; AND for roughness treated For dimensional controlworkpieces and (or) parts (and in some cases for a counter-surface) on CNC and GPM machines serve as measuring heads (IG) (sometimes called contact indicators). The IG (Fig. 12.7), consisting of a probe complete with an electronic unit and a wireless signal transmission device (usually on infrared rays), is located in the tool store, from where the manipulator moves it to the spindle (on boring-milling and boring machines) or turret head (on lathes). Fig. 12.7. Measuring head: 1- probe tip; 2 - probe; 3 - gear mechanism; 4 - the mechanism of balancing the probe; 5 - electrical contact; 6 - block driver of the touch signal; 7 - signal sent to the electronic unit or to the transmitter With relative movement of the probe tip and the controlled surface, they touch. The probe deviates from its original position, the electrical contact inside the IG opens, and the touch signal generated a special circuit enters through the electronic unit in the CNC, where the data obtained are compared with the set values \u200b\u200bof the corresponding parameter. Similar IGs are used to control the stocks and basing of the workpiece, for the intermediate control of workpieces on the machine during processing and the output control of the machined part on the machine. In this case, in order to determine the distance between two planes, the coordinates of three points on each of them are measured and their difference is calculated. To determine the position of the center of the hole, the coordinates of the three points in the radial section are measured and then the coordinates of the center of the circle passing through these three points are calculated (all these procedures are carried out automatically. When designing processing equipment, PAK and IG are usually not designed; special design organizations are involved in their development. The designer-developer of equipment integrates a commercially available or special device into the equipment. However, he must take care of developing algorithms for the joint functioning of the machine and the control device (measurement, calculations, decision-making recommendations). The stability of the processing process on modern machine tools with programmed control allows us not to integrate measuring devices into them, but to use a coordinate measuring machine (CMM) installed in the workshop for periodically monitoring the quality of processing. In this case, the machine operator or the installer sets up the machined part on the CMM, measures the parameters to be monitored and, depending on the results, sends the part for additional processing or the subsequent technological operation, and, if necessary, prepares the machine. Subsystem for monitoring the functioning of machine tools(Fig. 12.8) includes a number of measuring devices that record deviations from the norm (for example, overheating of the movement of the main drive is detected by a temperature sensor). At the output of these devices are formed Fig. 12.8. The structure of the subsystem for monitoring the functioning of mechanisms; IU, IU 2 ... IU „- measuring devices; D-sensor; PIC - primary signal processing; USO - a device for collecting and processing information; UPR - decision making device; OAI - solution implementation device normalized signals that enter the device for collecting and processing information, from where they are transmitted to the decision making device. Here, taking into account additional information, a certain decision is made, which will be implemented in the future in the form of appropriate commands. In their structure, microprocessor devices are identical to modern CNCs and differ from them only in the composition of the modules for communication with an external device, the presence of feedback sensors and measuring devices. Subsystem for diagnosing the state of mechanisms must ensure the functioning of the machine with minimal operator involvement. There are devices for diagnosing hydraulic drives of machines, rolling bearings, gearboxes, feed boxes and other similar devices. Monitoring and compensation of typical deformation nodes of the machine allows to ensure the accuracy of processing during long-term operation. So, due to heating, the spindle assembly shifts, which leads to a decrease in processing accuracy. Compensation in this case is based on a periodic measurement of the actual displacements of the assembly parts in space. Using the IG installed on the spindle of the machine, measure the position of the reference surface on its table or using the IG to control the tool mounted on the table of the machine, measure the position of the reference mandrel in the spindle. The difference in the results of sequential measurements determines the spindle offset for the corresponding period of time. Entering this value into the CNC memory allows you to correct the displacements specified in the control program, and thereby compensate for the effect of thermal deformations. Such diagnostic systems are designed by the designer of the machine, usually from commercially available or special elements, although in some cases it is necessary to develop special diagnostic devices. As such devices are often used bellows furniture relays. Basic concepts and definitions .............................................. .................................................. ..... 4 1. Structural diagrams of the regulatory object ............................................ .............................. thirteen 2. The sequence of selection of the automation system ............................................ ............... fifteen 3. Regulation of the main technological parameters ............................................ ........... 17 3.1. Flow control, cost ratio ............................................. ............... 17 3.2. Level control ................................................ .................................................. ..... nineteen 3.3. Pressure control ................................................ .................................................. . 21 3.4. Temperature control ................................................ ............................................. 22 3.5. Regulation of pH ................................................ .................................................. ............ 24 3.6. Regulation of composition and quality parameters ............................................. ................. 26 Automation of the main processes of chemical technology ............................................. ....... 27 4. Automation of hydromechanical processes ............................................. ........................ 27 4.1. Automation of the processes of moving liquids and gases ........................................ 27 4.2. Automation of separation and cleaning of heterogeneous systems ...................................... 31 5. Automation of thermal processes ............................................. .......................................... 32 5.1. Regulation of mixing heat exchangers ............................................... ................... 33 5.2. Regulation of surface heat exchangers ............................................... ......... 38 5.3. Automation of tube furnaces ............................................... ...................................... 42 6. Automation of mass transfer processes ............................................. ............................... 45 6.1. Automation of the rectification process ............................................... .......................... 46 6.2. Automation of the absorption process ............................................... ................................. 53 6.3. Automation of the process of absorption - desorption ............................................. ............. 57 6.4. Automation of the evaporation process ............................................... ............................ 59 6.5. Automation of the extraction process ............................................... ............................... 64 6.6. Automation of the drying process ............................................... ........................................ 66 6.6.1. The drying process in a drum dryer ............................................. ....................... 66 6.6.2. Automation of fluidized bed dryers ............................................. ................ 69 7. Automation of reactor processes ............................................. ...................................... 71 Regulation of technological reactors ............................................... ................................ 71 Test questions on the discipline for preparing for the exam .......................................... .. 74 Literature................................................. .................................................. ....................................... 76 Basic concepts and definitions Automation is a technical discipline that studies, develops, and creates automatic devices and mechanisms (that is, it works without the direct intervention of a person). Automation is a stage of machine production, characterized by the transfer of control functions from humans to automatic devices (technical encyclopedia). TOU- technological control object - a set of technological equipment and the technological process implemented on it. ACS- an automated control system is a human-machine system that provides the automated collection and processing of information necessary for optimal control in various spheres of human activity. The development of chemical technology and other industries where continuous technological processes predominate (petrochemical, oil refining, metallurgical, etc.) required the creation of more advanced control systems than local ASRs. These fundamentally new systems are called automated process control systems - industrial control systems. The creation of ACS TP was made possible thanks to the creation of computers of the second and third generations, an increase in their computing resources and reliability. APCS- they call ACS for the development and implementation of control actions on the TOU in accordance with the adopted control criterion - an indicator characterizing the quality of the TOU and taking certain values \u200b\u200bdepending on the control actions used. ATK- the set of jointly functioning TOU and industrial control system forms an automated technological complex. ACS TP differs from local ATS: Better organization of information flows; Almost complete automation of the processes of obtaining, processing and presenting information; The possibility of an active dialogue of operational personnel with the UVM in the management process to develop the most effective solutions; A higher degree of automation of control functions, including starting and stopping production. From control systems for automatic production such as workshops and automatic plants (the highest level of automation) ACS TP is characterized by a significant degree of human participation in control processes. The transition from industrial control systems to fully automatic production is constrained by: Imperfection of technological processes (the presence of non-mechanized technological operations; Low reliability of technological equipment; insufficient reliability of automation equipment and computers; Difficulties in the mathematical description of problems solved by a person in industrial control systems, etc.) The global goal of management TOU with the help of industrial control system consists in maintaining the extreme value of the control criterion when all conditions that determine Fig. 1.Typical functional structure of industrial control system. 1
- primary information processing (I); 2
- detection of deviations of technological parameters and indicators of the state of equipment from the set values \u200b\u200b(I); 3
- calculation of non-measurable quantities and indicators (I); 4
- preparation of information and implementation of exchange procedures with related and other ACS (I); 5
- prompt and (or) call display and registration of information; 6
- determination of the rational mode of the technological process (U); 7
- the formation of control actions that implement the selected mode. the set of permissible values \u200b\u200bof control actions. In most cases, a global goal is broken down into a series of particular goals; To achieve each of them, a simpler control problem is required. The function of ACS TP is the action of the system aimed at achieving one of the particular goals of management. Private management objectives, as well as the functions that implement them, are in a certain subordination, forming the functional structure of the industrial control system. Functions of industrial control system: 1. Information - collection, conversion and storage of information about the state of TOU; presentation of this information to operational personnel or its transfer for further processing. 2. Initial processing of information about the current state of the TOU. 3. Detection of deviations of technological parameters and equipment status indicators from the set values. 4. Calculation of values \u200b\u200bof non-measurable quantities and indicators (indirect measurements, calculation of TEC, forecasting); 5. Prompt display and registration of information. 6. Exchange of information with operational staff. 7. they maintain the extreme values \u200b\u200bof the control criterion in a changing production situation, they are divided into two groups: the first is the determination of optimal control actions; the second is the implementation of this regime through the formation of control actions on the TOU (stabilization, program control; program-logic control). Secondary functions provide solution to intra-system tasks. To implement the functions of industrial control systems, it is necessary: Technical support; Software; Informational; Organizational; Operational staff. Fig. 2.The technical structure of the CCC automatic process control system for operation in supervisor mode. The technical structure of the KTS automatic process control system in direct digital control mode: AI is a source of information; USO - communication device with the object; VK - computer complex; USOP - communication device with operational personnel; OP - operational staff; TSA - technical means of automation for the implementation of the functions of local systems; IU - executive devices. The technical support of the automated process control system is a set of technical means (KTS) Means of obtaining information about the current state of TOU; UVK (managed computing complex); Technical means for implementing the functions of local automation systems; Actuators directly implementing control actions on the TOU. The complex complex of many automatic process control systems includes mechanical automation from the composition of the electrical branch of the GSP. A specific component of the CCC is the UVK, which includes the actual computer complex (VC), communication devices of the VC with the facility (USO) and with operational personnel. The first and still common type of technical structures of industrial control systems is centralized. In systems with a centralized structure, all the information needed to control the ATC goes to a single center - the operator center, where almost all the technical means of the process control system are installed, with the exception of information sources and executive devices. Such a technical structure is the simplest and has several advantages. Its disadvantages are: The need for an excessive number of ACS TP elements to ensure high reliability; High cable costs. Such systems are suitable for relatively small and compact ATCs. a complete centralized structure, the core of which is a control microcomputer. Local subsystems through their micro-computers are integrated into a single system by a data transmission network. The number of terminals necessary for operating personnel to be connected to the ATC is connected to the network. The automatic process control software connects all the elements of a distributed technical structure into a single whole, which has a number of advantages: The ability to obtain high reliability indicators due to the splitting of automatic process control systems into a family of relatively small and less complex autonomous subsystems and additional backup of each of these subsystems through the network The use of more reliable means of microelectronic computing; Great flexibility in the composition and modernization of technical and software, etc. Most of the ICS functions are implemented in software; therefore, the most important component of ICS is its software (software), i.e. a set of programs that ensure the implementation of the functions of process control systems. ACS software is divided: Special. General software is bundled with computer hardware. Special software is developed when creating a specific process control system and includes pro- grams that implement its information and control functions. The software is created on the basis of mathematical software (MO). MO - a set of mathematical methods, models and algorithms for solving problems and processing information using computer technology. To implement the information and control functions of automatic process control systems, they create a special MO, which includes: Algorithm for the collection, processing and presentation of information; Control algorithms with mathematical models of the corresponding control objects; Algorithms for local automation. All interactions both inside the ICS, and with the external environment are various forms of information exchange, arrays of data and documents are required, which ensure the operation of all its functions during the operation of the ICS. The rules for the exchange of information and the information itself circulating in the automatic process control system form the information support of the automatic process control system. Organizational support of process control system is a set of descriptions of the functional, technical and organizational structures of the system, instructions and regulations for operational personnel, ensuring the specified operation of process control system. The operational personnel of the automatic process control system consists of technologists-operators who manage the technical control system, the operational personnel that ensures the functioning of the automatic process control system (computer operators, programmers, personnel for the maintenance of the equipment of the telephone exchange). The operational personnel of industrial control systems can work in the control loop or outside it. When working in the control loop, the OP implements all control functions or part If the operating staff works outside the control loop, it will set the automatic process control system and monitor its compliance. In this case, depending on the composition of the CCC, the automatic process control system can operate in two modes: Combined (supervisor); In the direct digital control mode, in which the UVK directly affects the actuators, changing the control actions on the TOU. The creation of industrial control system includes five stages: 1. Terms of Reference (TOR); 2. technical design (TP); 3. working draft (RP); 4. implementation of industrial control systems; 5. analysis of its functioning. At the stage of TK, the main stage is predesign research(R&D), usually carried out by a research organization in conjunction with a customer enterprise. The main task of pre-design research is the study of the technological process as an object of management. At the same time, the goal and quality criteria for the functioning of the TOU, technical and economic indicators of the prototype object, their relationship with technological indicators are determined; the structure of the TOU, ie, input actions (including controlled and uncontrolled disturbing influences, and control actions), output coordinates and relations between them; the structure of mathematical models of statics and dynamics, parameter values \u200b\u200band their stability (degree of stationarity of the TOU); statistical characteristics of disturbing influences. The most laborious task at the stage of pre-design research is the construction of mathematical models of TOU, which are subsequently used in the synthesis of process control systems. In the synthesis of local ASRs, linearized dynamics models are usually used in the form of linear differential equations of 1–2 order with delay, which are obtained by processing the experimental or calculated transition functions through different channels of action. To solve the problems of optimal control of static modes, finite relations are used, obtained from the equations of the material and energy balance of the TOU, or the regression equation. In problems of optimal control of dynamic modes, nonlinear differential equations are used, obtained from the equations of material and energy balance written in differential form. When performing pre-design research works, methods of analysis of automatic control systems, studied in the discipline "Theory of automatic control", and methods of constructing mathematical models, which are presented in the course "Computer simulation of objects and control systems", are used. The results obtained at the stage of pre-design research are used at the stage preliminary design of industrial control systemduring which the following work is carried out: Choice of criterion and mathematical formulation of the optimal control problem of the TOU, its decomposition (if necessary) and the choice of methods for solving global and local optimal control problems, on the basis of which the optimal control algorithm is subsequently constructed; Development of the functional and algorithmic structure of automatic process control systems; Determination of the amount of information about the state of the TOU and VK resources (speed, volume of storage devices) required to implement all the functions of the control system; Preliminary selection of KTS, primarily UVK; Preliminary calculation of the technical and economic efficiency of industrial control systems. The central place among the works of this stage is occupied by the mathematical formulation of the problem. chi optimal control TOU. The remaining tasks of this stage (except for the calculation of technical and economic efficiency) relate to the system engineering synthesis of ACS TP, during which the method of analogies is widely used. The accumulated experience in the development of automated process control systems for the TOU of varying degrees of complexity allows us to transfer the development of a number of functions and algorithms from the category of scientific work to the category of technical work performed by design. These include many information functions (primary processing of initial information, calculation of TEC, integration and averaging, etc.), as well as typical functions of local automation systems implemented in the automatic process control system (alarm, emergency blocking, regulation with using standard laws at NTSU, etc.). The final stage of the preliminary design of automatic process control systems is preliminary calculation of technical and economic efficiencydeveloped system. It is carried out by specialists in economics, however, automation specialists must prepare the initial data for them, so we will consider some key points. The main indicator of the economic efficiency of industrial control systems is the annual economic effect of its implementation, which is calculated by the formula E= (WITH2 - S2) - (C1 - S1) - En(K2 - K1) , where C1and C2- annual volumes of sales at wholesale prices before and after the introduction of industrial control systems, thousand rubles; S1and S2- the cost of production before and after the implementation of the system, thousand rubles; K1and K2- capital expenditures on the ATC before and after the introduction of the automated process control system, thousand rubles; En- regulatory industry coefficient of efficiency of capital investments in automation and computer technology, rubles / rub. The main sources of economic efficiency of automation systems for chemical and technological processes are usually an increase in the volume of sales of products and (or) a decrease in their cost. Improvement of these economic indicators is most often achieved by reducing the consumption of raw materials, materials and energy per unit of production due to more accurate maintenance of the optimal technological regime, increase product quality (grade and, consequently, price), an increase in equipment productivity due to a reduction in working hours due to unplanned process shutdowns caused by control errors, etc. At the stage of pre-design research, production reserves should be identified, which may be used thanks to the use of automation systems. For example, if, when using a local automation system, the technological unit is idle on average 20% of the planned working time, of which 1/4 is caused by operational personnel errors due to untimely detection of emergency situations, then the use of automated process control systems that implements forecast and analysis of production situations can eliminate these losses. Then the volume of output in physical terms will increase by 5%, which will lead to an increase in sales and lower self-value of the product. The accumulated experience in the automation of chemical production has shown that the reserves of economic efficiency that can be used due to the automation of technological processes usually range from 0.5 to 6%. At the same time, the better the technology has been worked out, the usually less reserves. However, not all identified (potential) reserves of economic efficiency can be used after the implementation of industrial control systems. Actual efficiency turns out to be less than potential due to the non-ideality of the automated process control system, which is manifested, in particular, in the incomplete adequacy of the mathematical model of the TOU, according to which the optimal mode is calculated, in the measurement errors of the output coordinates of the object, which also affect the accuracy of determining the optimal mode, in the failures of hardware and software elements, due to which the quality of the performance of certain functions and industrial control systems as a whole is reduced, etc. The real effect usually ranges from 25 to 75% of the potential nogo and, as a rule, the greater the potential effect, the less it is implemented. The main indicator of the technical and economic efficiency of industrial control systems is the payback period of the system, which is determined by the formula = K2 - K1 . (C2 - S2) - (C1 - S1) It should be no more than normative, which for the chemical industry is 3 The final stage of the first stage of the creation of automatic process control systems is the development of technical specifications for the design of the system, which should include a complete list of functions, a feasibility study of the feasibility of developing automatic process control systems, a list and scope of research and a schedule for creating the system. When developing non-standard automated process control systems, the first stage accounts for approximately 25% of the total labor input, including pre-design research –– 15%. When replicating ACS TP, the first stage can be eliminated or significantly reduced. The next step in the creation of an atypical automated process control system is the development of technical projectduring which the main technical decisions that implement the requirements of technical specifications. Work at this stage is carried out by research and design organizations. The main content of research is the development and deepening of pre-design research, in particular, the refinement of mathematical models and statements of optimal control problems, verification by computer simulation of the operability and efficiency of the algorithms chosen for the implementation of the most important information and control functions of industrial control systems. The functional and algorithmic structures of the system are clarified, information links between functions and algorithms are worked out, the organizational structure of industrial control systems is developed. A very important and time-consuming stage in the TP stage is the development of special system software. According to available estimates, the complexity of creating special software was close to the total volume of pre-design research and amounted to 15% of the total labor costs for creating an automated process control system. At the TP stage, the composition of the CCC is finally selected and calculations are made to assess the reliability of the implementation of the most important functions of the control system and the system as a whole. The total cost of labor for design is approximately 30% of the cost of creating an automated process control system. At the stage of implementation of automatic process control systems, installation and commissioning works are carried out, the sequence and contents of which are studied in the corresponding course. Labor costs at this stage account for about 30% of the total system costs. When developing prototype industrial control systems that are to be further replicated on the same type of technical specifications, it is important to analyze the functioning of the system, during which the effectiveness of decisions made during its creation is checked and the actual technical and economic efficiency of industrial control systems is determined. Any chemical production is a sequence of three main operations. 1. preparation of raw materials; 2. the actual chemical transformation; 3. The selection of target products. This sequence of operations is included in a single complex chemical technology system (CTS). A modern chemical enterprise, plant or plant as a large-scale system consists of a large number of interconnected subsystems, between which there are subordinate relations in the form hierarchicalstructures with three main steps. Each subsystem of a chemical enterprise is a combination of a chemical-technological system and an automatic control system; they act as a whole to obtain a given product or intermediate. Structural schemes of the regulatory object xv(u)⎨ xv(z) One of the stages of designing technological regulation systems ⎫ processes - the choice of structure meters of regulators. And the system Fig. 1.1.The structural diagram of the regulatory object. th process as an object of regulation. topics, and parameters of regulators are determined by the properties of technological Any technological process as an object of regulation (Fig. 1.1) is characterized by the following main groups of variables: 1. Variables characterizing the state of the process (their combination will be denoted by the vector y) These variables in the regulatory process must be maintained at a given level or changed according to a given law. The accuracy of stabilization of state variables can be different, depending on the requirements dictated by technology and the capabilities of the regulatory system. As a rule, the variables included in the vector y, are measured directly, but sometimes they can be calculated using the model of an object using other directly measured variables. Vector yoften called a vector of controlled variables. 2. Variables, the change of which the regulatory system can affect the object for the purpose of control. The combination of these variables is denoted by the vector xp(or u) regulatory impacts. Typically, regulatory actions are changes in the flow of material flows or energy flows. 3. Variables whose changes are not related to the impact of the regulatory system. These changes reflect the influence of external conditions on the controlled object, changes in the characteristics of the object itself, etc. They are called disturbing influences and are denoted by the vector xvor z. The vector of disturbing influences, in turn, can be divided into two components - the first can be measured, and the second cannot. The ability to measure disturbance makes it possible to introduce an additional signal into the control system, which improves the capabilities of the control system. For example, for a continuous isothermal chemical reactor, the controlled variables are the temperature of the reaction mixture, the composition of the stream at the outlet of the apparatus; regulatory actions can be a change in the flow rate of steam in the jacket of the reactor, a change in the flow rate of the catalyst and the flow rate of the reaction mixture; disturbing effects are changes in the composition of the raw material, the pressure of the heating steam, and if if the heating steam is easy to measure, then in many cases the composition of the raw material can be measured with low accuracy or insufficiently quickly. The analysis of the technological process as an object of automatic control involves an assessment of its static and dynamic properties for each channel from any possible control action to any possible adjustable parameter, as well as an assessment of similar characteristics through the communication channels of the controlled variables with the components of the disturbance vector. In the course of such an analysis, it is necessary to choose the structure of the regulatory system, i.e., decide with which regulatory influence one or another state parameter should be controlled. As a result, in many cases (by no means always) it is possible to isolate control loops for each of the controlled quantities, that is, to obtain a set of single-loop control systems. An important element in the synthesis of ASR of the technological process is the calculation of a single-circuit control system. In this case, it is required to select the structure and find the numerical values \u200b\u200bof the parameters of the regulators. As a rule, the following typical structures of control devices are used (typical laws of regulation): proportional (P) controller (R (p) \u003d -S1); integral (I) regulator (R (p) \u003d -S0 / p); proportional-integral (PI) control law (R (p) \u003d -S1 - S0 / p) and, finally, proportional-integral-differential (PID) law (R (p) \u003d -S1 - S0 / p - S2 · p ) When calculating the system, they check the possibility of using the simplest regulation law, each time evaluating the quality of regulation, and if it does not satisfy the requirements, go over to more complex laws or use the so-called circuit methods for improving quality. In the theory of automatic regulation, various methods have been developed for calculating ASR for given quality criteria, as well as methods for assessing the quality of transients with given parameters of an object and a regulator. At the same time, along with exact methods that require a lot of time and manual labor, approximate methods have been developed that allow one to relatively quickly evaluate the operating parameters of the controller or the quality of transients (the Ziegler – Nichols method for calculating controller settings; approximate formulas for evaluating integral quadratic criterion, etc.). It might be useful to read:
Exchange of information with related and superior ACS. The control functions provide
In connection with the introduction of microprocessor technology, the distributed technical structure of industrial control systems, i.e. divided into a number of autonomous subsystems - local technological control stations, geographically distributed over technological control areas. Each local subsystem is the same type of
Fig. 3.The technical structure of the KTS automatic process control system for operation in direct digital control mode.
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