Schemes of control and management of parameters of technological processes. Control and management of machine tools and automatic lines. Single-loop and multi-loop control systems
Despite the huge variety technological processes 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), thermodynamic. The processes of each group are based on common physical and chemical laws, which determines the significant similarity of their properties as objects of automation.
This makes it possible to develop typical automation schemes for objects of each group. However, one technological feature is not enough for typification of automation objects, because Processes of one group may have different hardware design (for example, drying in a drum dryer or in a fluidized bed dryer) and, as automation objects, differ significantly in their properties. Consequently, 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 control in chemical production.
For each typical object, one or more variants of automation systems can be developed.
Expense ACP. Most often, the problem arises of regulating the flow of gas, liquid or steam transported through a pipeline. Flow control in such a system is carried out by throttling the flow, which depends on the degree of opening of the control valve (see Figure 7.2):
Figure 7.2 - The simplest flow ACP
The object of regulation is actually a section of the pipeline between the flow sensor and the control valve, which can be considered a non-inertia amplifying link. Consequently, the dynamic response of a given part of the ACP is determined only by the dynamic properties of the flow sensor and the regulating body. PI controllers are usually used in the flow ACP to maintain the set flow rate without residual deviation.
Flow control systems use one of three ways to change flow:
- throttling the flow of a substance through a regulatory body installed on the pipeline (valve, gate, damper);
Changing the pressure in the pipeline using an adjustable energy source (for example, changing the number of revolutions of the pump motor or the angle of rotation of the fan blades);
- bypass, i.e., the excess of the substance has grown from the main pipeline into the bypass line.
Flow control after the centrifugal pump is carried out by a control valve installed on the discharge pipeline (Figure 7.3, a). When using a piston pump, the use of such an ACP is unacceptable, since when the regulator is operating, the valve may close completely, which will lead to a rupture of the pipeline (or surge if the valve is installed on the suction side of the pump). 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 throttling the flow in the bypass pipeline. When using piston pumps, the regulating elements must not be installed on the discharge pipeline, because a change in the degree of opening of such a body leads only to a change in pressure in the discharge line, while the flow rate remains constant. Complete closure of the regulating body may cause damage to the pump. In this case, the regulator is installed on the bypass line connecting the suction and discharge pipelines (Figure 7.3, 6).
The disadvantage of this method of regulation is the low efficiency. More economical is the method of regulation by changing the performance of the pump: the number of revolutions of the shaft, the piston stroke, the angle of the blades.
The number of shaft revolutions can be changed:
1. By switching the stator winding to a different number of pole pairs,
2. By introducing a rheostat into the motor rotor circuit,
3. By changing the frequency of the supply current,
4. Applying adjustable slip clutches between the pump and the asynchronous motor.
The regulation of the flow of bulk solids is carried out by changing the degree of opening of the control damper at the outlet of the bunker (Fig. 7.4, a), or by changing the speed of the conveyor belt. With this option, the flow meter is a weighing device that determines the mass of material on the conveyor belt (Figure 7.4, b).
1 - bunker. 2 - conveyor; 3 - regulator; 4 - control damper; 5 - electric motor
Figure 7.4. Flow control schemes for bulk solids:
Regulation of the ratio of consumption of two substances can be carried out in three ways:
With an unspecified total productivity, the consumption of one substance (Figure 7.5, a) G1, called the "leading", can change arbitrarily; the second substance is supplied at a constant ratio γ with the first, so that the “guided” flow rate is equal to JG1. Sometimes, instead of a ratio controller, a ratio relay and a conventional controller for one variable are used (Figure 7.5, b). The output signal of the relay 6, which sets the given ratio coefficient γ, is given as a task to the regulator 5, which ensures the maintenance of the “guided” flow rate.
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 case of a change in the target for flow rate G1, the flow rate G2 will automatically change (in a given ratio with G1).
With a given total load and correction factor for the third parameter. ACP cost ratio is an internal loop in cascade system regulation 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 that G2 = JfyJG1 (Figure 7.5, d). A feature of setting up cascade ACPs is that the internal controller is given a limit< 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 - restriction device.
Figure 7.5. Cost ratio regulation schemes.
Mixing liquids. When developing standard solution Under the control object we mean a container with a mechanical stirrer, 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 can change if the technological regime of previous processes is violated. The consumption of the mixture is determined by the subsequent technological process.
Required during the mixing process:
1. Maintain the material balance of the mixer, i.e. F A + F B = F mixture.
2. Maintain a constant concentration of the mixture, i.e. Q of the mixture = const.
To maintain the material balance, the level of the mixture in the tank should be selected as the controlled variable. Level constancy 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 ACP level
If the flow rate of liquid B varies greatly during level control, a concentration-corrected liquid flow ratio controller should be used to improve the quality of concentration control. This regulator contributes to the reduction of concentration disturbances that occur during the initial change in fluid flow. When other disturbing influences arrive, for example, with a change in the concentration of components in liquids, the setting of the flow rate ratio will change (Figure 7.7).
Figure 7.7 - Example of 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 install a component concentration regulator in the mixture or a 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 inflow of liquid is equal to the flow, and the rate of level change is zero.
IN general case level change is described by an equation of the form:
where S- the area of the horizontal (free) section of the apparatus; G ex, G ex- fluid flow rates at the inlet to and outlet of the apparatus; G o6- the amount of liquid formed (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 control, in which the level in the apparatus 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 control, which ensures the stabilization of the level at a given value, i.e. L = L .
1 - pump; 2 - apparatus; 3 - level indicator; 4 - level controller; 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 level of condensate determines the actual heat exchange surface. In such ACPs, to control the level without a static error, they use PI controllers. P-regulators are used only in cases where 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 a static error.
In the absence of phase transformations in the apparatus, the level in it is regulated in one of three ways:
Changing the flow rate of the liquid at the inlet to the apparatus (regulation "on the inflow", Figure 7.10, a);
Change in the flow rate of liquid at the outlet of the apparatus (regulation "on the drain", Figure 7.10, b);
Regulation of the ratio of liquid flow rates at the inlet to and outlet of the apparatus with level correction (cascade ACP, Figure 7.10, c); disabling the correction loop can lead to accumulation of errors in level control, because due to inevitable errors in setting the ratio controller, the liquid flow rates at the inlet and outlet of the apparatus will not be exactly equal to each other, and due to the integrating properties of the object, the level in the apparatus will continuously increase (or decrease ).
a - regulation "on the inflow"; b - regulation "on the drain", c - cascade ACP (1 - level controller, 2 - control valve, 3, 4 - flow meters, 5 - ratio controller).
Figure 7.10 - Schemes of continuous level control:
1 - evaporator; 2 - level regulator, 3 - control valve
Figure 7.11 - Scheme of level control in the evaporator
In the case when hydrodynamic processes in the apparatus are accompanied by phase transformations, the level can be controlled by changing the supply of the coolant (or coolant). In such devices, the level is interconnected with other parameters (for example, pressure), so the choice of the level control method in each specific case must be carried out taking into account the remaining control loops. A special place in level control systems is occupied by level ACPs in apparatuses with a fluidized (pseudo-liquefied) layer of granular material (Figure 7.12).
Steady maintenance of the level of the fluidized bed is possible within rather narrow limits of the ratio of the gas flow rate and the mass of the bed. With significant fluctuations in the gas flow rate (or the flow rate of granular material), the regime of entrainment of the layer or its settling occurs. Therefore, particularly high demands are made on the accuracy of the fluidized bed level control. As regulatory influences, the flow rate of granular material at the inlet or outlet of the apparatus (Figure 7.12, a) or the gas flow rate for bed liquefaction (Figure 7.12, b) is used.
a - removal of granular material, 6 - change in gas flow (1 - apparatus with a fluidized bed, 2 - level controller, 3 - regulatory body).
Figure 7.12 - Fluidized bed level control:
ACP pressure. Pressure is an indicator of the ratio of the flow rates of the gas phase at the inlet to the apparatus and the outlet from it. The constancy of pressure indicates the observance of the material balance in the gas phase. Usually, the pressure (or vacuum) in a process plant is stabilized in one apparatus, and throughout the system it is set in accordance with the hydraulic resistance of the line and apparatuses. For example, in a multi-shell evaporator (see Figure 7.13, a), the vacuum in the last evaporator is stabilized. In the rest of the apparatus, in the absence of disturbances, a rarefaction is established, which is determined from the conditions of the material and heat balances, taking into account the hydraulic resistance of the technological line.
In cases where pressure significantly affects the kinetics of the process (for example, in the process of rectification), a pressure stabilization system is provided in separate apparatuses (Figure 7.13, b). In addition, when regulating the process of binary distillation, the boiling point of the mixture is often used as an indirect indicator of the composition of the mixture, which is unambiguously related to the composition only at constant pressure. Therefore, in product distillation columns, special pressure stabilization systems are usually provided.
1,2 - evaporators; 3 - barometric condenser; 4 - vacuum regulator;
5 - control valve.
Figure 7.13a - Vacuum control in a multi-effect evaporator
1 - column; 2 - dephlegmator; 3 - reflux tank; 4 - pressure regulator;
5 - control valve
Figure 7.13B - ACP of pressure in the distillation column
Vacuum control in a multi-effect evaporator. In this system, the regulating action is the flow of cooling water into the barometric condenser, which affects the rate of condensation of the secondary steam.
Differential pressure regulation. In such devices, the pressure drop is regulated, which characterizes the hydrodynamic regime, which affects the course of the process (Figure 7.14).
a - in a column apparatus with a packing; b - in an apparatus with a fluidized bed (1 - apparatus; 2 - differential pressure regulator; 3 - control valve).
Figure 7.14 - Scheme of differential pressure control
Generally ACP pressure liquid, gas or steam transported through a pipeline has much in common with ACP flow, because objects of regulation have the same properties. Sometimes, to regulate the pressure in pipelines of steam or compressed air, P-regulators direct action.
In the absence of sharp and significant disturbances in amplitude, they provide good quality regulation 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 an output coordinate in the regulation of thermal processes. The dynamic characteristics of objects in temperature control systems depend on the physicochemical parameters of the process and the design of the apparatus. That's why general recommendations it is impossible to formulate the temperature for the choice of ACP, and an analysis of each specific process is required.
TO common features ACP temperature can be attributed to the significant inertia of thermal processes and industrial temperature sensors. Therefore, one of the main tasks in the design of temperature ACP 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 - protective cover; 2 - air gap; 3 - thermometer wall; 4 - working fluid.
Figure 7.15. Schematic (a) and structural (b) diagrams of the thermometer
The block diagram of a thermometer can be represented as serial connection four thermal capacities (Figure 7.15, b): a protective cover 1, an air gap 2, a thermometer wall 3 and the actual working fluid 4. If we neglect the thermal resistance of each layer, then all elements can be approximated by aperiodic links of the 1st order, the equations of which have the form:
M j - mass, respectively, of the cover, air gap, wall and liquid; c pj - specific heat capacities; α j1 , α j2 - heat transfer coefficients; Fj1, Fj2 - heat transfer surfaces.
As can be seen from the last equation, the main directions for reducing the inertia of temperature sensors are:
An increase in the heat transfer coefficients from the medium to the cover as a result right choice sensor installation locations; in this case, the velocity of the medium must be maximum; ceteris paribus, it is more preferable to install thermometers in the liquid phase (compared to gaseous), in condensing vapor (compared to condensate), etc.;
Reducing the 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 the protective cover;
Selecting the type of primary converter; for example, when choosing a resistance thermometer, a thermocouple or a manometric thermometer, it must be taken into account that the thermocouple in a fast-response version has the least inertia, and the manometric thermometer has the largest.
ACP pH number. pH control systems can be divided into two types, depending on the required control accuracy. If the rate of change in pH is low, and the allowable limits of its fluctuations are wide enough, positional control systems are used that maintain pH within the specified limits: pHn ≤ pH ≤ pHv. The second type includes systems that provide control of processes in which precise maintenance of pH at a given value is required (for example, in neutralization processes). For their regulation, continuous PI or PID controllers are used.
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 consumption of reagents. figure 7.16 shows a titration curve that characterizes the dependence of pH on acid consumption G 1 . For various given pH values, three characteristic sections can be distinguished on this curve: the first (middle), related to almost neutral media, is close to linear and is characterized by a very large amplification factor; the second and third sections, related to strongly alkaline or acidic environments, have the greatest curvature.
In the first section, the object, according to its static characteristic, approaches the relay element. In practice, this means that when calculating a linear ACP, the controller gain is so small that it goes beyond the operating settings of industrial controllers. Since the neutralization reaction itself takes place almost instantly, the dynamic characteristics of the apparatuses are determined by the mixing process and, in apparatuses with agitators, are described quite accurately by differential equations of the 1st order with a delay. At the same time, 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 controller and the delay in the impulse lines begin to affect.
Figure 7.16 - Dependence of the pH value on the consumption of the reagent
To ensure stable pH regulation, special systems are used. Figure 7.17a shows an example of a pH control system with two control valves.
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, which has a large nominal diameter, is used for rough flow control and is set to the maximum range of the regulator output signal [хрн,хрв] (Figure 7.17, b, curve 1). Valve 2, which serves for fine control, is designed for a smaller throughput and is configured in such a way that at x p = x 0 p + Δ it is completely open, and at x p = 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 may turn out to be unacceptably large. In this case, more accurate results are obtained by a piecewise linear approximation (Figure 7.18), in which the linearized object has a variable gain.
Figure 7.18 - Piecewise linear approximation of the static characteristic of the object when adjusting the pH
Figure 7.19 shows a block diagram of such an ACP. Depending on the pH mismatch, one of the regulators is activated, tuned to the corresponding gain of the object.
Figure 7.19 - Structural 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 precise maintenance of the quality parameters of products (concentration of a certain substance in a stream, etc.). These parameters are difficult to measure. In some cases, chromatographs are used to measure the composition, which provide measurement results at discrete points in time (according to the duration of the chromatograph cycle).
The discreteness of the measurement can lead to significant additional delays and a decrease in the dynamic accuracy of the regulation. To reduce the undesirable influence of measurement delay, a model is used to relate product quality to variables that are measured continuously. This model can be quite simple; the coefficients of the model are refined 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 methods of quality regulation is regulation by an indirect calculated indicator with the refinement of the algorithm for its calculation given by direct analyses. Between measurements, the quality index of a product can be calculated by extrapolation of previously measured values. The block diagram of the product quality parameter control system is shown in Figure 7.20. The computing device in the general case continuously calculates the estimate of the quality indicator ~ (t) according to the formula:
in which the first term reflects the dependence on continuously measured process variables or quantities dynamically associated with them, for example, derivatives, and the second - on the output of the extrapolating filter.
To improve the accuracy of composition and quality control, instruments with an automatic calibration device are used. In this case, the control system performs periodic calibration of the composition analyzers, correcting their characteristics.
1 - object; 2 - quality analyzer; 3 - computing device; 4 - regulator
Figure 7.20 -. ACP Flowchart of Product Quality Parameter:
As an example, consider decision making process in automation one of the common typical processes.
Automation of the mixing process. general characteristics 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 throughout the entire volume under the action of an impulse transmitted to the medium by an agitator, liquid or gas jet.
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1 Ministry of General and vocational education Russian Federation Tver State Technical University V.F. Kommissarchik Automatic control of technological processes Tutorial Tver
2 UDC 6.5 Automatic control of technological processes: Textbook Second edition, extended / V.F. commissioner; Tver State Technical University, Tver, 48s. The methods of calculation of automatic control systems of technological processes of various types are considered. Designed for specialty students. "Automation of technological processes and production" in the study of the discipline of the same name. Prepared at the Department of Automation of Technological Processes of the Tver State technical university.
3 3 Introduction One of the most important tasks of automation of technological processes is automatic control, which aims to maintain constancy, stabilize the set value of controlled variables or change them according to a law set in time, program control with the required accuracy, which makes it possible to obtain products of the desired quality, as well as safe and economical operation of technological equipment. As controlled variables, regime level, temperature, pressure, flow rate or qualitative humidity, density, viscosity, composition, etc. are usually used. indicators of the functioning of technological processes that characterize the material or energy balance in the apparatus and the properties of the product. The task of automatic regulation is realized by means of automatic control systems of ACP. The block diagram of a closed ACP is shown in Fig. F RO x OP S P - ass Fig..
4 4 In fig. marked: OR object of regulation technological process or apparatus; y is the controlled variable; х regulatory influence, with the help of which the regulation process is carried out. Regulatory influences are usually the flow rates of liquid, gaseous, granular bodies; RO is a regulating working body, with the help of which the consumption of energy substance is changed. To change the flow rates of liquid and gaseous bodies, throttling-type working bodies with a variable flow area are widely used; S is the position of the end effector, usually measured in % stroke RO, such as valve stem travel or damper rotation. Since the regulatory impact x, as a rule, is not measured, S is usually taken as the regulatory impact, thereby attributing RO to the object of regulation; F - disturbing influences that affect the value of the controlled variable; Р - automatic regulator - a set of elements designed to solve the problem of regulation; set - the set value of the controlled variable, which must be supported by the controller; - a comparing device that generates an error mismatch signal: set As an example, in fig. shows the scheme for controlling the temperature of the product θ pr at the outlet of the heat exchanger by changing the supply of coolant G.
5 5 G pr θ pr R G Fig.. One of the main perturbations in this system is the flow rate of the heated product G pr. The reason for regulation in a closed ACP is the occurrence of an error. When it appears, the controller changes the control action x until the error is completely eliminated in an ideal system. Thus, the ASR is designed to maintain the controlled variable at a given level with fluctuations in disturbing influences within certain limits. In other words, the main task of the regulator is to eliminate the mismatch by changing the regulatory action. The most important advantage of a closed ACP is that it responds to any disturbance that leads to a mismatch. At the same time, such systems are fundamentally inherent in the control error, since the occurrence
6 6 mismatch always precedes its elimination and, in addition, a closed ACP under certain conditions can become unstable. The main tasks that arise in the calculation of the ACP are: Mathematical description of the object of regulation;. Rationale block diagram ACP, type of regulator and formation of requirements for the quality of regulation; 3. Calculation of the controller settings; 4. Analysis of the quality of regulation in the system. The purpose of calculating a closed ACP is to ensure the required quality of regulation. Under the quality of regulation, we mean the values of indicators characterizing the shape of the transient process curve in a closed ACP with a step action at its input. An approximate view of the transient characteristics of a closed ASR along the channels of the driving and perturbing, in a particular case, regulatory actions is shown in Fig. 3. The transient response of a closed system along the channel of the driving influence, the line y fact in fig. 3a reflects the nature of the transition of the controlled variable from one steady value to another. x a y ass b y id y fact y fact y id Fig. 3.
7 7 It would be ideal if this transition was made abruptly line y id 3b reflects the process of perturbation suppression by the system. It would be ideal if the system did not react at all to the perturbation of the line y id. This manual discusses methods for solving typical problems that arise in the calculation of ACP of various types, which are used in the practice of automating technological processes.. Mathematical description of regulated objects [4].. Main characteristics and properties of regulated objects. static or dynamic. Static is a steady state in which the input and output values of the object are constant in time. This definition is valid for persistent static objects. Dynamics is a change in time of the output variable of the object due to a change in the input variable or non-zero initial conditions. Static characteristics of regulated objects The behavior of a regulated object in statics is characterized by a static characteristic "input-output", which represents the relationship between the steady values of the output and input variables: fset st According to the type of static characteristics, linear and non-linear objects are distinguished. The static characteristic of a linear object is a straight line passing through the origin with the equation
8 8 K A characteristic with the equation K b, which does not pass through the origin, can be reduced to a linear one, denoting b ". Objects whose static characteristics differ from a straight line are non-linear. 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 the input action Physical meaning: change of the controlled variable per unit of the input action, i.e. the transfer coefficient characterizes the steepness of the static characteristic function x For linear objects Ku / constant, for nonlinear K is When calculating the ASR, nonlinear characteristics are usually linearized. Widespread use is the linearization of the tangent by the linear approximation of the expansion into a Taylor series. Let x, y be the point in the vicinity of which the function f is linearized. Considering ddd we find d When using the linearized equation, it follows
9 9 a sufficiently small neighborhood of the point x. In addition, since the expression includes the derivative of the function f, this method of linearization is suitable only for differentiable functions. Dynamic characteristics of objects of regulation. Differential Equation The main dynamic characteristic of controlled 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 be conditionally considered as containers with ideal instantaneous mixing. Variables in such objects depend only on time and do not depend on the coordinates of the measurement point of the variable. Partial derivative 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 of variables depend not only on time, but also the coordinates of the point of measurement of the variables, therefore, the differential equations include not only derivatives with respect to time, but also with respect to coordinates. Usually, in calculations, partial differential equations are approximated by a system of ordinary differential equations. In what follows, 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 whole equation, m is the order of the right side. Since the real objects of regulation are 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 displacement theorem, i.e. L e τ ( τ) 4 This property allows one to find images of differential equations with retarded argument. Differentiating the original under zero initial conditions corresponds to multiplying the image by p: d L d, so formally the variable p can be considered a symbol of differentiation. In the static In the general case, d L d 5 Since integration is the inverse of differentiation, the integration of 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 represents an algebraic expression that can be resolved with respect to the image of the output variable ur and then go back 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 make it easier to find the image from the original and the original from the image, correspondence tables have been compiled between the originals and their images for the simplest functions. These tables are given in manuals on the Laplace transform and in textbooks on control theory. To find the originals of complex images, the formula for decomposing an image into simple fractions is used. see 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, the transfer coefficient is a static characteristic. The static rest is a particular case of the dynamics of motion. Therefore, K is a special case of W in statics. Since p in statics, then K W 6 13 3 Time characteristics The time characteristic of an object is its response to a typical aperiodic signal. As input signals, a step function or its derivative - δ - function is most often used. The response of an object or any dynamic link to a step function of unit amplitude, a single step function, is called the transient response of the link object h. The reaction of an object to a step of arbitrary amplitude x is called the acceleration curve of the object (Fig. 4). To obtain the transient response from the acceleration curve y, divide each ordinate of the acceleration curve by the step amplitude: h / Fig. 4. Fig. 5. The reaction of the object to the δ function in real conditions on an impulse of finite duration and amplitude, for example, a rectangular one is called the impulse response of the weight function of the control object fig. five. 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 plant, 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 6. Fig. 7. The values of m and ϕ depend on the frequency of the input signal. Since we are interested in changing two magnitudes of amplitude and phase at once, it is convenient to consider the frequency characteristics in the complex plane. The harmonic input signal is represented on the complex plane by the vector j, the length modulus of which is equal to the amplitude x m, and the slope angle argument is equal to the oscillation phase fig. 7: j m e j The symbol in this case means "depicted". 15 5 Similarly, the output signal of the object is depicted in the complex plane by the vector j: m e j ϕ j Images j and j are called Fourier images 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 FTF or the complex frequency response W j: jm jϕ W jejm A e jϕ frequency inputs. 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 function can be found by replacing the variable p by j in the transfer function W, i.e. assuming j: bm W j j n m j n LL b LL What is the difference between a transfer function and a frequency transfer function? The transfer function reflects the behavior of the object of regulation or any dynamic link in dynamics with an arbitrary form of input action. The frequency transfer function reflects 16 6 the behavior of the link object only in the steady state of harmonic oscillations. Thus, the frequency transfer function is a special case of the transfer function, just as the imaginary variable is a special case of the complex variable p. j is The frequency transfer function is written in algebraic form in Cartesian coordinates: W j P jq, [ W j ]; Q Jm[ W j ], P Re or in exponential form in polar coordinates: W j W j A e jϕ [ W j ] A W j; ϕ rg The hodograph of the vector W j the graph described by the end of the vector when the frequency changes from 0 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. 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 frequency are called the amplitude-frequency response and the phase-frequency phase response, respectively, fig. 9. The AFC contains the same information about the link object as the AFC and PFC combined. j A ϕ ϕ A 8. Fig. nine. 17 7 Basic properties of regulated objects. Load Load is the amount of substance or energy taken from the regulated object during operation. The change in load is usually the main disturbing influence in the control system, because leads to an imbalance between the inflow and outflow of energy matter in the object, which causes a change in the controlled variable, for example, the liquid level in the tank (Fig. Q pr H Q st Fig.. In addition, a change in load leads to a change in the dynamic characteristics of the object. For example, in a container with perfect mixing, rice. the time constant is equal to the ratio of the volume of liquid stored in the container 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 is able to accumulate. The capacitance characterizes the inertia of the regulated object. Objects of regulation can be single- and multi-capacity. Multi-capacity objects consist of two or more tanks separated by 18 8 transient resistances. The number of containers determines the order of the object's differential equation. For example, the liquid container in Fig. refers to the number of single-capacity 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 container is the amount of heat in the heated liquid in the annulus. The second container is the amount of heat in the coolant inside the tubes. The third capacity is the amount of heat in the walls of the pipes, this capacity is usually small compared to the others, and it is neglected. Self-leveling Self-leveling is the ability of an object to restore the balance between the inflow and outflow of energy matter due to a change in the controlled variable due to internal negative feedback in the regulated object. For example, in a container with a free drain fig. when the inflow increases, the level increases and thus the runoff increases until the balance between inflow and runoff is restored. The greater the self-leveling value, the less the controlled variable deviates under the influence of disturbances. Thus, self-leveling facilitates the work of the automatic regulator. Depending on the value 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 responses end in steady state 19 9 the section on which the controlled variable comes to a state of rest and ceases to change Fig., curve. 3 Fig. Quantitatively, the self-leveling value is characterized by the self-leveling coefficient ρ, which represents the modulus of the reciprocal of the static transfer coefficient of the object: ρ K The self-leveling coefficient shows how much the input variable of the object must 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-alignment, objects with zero self-alignment, include the so-called neutral or astatic objects, representing 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 container with forced draining fig. Q pr N Q st The steady section of the transient response of an astatic object is a straight line on which the controlled variable changes at a constant rate. The curve in Fig. and has the meaning of the rate of change of the controlled variable per unit of input. There are objects in which, under certain conditions, an uncontrolled process occurs. 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 time interval from the moment the disturbance is applied to the beginning of the change in the controlled variable. Distinguish between pure and capacitive delay. Pure transport delay τ is the time that the energy substance flow spends on passing the distance from the point of perturbation to the point of measurement of the controlled variable in a single-capacity object. An example of a link with a pure delay is a belt feeder conveyor fig. 3. The pure delay time 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 3. Fig. 4. 22 In multicapacitive objects, several capacitances are connected in series, which causes a slowdown in the flow of energy substance from one capacitance to another and leads to capacitive delay. Figure 4 shows the transient characteristics of one n, two - n, and multicapacitive nm objects. With the number of capacitances n>, an inflection point P appears in the transient response. With an increase in n, the initial section of the transient response gravitates 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 retardation, the manipulated variable is zero for the duration of the lag. With capacitive delay, it changes, although very little. In the time domain, the transport and capacitive delays appear approximately the same, while in the frequency domain, the behavior of these links differs 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 the capacitive delay from the pure one on the experimental characteristic. Therefore, if the net delay is determined from the experimental acceleration curve, its value is always subjective, i.e. depends on the researcher. Delay sharply worsens the quality of regulation in the ACP ... Methods mathematical description objects of regulation Methods of mathematical description of objects of regulation can be divided into analytical, i. not requiring an experiment 23 3 at an industrial facility and experimental i.e. based on the results of the experiment. Analytical methods are called obtaining mathematical models objects based on the analysis of physical and chemical processes occurring in the object, taking into account its design and characteristics of the processed substances. Advantages of analytical models of objects. No on-site industrial experiments are required. Therefore, these methods are suitable for finding object models at the stage of their design or, if it is impossible pilot study characteristics of regulated objects. Analytical models include design characteristics of objects and indicators of the technological mode of their operation. Therefore, such models can be used to select the optimal design of the apparatus and optimize its technological regime. 3. Analytical models can be used for similar objects. However, analytical models are quite complex. In real objects, three types of processes can occur simultaneously: chemical transformations, heat and mass transfer. Simultaneous accounting of all these processes is quite a 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 relation that describes the experimental data with the required accuracy. When taking time characteristics, the object is in a transitional mode from one steady state to another. When removing the frequency characteristics, the object is introduced into the steady state of harmonic oscillations. Therefore, obtaining frequency 24 4 characteristics, in principle, makes it possible to obtain more representative information about the object, to a much lesser extent dependent on random perturbations acting on the object. But the frequency response experiment is more time consuming compared to the time response experiment and requires special equipment. Therefore, the most accessible in real conditions is to obtain temporal characteristics. However, it should be noted that experimental models of objects can only be used for those objects and those conditions of their functioning for which the experiment was carried out..3. Obtaining and Approximation of the Time Characteristics of Regulated Objects Preparation and Conduct of the Experiment When developing the scheme of the experiment for taking the temporal characteristics of regulated objects, issues related to the measurement and registration of the test effect and the controlled variable are solved. The planning 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 the step action is unacceptable for the object of regulation without self-leveling or a long-term deviation of the controlled variable from the nominal value is unacceptable, a rectangular impulse type action is used. The impulse response thus obtained, in accordance with the principle of superposition for linear objects, can be rebuilt into an acceleration curve. 25 5 When choosing the amplitude of the test impact, a compromise is sought between the following conflicting requirements. On the one hand, the amplitude of the input action must be large enough to reliably distinguish the useful signal against the background of measurement noise. On the other hand, too large deviations of the controlled variable can lead to disturbances in the operation of the facility, leading to a decrease in product quality or the emergence of an emergency mode. In addition, with large disturbances, the nonlinearity of the static characteristics of the object affects. When determining the number of experiments, it is useful to take into account the following factors: the linearity of the static characteristics of the object, the degree of noisiness of the characteristics, the magnitude of load fluctuations, and the nonstationarity of the characteristics over time. Before the experiment, the object must be stabilized in the vicinity of the nominal mode of its operation. The time-characterization experiment 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 set with low-frequency noise. Approximation of transient characteristics of regulated objects. The approximation problem includes three stages. Choice of the approximating transfer function. The transient characteristics of objects with self-alignment and lumped parameters are approximated by a fractional-rational transfer function in the general case with a pure delay of the form: 26 6 W rev K rev 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 integrator is added as a multiplier. As practice shows, satisfactory approximation accuracy is achieved when 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 approximation accuracy, it is necessary to build a calculated characteristic and determine the maximum approximation error. The expressions for the transient responses corresponding to some approximating transfer functions are given in Table. When calculating on a computer in the expressions for the transient responses, one should go to a discrete time τ 7 i sampling interval, and if there is a pure delay in the model 7, the argument at ii at i > τ to Approximation of the transient characteristics of objects with self-alignment by an inertial link of the first order with a delay 27 7 W K e τ 8 To determine τ and T to the transient characteristic of Fig. 5, a tangent AB is drawn at the inflection point C, the inflection point corresponds to the maximum angle α between the tangent and the abscissa axis set B C set O τ α A D Segment OA cut off by the tangent on the abscissa axis is taken as the time of pure delay τ : τ ОА 5. The transfer coefficient K is found as the ratio of the increments of the output and input values in steady state: set K 9 set 28 8 Table. model Transfer function Roots of the characteristic equation Transient characteristic K e K, - step action amplitude K α β ee K β α β α β α β 3 K α j ±, α α α rcg e K sin 4 b K α β ebeb K β α α β β α β α α β 5 b K α j ±, sin α α α α α b rcg ebb K α β γ 3 eee K γ β α γ β γ α γ αβ γ β α β αγ γ α β α βγ K α j ±, γ 3 e rcg e γ 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 K α j ±, γ 3 [ e b b b rcg e b b K 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 preliminarily normalized from to by the formula ~ ; ~ On the normalized curve in Fig. 6, two points A and B are selected as interpolation nodes through which the calculated curve must pass. ~ B ~B ~A A A B 6. The normalized transient response of the link with transfer function 8 is equal to 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 Resolving this system with respect to τ and T, we obtain: 31 3 ~ ~ B ln AA ln B τ ln ~ ln ~ ABA τ B τ ln ~ ln ~ AB or W К 4 The parameters of models 3, 4 can be easily determined by drawing the asymptote VS to the steady section of the acceleration curve Fig.6.: С А α В Fig. 6. K d / d set gα set OV OA set 5 τ OA for model 3 32 3 TOA for model 4 Approximation of the transient responses of control objects by an n-th order link there are. To eliminate the component due to pure delay, all abscissas of the acceleration curve should be reduced by the amount of pure delay τ, i.e. move the origin to the right by τ. At the same time, in the transfer function of an object with a pure delay W about W e " about 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. Bα Fig.8. - When approximating the transient response of an object without self-levelling, it is represented as the difference between two characteristics Fig. 8: 33 33 To do this, we draw the asymptote VS to the steady section of the characteristic and the ray OA is parallel to VS. Subtracting from, we find. - transient response of the integrating link with the transfer function W K The coefficient K is still found by formula 5: K gα mouth is the transient response of the object with self-alignment. It corresponds to the transfer function W. Due to the linearity of the Laplace transform, the transfer function of the object corresponding to the characteristic is equal to: W К W W W о The coefficients of the transfer function W can be found using the method described below. Bringing the expression for W about to a common denominator, we obtain the desired transfer function of the object without self-alignment. Determination of the coefficients of the transfer function of an object using the Simoyu area method 34 34 In practice, as noted, n.3; m,. The transmission coefficient about K, as always, is determined by the formula 9. To simplify the calculations, we normalize the acceleration curve of the object in the range - according to the formula. For a normalized curve ~ with a single input action about K. Let's write the inverse expression of the transfer function 6 and expand it into an infinite series in powers of p: mn about SSS b WL 7 Bringing 7 to a common denominator and equating the coefficients at 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 with m SSS 9 equations. 35 35 So, system 8 or 9 allows you to determine the coefficients of the transfer function 6 through the still unknown expansion coefficients S. To determine the latter, consider the Laplace image of the deviation of the normalized transient response from the steady state value: L about ( ~ ) L() L( ~ ) [ W р ] From we find W rev ( L[ ~ ]), or taking into account the definition of the Laplace transform 3: W rev [ ~ ] ed Expanding the function e into a power series: e!! 3 3 L L, 3!! we can represent the integral in the expression as a sum of integrals: ~ e d ~ d d ~ d! ~! ~dL! Substituting the expansions 7 and β, multiplying the power series from and equating the coefficients at the same powers of p in the resulting relation, we obtain the following expressions for the coefficients S. 36 36 3!! ~, 6 ~ ~, ~, ~ d i S S d S S S S d S S S d S S d S i i i LLLLLLLLLLLLLL In practical calculations, integrals 3 are determined by numerical methods. For example, when using the trapezoid method, the expressions for the coefficients S become: 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 values. S is the area weighted with the weight function S and so on. Thus, 37 37 coefficients S are some weighted areas, which determines the name of the method. If during the calculations the -th coefficient S turned out to be negative, it is necessary in model 6 to reduce n by one or increase i.e. reduce the difference n-m. The functional diagram of a closed ASR has the form of Fig. 9 set S x H SU FU IM RO OR IE F Automatic regulator Fig. 9. Object of regulation 9 is marked: Z - the setter of the controlled variable serves to set its desired desired value; SU - comparing device, generates a mismatch signal; ass FU - forming device, serves to form the law of regulation in electrical regulators together with IM; IM - actuator, drives the RO; 38 38 RO - regulatory working body, serves to change the regulatory impact x; OR itself is 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 related both to the object and to the controller. In those cases when the measuring element is used to remove the time characteristic, it is referred to the object. Thus, the automatic regulator includes a setpoint adjuster that compares the device, the forming device and the actuator ... Classification of regulators by external energy consumption According to this criterion, regulators are divided into regulators of direct and indirect action. In direct action regulators, the energy of the regulated medium itself is used to rearrange the working body. For example, in a direct-acting liquid level regulator, the energy of the liquid, the level of which is regulated, is used to rearrange the working body. Direct acting regulators are simple, cheap, but do not provide high quality regulation. Their disadvantages are also the difficulty of implementing complex regulatory laws and obtaining great efforts to rearrange the working body. In indirect action regulators, the energy of an external source is used to rearrange the working body, according to the form of which 39 39 distinguish between electric electronic, pneumatic, hydraulic, combined regulators. Electric regulators have a number of advantages. Their main disadvantage in the usual design is the inability to use in fire and explosive environments. Pneumatic regulators are deprived of this shortcoming. The main advantage of hydraulic regulators is the increased power of the actuator with relatively small dimensions. Combined controllers allow you to combine the advantages of different types of controllers. For example, electro-pneumatic systems combine the advantages of electric regulators with the ability to operate pneumatic actuators in flammable and explosive environments. In recent years, programmable controllers have found widespread use for the implementation of local automation systems. The choice of the type of regulator is dictated by various considerations: the nature environment, working conditions, special requirements..3. Classification of regulators according to the law of regulation Under the law of regulation understand the equation of the dynamics of the regulator. Five typical control laws are known: proportional P, integral I, proportional-integral PI, proportional-differential PD and proportional-integral-differential PID. Proportional static controllers Equation of the dynamics of the P-controller K 5 40 4 where is the mismatch of the controlled value, ass x is the control action more precisely, the increment of the control action relative to the constant component, therefore it is more correct to write x - x in 5 instead of x, but x is usually omitted, K is the transfer coefficient P of the regulator. As we can see from 5, the regulatory effect of the P controller is proportional to the mismatch, i.e. The P controller is an inertialess link with a 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, the ACP with the P controller has good dynamic properties. The disadvantage of systems with a P regulator is the presence of a static error. For a single controller, the value of this error is determined from the controller equation: F K K 41 4 FK ZCF F K about Kob K p, where perturbation. К ЗCF - closed-loop system transfer coefficient by As you can see, the static error in a system with a P controller is inversely proportional to its transfer coefficient, the limiting value of which is determined by the required stability margin of the closed ACP. Proportional controllers are used in the automation of low-inertia control objects, when the value of K can be chosen by an error. large enough to reduce the static Integral astatic regulators the control action in this case is proportional to the integral of the mismatch. The transfer coefficient of the I-controller K d / d has the meaning of the rate of change of the regulatory action per unit of mismatch. Transfer function: K W Frequency transfer function: 42 4 K K W j j e The advantage of the And controller is the zero static error. It follows from 6 that this error is equal and vanishes in statics. d / d K At the same time, since the PFC of the AND controller ϕ π, the system with the AND controller has very poor dynamic properties, because this controller introduces a negative phase shift in phase π into the system. Integral controllers can only be used in the automation of almost inertia-free objects. ACP with AND controller and plant without self-alignment is structurally unstable, π j i.e. unstable at any controller settings. Proportional-Integral Controllers The regulation law of a PI controller can be written in two forms: K K d K d 7 T The control action of a PI controller is the sum of the P and I components with proportionality coefficients K and K. Comparing the two forms of writing the control law, we obtain: K , K T I I 43 43 where T and isodrom time. K >> Transfer function and frequency transfer function: W W K j K K K, K e I K jrcg K From the last expression it can be seen that in the region of low frequencies at K PI the controller behaves like an AND controller. At high K frequencies, K >>, i.e. The PI controller behaves like a P controller. This allows the PI controller to combine the advantages of an AND controller in statics and a P controller in dynamics. The physical meaning of the isodrom time can be explained by the transient response of the PI controller fig. As can be seen from this figure, T I is the doubling time of the P component of the PI control action, or, equivalently, the time by which the PI control action leads the AND control action. The value of T and characterizes the speed of integration. The more T and the slower the integration speed. With T & PI, the controller becomes a P controller. K x PI I K P I Fig.. 44 44 So, ASR with a PI controller has a zero static error due to the presence of an AND component in the control law. This is true for all regulators with an AND component. As can be seen from the PFC of the PI controller in Fig., in the region of operating frequencies 3 ϕ slave π Fig.. of the operating frequencies, the PI controller introduces a negative phase shift of approximately -3 into the system. This is much less than the I controller, but more than the P controller. Therefore, the dynamic properties of an ASR with a PI controller are much better than with an I controller, but worse than with a P controller. Proportional - differential regulators The law of regulation of an ideal PD regulator: d d K K K P, 8 d d where K, K are the coefficients of proportionality of the P- and D- components of the control law. T P lead time. Transfer and frequency transfer functions: W W K K j K K K e P, K jrcg K 45 45 It can be seen from the last expression that at low frequencies the PD regulator behaves like a P regulator, and at high frequencies it behaves like a differentiator. Since an ideal differentiating link is physically unrealizable, real PD controllers use a real inertial differentiating link. 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, ASR with a PD controller also has a static error. As can be seen from the PFC Fig.3, ϕ π ideal -3 real slave 3. In the region of operating frequencies, the PD regulator introduces a positive phase shift into the system, increasing its stability margin. Therefore, an ASR with a PD controller has the best dynamic properties. For the same reason, the value of K can be chosen larger than in the case of P 46 46 regulator. Therefore, the static error in an ASR with a PD controller is less than in a system with a P controller. However, PD regulators are practically not used, because in the presence of high-frequency interference superimposed on a 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 lead time, we can say that T P is the time for which the regulatory action of the PD controller is ahead of the regulatory action P of the controller 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 I Transfer functions of the ideal and real PID controllers: 47 47 WW K K K K K K K I P, Frequency Transfer Function of an Ideal PID Controller: .5 in the area of operating frequencies PID controller is the same as ϕ π ideal work real π 5. and P regulator, does not introduce a negative phase shift into the system. In order to increase the noise immunity of the PID controller, in practice, the ratio of lead time/isodrome time 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 the static error is unacceptable, the controller must contain an AND term. In the order of deterioration of the 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 controllers are practically not used, and PI controllers are used with a restriction of 3. In practice, PI and PID control laws are most widely used. 3. Calculation of regulator settings in linear continuous systems [ 4] 3. Quality of regulation 6. Main indicators of quality. Maximum dynamic deviation dyn - the largest deviation of the controlled variable from its set value in the transient process Index dyn m set In a stable ACP, the first deviation is the maximum. dyn characterizes the dynamic accuracy of regulation. Residual deviation residual non-uniformity ct - absolute static control error, defined as the difference between the steady value of the controlled variable and its set value: 49 49 ct set ref Static mode value. m st characterizes the accuracy of regulation in the set ass dyn 3 δ st Fig Degree of attenuation ψ - the ratio of the difference between two adjacent amplitudes of oscillations directed on one side of the steady value line, to the larger 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 that allow assessing the quality directly from the transient curve, for 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 a transient curve at hand. Such criteria, in particular, include integral quality criteria representing integrals over time 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 ratio: I lin d mouth From a geometric point of view, the criterion I lin is the area between the curve and the line mouth. The value of I lin depends on all quality indicators, except for Art. In this case, with a decrease in dyn, etc. By improving the quality of regulation, the value of Ilin decreases, and with an increase in the oscillatory process of the transient, Ilin also decreases, although the quality of regulation deteriorates. So, a decrease in Ilin 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, such controller settings can be considered as the best, at which the value of Ilin 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 control object with self-leveling and PI controller I lin, 3 K i.e. the minimum I lin is achieved at the maximum of the integral component of the regulatory action, or, which is the same, the best quality of the transient process is achieved at the maximum K. For oscillatory transients, other integral criteria are used, for example, I mod set d, but this criterion cannot be calculated through the coefficients of the differential equations. This shortcoming is deprived of the quadratic integral criterion I quarter: I quarter mouth d 3. 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 transient processes. On the contrary, processes with a short control time can be obtained by increasing the dynamic error. Therefore, regarding the desired values of quality indicators in a closed ACP, a compromise decision has to be made. Transient processes with certain quality indicators are recommended when calculating the ASR as typical ones. In the method of extended frequency 52 5 characteristics The main indicator of quality is the degree of attenuation ψ, i.e. fluctuation of the transient process, since this indicator characterizes the stability margin of the ASR. Processes for which ψ,75,9, i.e. the third oscillation 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 of the controller settings, are called optimal in the sense of the specified criterion. For example, in the method of extended frequency responses, the task is to select the controller settings in such a way that, in addition to the given oscillation of the transient process, the minimum value of the criterion I lin is provided. Such a process is optimal in the sense of criterion I lin. Simplified formulas for calculating regulator settings. simplified formulas are given for determining the settings of regulators that provide a given oscillation of the transient process. The formulas are derived from the results of ACP modeling. Static objects are represented by a model of an inertial link with a pure delay 8, astatic objects by a model of an integrating link with a delay 3 Lecture 3 Mathematical description of control systems In control theory, in the analysis and synthesis of control systems, they deal with their mathematical model. The mathematical model of the ACS 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) regulate the parameters of the technological process; 2) suppress noise Equations of dynamics and statics. Linearization At a certain stage of development and research of an automatic control system, its mathematical description is obtained, a description of the processes occurring in the system METHODOLOGICAL INSTRUCTIONS for homework at the TCB course Study of a nonlinear automatic control system DEFINITION OF INITIAL DATA Initial data for homework are given Fundamentals of Management Theory Doctor of Technical Sciences Mokrova Natalia Vladislavovna Dynamic characteristics of regulated objects 1. Time characteristics. acceleration curve. Pulse transition function. 2. Solution of differential FGBOU VPO "Omsk State Technical University" SECTION II CONTINUOUS LINEAR AUTOMATIC CONTROL SYSTEMS Lecture 4. DYNAMIC LINKS. GENERAL CONCEPTS, TIME CHARACTERISTICS AND FREQUENCY Practical lesson TRANSFER FUNCTION FREQUENCY CHARACTERISTICS Goals and objectives of the work As a result of mastering the topic, the student should be able to obtain an operator equation from a given differential equation; Lecture 5 Automatic regulators in control systems and their settings Automatic regulators with typical control algorithms relay, proportional (P), proportional-integral (PI), Calculation of the dynamic characteristics of linear automatic control systems Determine the weight function g(t) and the transition function h(t) of a linear automatic control system 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 installations are referred to as standard control objects. For Lecture 8 33 ONE-DIMENSIONAL STATIONARY SYSTEMS APPLICATION OF THE FOURIER TRANSFORMATION 33 Description of signals and systems Description of signals To describe deterministic signals, the Fourier transform is used: it Federal State Budgetary Educational Institution of Higher Professional Education KAZAN NATIONAL RESEARCH TECHNICAL UNIVERSITY them. A.N.TUPOLEVA-KAI Department of Television Lecture 4 Typical dynamic links Automatic control systems are conveniently represented as a connection of elements, each of which is described by an algebraic or differential equation LABORATORY WORK 5 TYPICAL LINKS OF AUTOMATIC SYSTEMS The purpose of the work is to study the dynamic properties of 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 LINKS OF SYSTEMS 1. Typical links of systems: characteristics and equations; physical models. Lecture plan: UDC: 62-529 AUTOMATIC CONTROL 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 Deterministic Models Continuously deterministic models are used to analyze and design dynamic systems with continuous time, the process of 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 response of the signal Amplitude-frequency and phase-frequency spectra Spectral characteristics Autumn semester of the academic year Topic 3 HARMONIC ANALYSIS OF NON-PERIODIC SIGNALS Direct and inverse Fourier transforms Spectral characteristic of the signal Amplitude-frequency and phase-frequency spectra 4. MEMBRANE TRANSITION RESPONSE 4.1 Time characteristics of a dynamic system 64 Lecture 6 OPERATOR METHOD OF ANALYSIS OF ELECTRIC CIRCUITS Plan Laplace transform Properties of Laplace transform 3 Operator method of analysis of electrical circuits 4 Definition of the original from the known Seminar 4. ANALYSIS OF AUTO-OSCILLATIONS BY THE METHOD OF HARMONIC LINEARIZATION Statement of the problem A closed system with one non-linear element is considered. g F (z W (s x Fig.) Federal Agency for Education State Educational Institution of Higher Professional Education Vladimir State University Department of Plastics Processing Technology UDC Fulfilled by: Accepted by: Umarov D. 1-14 IKSUTP Abdurakhmanova M.I. Stability Analysis of ACS The practical suitability of control systems is determined by their stability and acceptable quality of control. Under 54 Lecture 5 FOURIER TRANSFORM AND SPECTRAL METHOD OF ANALYSIS OF ELECTRIC CIRCUITS 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 Regulating the power supply in each of the steam generators (SG) is reduced to maintaining a material balance between steam removal, blowdown and supply Mathematical schemes: D-schemes Continuously deterministic models are used to analyze and design dynamic systems with continuous time, the process of functioning of which is described by 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 control and control object. Lecture 5. 8.3. ANALYSIS OF AUTOOSCILATIONS BY THE METHOD OF HARMONIC LINEARIZATION 8.3.. Statement of the problem A closed system with one non-linear element is considered. F W s x Learning free movement Institute Direction of training AVTI 70404 Management in technical systems Bank of tasks for a special part of the entrance examination to the master's program Exam ticket task 6 (5 points) Topic Topic 8 DISCRETE ACS Lecture 7 General concepts and definitions of the theory of discrete ACS. 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 The frequency characteristics of ACS characterize the response of systems to a sinusoidal input action in a steady state. Frequency features include: THE THEORY OF STABILITY OF LINEAR SYSTEMS 1. Basic terms and definitions Any ACS is always affected by external perturbations that can disrupt its normal operation. A properly designed ACS should 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 Determining the parameters of typical dynamic links Robotics RAR1300 Sergei Pavlov TTÜ Virumaa Kolledž Drive control Control of the movement of a working machine or machine means control of the position, speed and acceleration of a system that TAU Practical exercises Assignments for control work and guidelines for its implementation Practical lesson AFCH, LAH, transient and weight characteristics of typical dynamic links Most Lecture 6 CIRCUITS OF PERIODIC NON-SINUSOIDAL CURRENT Plan Trigonometric form of the Fourier series Fourier series in complex form Complex frequency spectrum 3 Powers in non-sinusoidal current circuits Coefficients, SEMINAR Basic concepts. Compilation (derivation) of a differential equation. The concept of solving a differential equation. Solution by the method of separable variables. Solving a linear differential equation Fundamentals of circuitry BASICS OF CIRCUIT ENGINEERING...1 1. BASIC PROVISIONS...1 2. AMPLIFICATION OF WEAK SIGNALS...6 3. AMPLIFICATION OF STRONG SIGNALS...14 4. BASICS OF MICROCIRCUIT ENGINEERING OF AMPLIFIERS...18 1. Basic provisions Fundamentals of Management Theory Doctor of Technical Sciences Mokrova Natalia Vladislavovna Lecture 7 Non-linear automatic control systems 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 CIRCUITS Plan Operator input and transfer functions Poles and zeros of functions of circuits 3 Conclusions Operator input and transfer functions The operator function of a circuit is called I Study of the dynamics of typical automation links 1 Ideal amplifier (zero-order aperiodic link - AP-0) and real amplifier (first-order aperiodic link - AP-1) Purpose of work: to investigate Adjustment and adjustment of automatic regulators. 1. Special cycle 1.1. Introduction The main stages and dates in the development of automatic control. Before 1600 Float control system Laboratory work 1 1 DYNAMIC CHARACTERISTICS OF TYPICAL LINKS 1. The purpose of the work Ministry of Education of the Republic of Belarus Educational 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 (AED). PARAMETERS AND CHARACTERISTICS OF AED 1. 1. General information about analog electronic devices (AED), principles of their construction Analog signals Laboratory work 1 1 TYPICAL UNITS OF ACS 1. Purpose of the work 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 control them, you must have UDC 681.52 ALGORITHMS FOR SOLVING THE IDENTIFICATION PROBLEM N.V. Plotnikova, N.S. Kalistratova, O.N. Malyavkin Recently, in connection with the presentation of ever higher requirements for management processes in various Topic 2. Basic concepts and definitions in the theory and practice of automatic control of life support parameters (2 hours) In order to ensure the normal operation of the regulated object (OR) 54 Lecture 5 Fourier transform AND SPECTRAL METHOD FOR ANALYSIS OF ELECTRIC CIRCUITS Plan Spectra of aperiodic functions and Fourier transform 2 Some properties of the Fourier transform 3 Spectral method Zaitsev G. F. Theory of automatic control and regulation Second edition, revised and supplemented Approved by the Ministry of Higher and Secondary Specialized Education of the USSR as a textbook 1.1. Methods for analyzing the nonlinear inertial properties of analog devices In the literature devoted to the analysis of the nonlinear inertial properties of analog devices, several The set of single 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 next operation is shifted relative to the beginning of the previous one. Process control is an organizational and technical problem, and it is solved today by creating automatic or automated process control systems. Goal management technological process it can be: stabilization of some physical quantity, changing it according to a given program, or, in more complex cases, optimization of some generalizing criterion, the highest productivity of the process, the lowest cost of the product, etc. Typical process parameters subject to control and regulation include flow rate, level, pressure, temperature and a number of quality indicators. Closed systems use the current information about the output values, determine the deviation ε( t) controlled variable 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 a deviation control system, is the system shown in Figure 1 for stabilizing the water level in a tank. The system consists of a measuring transducer (sensor) of the 2nd level, a control device 1 (regulator) and an actuator 3 that controls the position of the regulating body (valve) 5.
Rice. 1. Functional diagram of the automatic control system: 1 - regulator, 2 - level measuring transducer, 3 - actuator, 5 - regulator. Flow control Flow control systems are characterized by low inertia and frequent parameter pulsation. Typically, flow control is throttling the flow of a substance using a valve or gate valve, changing the pressure in the pipeline by changing the speed of the pump drive or the degree of bypass (diverting 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, for bulk materials - in Figure 2, b.
Rice. 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 it is required to stabilize the ratio of the costs of two or more media. In the scheme shown in Figure 2, c, the flow to G1 is the leader, and the flow G2 = γ G is the follower, where γ is the flow ratio coefficient, which is set during the static adjustment of the regulator. When the master stream G1 is changed, the FF controller proportionally changes the slave stream G2. The choice of the control law depends on the required quality of parameter stabilization. Level control Level control systems have the same features as flow control systems. In the general case, the level behavior is described by the differential equation D(dl/dt) = G in - G out + G arr, where S is the area of the horizontal section of the 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 the medium increasing or decreasing in the tank (may be 0) per unit time t. The constancy of the level indicates the equality of the amounts of supplied and consumed liquid. This condition can be provided by influencing the supply (Fig. 3, a) or flow (Fig. 3, b) of the liquid. In the version of the regulator shown in Figure 3, c, the results of measuring the supply and flow of liquid are used to stabilize the parameter. The pulse on the liquid level is corrective, it eliminates the accumulation of errors due to the inevitable errors that occur when the flow and flow change. The choice of the control law also depends on the required quality of parameter stabilization. In this case, it is possible to use not only proportional, but also positional controllers.
Rice. 3. Schemes of level control systems: a - with an effect on the supply, b and c - with an effect on the flow 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) = G in - G out + G arr, where V is the volume of the apparatus, p is the pressure. The pressure control methods are similar to the 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 physical and chemical parameters of the process and the design of the apparatus. A feature of such a system is a significant inertia of the object and often of the measuring transducer. The principles of implementation of temperature controllers are similar to the principles of implementation of level controllers (Fig. 2), taking into account the management of energy consumption in the facility. The choice of the control law depends on the inertia of the object: the larger it is, the more complex the control law. The time constant of the measuring transducer can be reduced by increasing the speed of the coolant, reducing the thickness of the walls of the protective cover (sleeve), etc. Regulation of product composition and quality parameters When regulating 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 control 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.
Rice. 4. Scheme of the product quality control system: 1 - object, 2 - quality analyzer, 3 - extrapolation filter, 4 - computing device, 5 - regulator. The computing device 4, using a mathematical model of the relationship between the parameters Y(t) and Y(ti ), continuously evaluates the quality index. The extrapolation filter 3 provides an estimated product quality parameter Y(ti ) between two measurements. On universal machines, the control of the parameters of the technological process and the machine is carried out by the machine operator. He also makes decisions on equipment restructuring, equipment shutdown, coolant supply, etc. Maintaining the operating parameters of the GPM equipment (flexible production module) or automatic line is carried out control system(Fig. 12.1), which includes means of monitoring and diagnosing, which allows, when using the GPM, to refuse the personnel directly involved in the technological process. The PMG control system uses two sources of information: a program for monitoring deviations from the normal functioning of the PMG and information coming from diagnostic devices, such as feedback sensors that measure the movement parameters (speed, coordinates) of the working bodies of the machine and its auxiliary mechanisms or automation devices. Rice. 12.1. Additional means designed to perform the functions of an operator are combined into a system that includes control and measuring and diagnostic devices and devices (with sensors for determining the value of monitored parameters), devices for collecting and initial processing of information and decision making. In case of replacement of the operator, the system should: monitor the operation of the mechanisms of the GPM, the progress of the working process, the quality of the finished product, detect deviations from the normal the functioning of the GPM, including those that have not yet led to failures and failures, but in the future may become their cause; fix failures and failures; to form 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 operation of the GPM, call the serviceman and inform him of information about the reason for the deviation from normal functioning. The machine tool maintenance system consists of several subsystems that work together or autonomously, depending on design solutions or production conditions. These include the subsystem for monitoring the state of the cutting tool, the subsystem for quality control, the subsystem for monitoring the functioning of machine mechanisms and the 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). Small axial tools (drills, taps, end mills with a diameter of up to 6-8 mm), as well as other tools, are subjected to periodic control, if the current control of its condition is impossible or impractical. To implement this procedure, a command to stop the machine must be given. The control device can be located in the working area of the machine, on the node that carries the tool, in the tool magazine. The measurement method is usually direct, using inductive, electromechanical or photoelectric sensors. On fig. 12.2 shows a diagram of monitoring the state of tool 2 on a multi-purpose machine 6. After processing workpiece 1 and retracting the tool, probe 3 comes into contact with the drill. When the tool breaks, the position of the probe changes, as a result of which lever 4 turns and ceases to act on the electric contact sensor (limit switch) 5. At the signal of the latter, the control system gives a command to stop processing and replace the tool with an understudy or call the adjuster. As a sensor, a BVK type sensor or a Hall sensor can be used, which significantly increases its service life and trouble-free operation. For status monitoring cutting tool on the lathe use the method of measuring the coordinate of the vertex of the cutter. After of the next pass, the cutter moves to the control position, and if there is no electrical contact between the cutter tip and a special contact plate, a signal is given to interrupt the technological process of processing, followed by a tool change or a call for an adjuster. head; 3- tool; 4 - machine spindle Rice. 12.2. Scheme of control of the cutting tool on a multi-purpose machine Rice. 12.3. Placement of the measuring head on a multi-purpose machine: 1 - table; 2- measuring For control the tool located in the magazine of the multi-purpose machine, television cameras made on the basis of CCD matrices are used, 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 identify 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 short, which allows the measurement to be carried out without stopping. Regardless of the tool size, the camera is always in the same position. Periodic control is carried out and if necessary, enter a correction into the control program in case of replacing a worn or broken tool with an understudy. To do this, by means of a measuring head with a touch sensor on turning machine tools measure the reach of cutters, on multi-purpose ones (see Fig. 12.3) - the length and diameter of the tool. The measuring head occupies a certain position in the working area of the machine: on the multi-purpose table or on the headstock of a lathe. Such measurements make it possible to "bind" the tool to the machine's coordinate system, obtain information about the presence of the tool in the spindle, control its wear and integrity. The current state control is subjected to axial tool with a diameter of more than 8... 12 mm, as well as cutters and cutters different kind. Control is carried out in the cutting process; its purpose is to prevent emergency situations that occur when a tool breaks suddenly. The monitoring method is mainly indirect (by torque, main drive motor current, load, acceleration, etc.). So, when the tool becomes blunt, the cutting force increases, and, consequently, 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 value of the gear ratio of the kinematic chain between the engine and the spindle assembly. Before the start of each cutting cycle, the idle load must be measured and stored. Measurement of the axial load on the lead screw of the machine using strain gauge, the screw built into the support allows you to monitor the wear of the tool, as well as the change in the mode of its operation during the 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 from interference. The sensor is of low inertia, i.e. can register fast-changing loads caused, for example, by uneven rotation of the lead screw within one revolution. To measure the load experienced by turrets, spindle boxes and spindle assemblies, strain gauges are built into them, made in the form of strain bearings. The rotation of each bearing ball under the appropriate load causes local deformation of the outer ring, perceived by strain gauges placed in a groove on the outer surface of the ring. When processing the output signal of the sensor, one should take into account its pulsation, the frequency of which is directly related to the spindle speed. To measure the load acting on various nodes, it is widely used overhead piezo sensors(Fig. 12.4). Their sensitivity is higher than that of thermistors, and the bandwidth allows you to fix fairly fast changes in the load acting on the tool. Structural solutions implemented when using such sensors are different. For example, they are built into a slab placed under Rice. 12.4. Piezo sensors for measuring cutting force: but concept of measurement; b - its constructive implementation; (1 - elastic element; 2 - piezoelectric sensor; 3 - machine part; 4 - contact surfaces, / - measuring base of the sensor; R,- tension-compression force; R, - pressing force under the turret head of a lathe. For creating preload, the piezoelectric sensor should protrude above the surface by 10 ... 15 microns. Tool wear can be determined by the magnitude of the elastic wave acceleration, which propagates from the cutting zone to the sensor installation site (1accelerometer), fixing vibroacoustic emission. If the tool is rotating, the sensor installed on the machine table; if the tool is stationary, and the workpiece rotates - on the tool holder or on the body of the turret. When using such sensors, it is necessary for tools each type to pre-determine the frequency range, in which shows the relationship between the parameters to the greatest extent vibroacoustic emission with wear or breakage of the tool. The number of joints between the workpiece (or tool) and the sensor should be reduced as much as possible, as they have a deforming effect (weaken vibrations), which makes measurements difficult. The operating time of the tool is measured timer, plunging and cutting time - force sensor or acceleration(the moments of the beginning and end of the cutting process are fixed), the magnitude of the components of the cutting forces - pressure sensors in hydrostatic spindle bearings or magnetoelastic sensors, measuring cutting torque, EMF - millivoltmeter, electrical resistance of the contact between the workpiece and the tool - ohmmeter. It should be taken into account that the reliability of automatic control of the state of the cutting tool is relatively low. The reasons may be microcracks in the cutting part, heterogeneity and local fluctuations in the hardness of both the processed and tool material, and other factors that cannot be determined by automatic means. Therefore, it is recommended double control tool 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 tool are not developed. The designer chooses a commercially available or orders a special sensor, the characteristics of which correspond to the task, and embeds it in the appropriate area of the machine. Various devices used in the cutting tool condition monitoring subsystem are described in the literature. One such device is the Monitor system used in the GPM. Monitoring system with a contact indicator (see Fig. 12.5) is based on information coming from the machine feed drive and sensors that record the movement of the table and spindle assembly. Three arrays of data are entered into the Monitor: 1) constants that determine the device setting on a particular machine, the type of control and the signal level from the sensor (for example, current); 2) instrument questionnaires containing permanent data on the characteristics of specific instruments; 3) a control program compiled for each processed workpiece. Data is entered using the keyboard; information is displayed on a display screen or a digital display. Rice. 12.5. Monitoring scheme with contact indicator: 1 - contact indicator; 2 - workpiece (detail); 3 - control panel; 4 - information input device; 5 - terminals; 6 - head control computer; 7- counter; 8 - impulse lines TO quality control subsystem devices(Fig. 12.6) includes active control devices (PAK) used in mass and large-scale production, and touch sensors used in mass production. If necessary automatic control sizes, shapes and the accuracy of setting the workpiece and (or) the machined part on different Rice. 12.6. Typical schemes for controlling the accuracy of processing when using PAC (o) and auto-adjustment ( 6)
processing stages use PAK, which can be located both in the working area of the machine (Fig. 12.6, but), and with automatic cycle control. At the same time, two information flows are organized in the machine control system. The first provides the processing process according to a given program, the second is used to adjust the level of adjustment. The operator is also involved in the management of the processing process, his task is to adjust the level of machine settings and active controls. In the second flow of information, there are two control loops: the loop / refers to the automatic control system by means of a HSS or auto-adjuster (Fig. 12.6, b), contour II- to the system of manual adjustment of the processing process using a conventional measuring device. The schemes are conditionally marked: TO - technological operation; IO - the executive body of the machine; MP - mechanism for adjusting the machine; BUT for roughness processed For dimensional control workpieces and (or) parts (and in some cases for the counter-surface) on CNC and GPM machines are measuring heads (MG) (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 magazine, from where the manipulator moves it to the spindle (on drilling-milling-boring machines) or turret head (on lathes). Rice. 12.7. Measuring head: 1 - probe tip; 2 - probe; 3- transmission mechanism; 4 - probe balancing mechanism; 5 - electrical contact; 6 - touch signal generator; 7 - signal sent to the electronic unit or to the transmitter With the 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 by a special circuit, it enters the CNC through the electronic unit, where the received data is compared with the given values of the corresponding parameter. Similar IGs are used to control allowances and basing the workpiece, for intermediate control of workpieces on the machine during processing and output control of the machined part on the machine. At the same time, 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 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; their development is carried out by special design organizations. The equipment designer builds a commercially available or custom instrument into the equipment. However, he must take care of the development of algorithms for the joint functioning of the machine and the control device (measurement, calculations, decision recommendations). The stability of the machining process on modern machine tools with program control makes it possible not to build measuring devices into them, but to use the coordinate measuring machine (CMM) installed in the workshop for periodic quality control of machining. In this case, the machine operator or adjuster installs the machined part on the CMM, measures the controlled parameters, and, depending on the results obtained, directs the part for additional processing or a subsequent technological operation, and, if necessary, makes adjustments to the machine. Subsystem for monitoring the functioning of machine mechanisms(Fig. 12.8) includes a number of measuring devices that detect deviations from the norm (for example, overheating of the movement of the main drive is recorded by a temperature sensor). At the output of these devices, Rice. 12.8. The structure of the subsystem for monitoring the functioning of mechanisms; IU, IU 2 ... IU - measuring devices; D - sensor; POS - primary signal processing; USO - device for collecting and processing information; UPR - decision making device; URR - decision 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 is subsequently implemented 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 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 operation of the machine with minimal operator involvement. There are devices for diagnosing hydraulic drives of machine tools, rolling bearings, gearboxes, feed boxes and other similar devices. Control and compensation of typical deformation units of the machine make it possible to ensure the accuracy of processing during long-term operation. So, due to heating, the spindle assembly is displaced, which leads to a decrease in processing accuracy. Compensation in this case is based on the periodic measurement of the actual displacements of the assembly parts in space. With the help of the IG installed on the machine spindle, the position of the reference surface on its table is measured, or with the help of the IG for tool control installed on the machine table, the position of the reference mandrel in the spindle is measured. The difference between the results of successive measurements determines the displacement of the spindle 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 machine designer, usually from mass-produced or special elements, although in some cases it is necessary to develop special diagnostic devices. Bellows membrane relays are often used as such devices. Basic concepts and definitions ............................................... ................................................. ..... 4 1. Structural diagrams of the object of regulation .............................................. .............................. 13 2. Sequence of choosing an automation system............................................... ............... 15 3. Regulation of the main technological parameters.................................................... ........... 17 3.1. Flow rate regulation, flow ratio .............................................................. ............... 17 3.2. Level control .................................................................. ................................................. ..... 19 3.3. Pressure regulation .................................................................. ................................................. .21 3.4. Temperature control .................................................................. ............................................. 22 3.5. pH regulation .................................................................. ................................................. ............ 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 processes for the movement of liquids and gases .................................................... 27 4.2. Automation of separation and purification of heterogeneous systems............................................... 31 5. Automation of thermal processes............................................... ......................................... 32 5.1. Mixing heat exchanger control .................................................................. ................... 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. Drying process in a drum dryer .............................................. ....................... 66 6.6.2. Automation of Fluidized Bed Dryers .............................................................. ................ 69 7. Automation of reactor processes.................................................... ....................................... 71 Regulation of process reactors .................................................................. ................................... 71 Control questions on the discipline to prepare for the exam .......................................................... .. 74 Literature................................................. ................................................. ............................................... 76 Basic concepts and definitions Automation is a technical discipline that deals with the study, development and creation of automatic devices and mechanisms (i.e. works without direct human intervention). Automation is a stage of machine production, characterized by the transfer of control functions from a person to automatic devices (technical encyclopedia). TOU- technological object of control - a set of technological equipment and the technological process implemented on it. ACS- automated control system is a man-machine system that provides automated collection and processing of information necessary for optimal control in various areas 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 automatic control systems. These fundamentally new systems are called automated process control systems - APCS. Creation of automated process control systems became possible due to the creation of computers of the second and third generations, increase in their computing resources and reliability. APCS- call the ACS for the development and implementation of control actions on the TOU in accordance with the accepted control criterion - an indicator that characterizes the quality of the work of the TOU and takes certain values depending on the control actions used. ATC- a set of jointly functioning TOU and APCS forms an automated technological complex. APCS differs from local ACS: Better organization of information flows; Almost complete automation of the processes of obtaining, processing and presenting information; Possibility of active dialogue between the operating personnel and the Department of Management in the process of management in order to develop the most effective solutions; A higher degree of automation of control functions, including the start and stop of production. From control systems for automatic production such as workshops and automatic plants (the highest level of automation), automated process control systems differ in a significant degree of human participation in control processes. The transition from automated process control systems to fully automatic production is constrained by: Imperfection of technological processes (presence of non-mechanized technological operations; Low reliability of technological equipment; insufficient reliability of automation and computer technology; Difficulties in the mathematical description of tasks solved by a person in automated process control systems, etc.) Global goal of management TOU with the help of APCS consists in maintaining the extreme value of the control criterion when all the conditions that determine Rice. one. Typical functional structure of process control systems. 1
– primary information processing (I); 2
– detection of deviations of technological parameters and indicators of the state of the equipment from the established values (I); 3
- calculation of non-measurable quantities and indicators (I); 4
– preparation of information and implementation of exchange procedures with related and other automated control systems (I); 5
– operational and (or) on-call display and registration of information; 6
- determination of the rational mode of the technological process (U); 7
– formation of control actions that implement the selected mode. the set of admissible values of control actions. In most cases, the global goal is broken down into a number of sub-goals; each of them requires solving a simpler control problem. The APCS function is called the actions of the system aimed at achieving one of the private goals of management. Private management goals, as well as the functions that implement them, are in a certain subordination, forming the functional structure of the APCS. APCS functions: 1. Informational - collection, transformation and storage of information about the state of the TOU; presentation of this information to operational personnel or its transfer for further processing. 2. Primary processing of information about the current state of the TOU. 3. Detection of deviations of technological parameters and indicators of the state of the equipment from the set values. 4. Calculation of values of non-measurable quantities and indicators (indirect measurements, calculation of TEP, forecasting); 5. Operational display and registration of information. 6. Exchange of information with operational personnel. 7. ensure the maintenance of extreme values of 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 mode by forming control actions on the TOU (stabilization, program control; program-logical control). Secondary functions provide the solution of intrasystem tasks. To implement the functions of the automated process control system, it is necessary: Technical support; Software; Informational; Organizational; Operational staff. Rice. 2. Technical structure of CTS APCS for operation in supervisory mode. Technical structure of the CTS APCS 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 personnel; 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 complex of technical means (CTS), Means of obtaining information about the current state of the TOU; UVK (controlled computing complex); Technical means for implementing the functions of local automation systems; Executive devices that directly implement control actions on the TOU. The TS complex of many automated process control systems includes mechanical means of automation from the electrical branch of the GSP. A specific component of the CTS is the CTS, which includes the actual computer complex (CC), communication devices for the CC with the object (USO) and with operational personnel. The first and still widespread type of technical structures of automated process control systems is centralized. In systems with a centralized structure, all the information necessary to control the ATK goes to a single center - an operator station, where almost all the technical means of automated process control systems are installed, with the exception of information sources and executive devices. This technical structure is the simplest and has a number of advantages. Its disadvantages are: The need for an excessive number of APCS elements to ensure high reliability; High cable costs. Such systems are expedient for relatively small power and compact ATCs. a complete centralized structure, the core of which is a control micro-computer. Local subsystems via their microcomputers are integrated into a single system by a data transmission network. The number of terminals required for ATC control for operational personnel is connected to the network. The APCS software connects all elements of a distributed technical structure into a single whole, which has a number of advantages: The possibility of obtaining high reliability indicators by splitting the automated process control system into a family of relatively small and less complex autonomous subsystems and additional redundancy of each of these subsystems through the network; Application of more reliable means of microelectronic computer technology; Great flexibility in the composition and modernization of hardware and software, etc. Most of the APCS functions are implemented in software, so the most important component of the APCS is its software (SW), i.e. a set of programs that ensure the implementation of APCS functions. The APCS software is divided into: Special. The general software is delivered complete with computer equipment. Special software is developed when creating a specific process control system and includes programs that implement its information and control functions. The software is created on the basis of software (MS). 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 APCS, a special MO is created, which includes: Algorithm for collecting, processing and presenting information; Control algorithms with mathematical models of the corresponding control objects; Algorithms for local automation. All interactions both within the APCS and with the external environment are various forms of information exchange, data and document arrays are needed that ensure the performance of all its functions during the operation of the APCS. The rules for the exchange of information and the information itself circulating in the APCS form the information support of the APCS. The organizational support of the APCS is a set of descriptions of the functional, technical and organizational structures of the system, instructions and regulations for operational personnel, which ensures the specified functioning of the APCS. The operational personnel of the automated process control system consists of technologists-operators who manage the TOU, operational personnel ensuring the functioning of the automated process control system (computer operators, programmers, maintenance personnel for the CTS equipment). The operational personnel of the automated process control system can work in the control loop or outside it. When working in the control loop, the OP implements all control functions or part of them, If the operational personnel works outside the control loop, he will set the operating mode for the automated process control system and monitor its observance. In this case, depending on the composition of the CTS, the APCS can operate in two modes: Combined (supervisory); In the direct digital control mode, in which the UVC directly affects the actuators, changing the control actions on the TOU. The creation of an automated process control system includes five stages: 1. terms of reference (TOR); 2. technical project (TP); 3. working draft (WP); 4. introduction of automated process control systems; 5. analysis of its functioning. At the TK stage, the main stage is pre-project research work(R&D), usually carried out by a research organization jointly with a customer enterprise. The main task of pre-project R&D is the study of the technological process as a control object. At the same time, the purpose and criteria for the quality of the functioning of the TOU, technical and economic indicators of the prototype object, their relationship with technological indicators are determined; TOU structure, i.e. input actions (including controlled and uncontrolled disturbing actions, and control actions), output coordinates and connections between them; the structure of mathematical models of statics and dynamics, the values of parameters and their stability (the degree of stationarity of the TOU); statistical characteristics of disturbing influences. The most time-consuming task at the stage of pre-project R&D is the construction of mathematical models of TOU, which are subsequently used in the synthesis of process control systems. When synthesizing local ASRs, linearized dynamics models are usually used in the form of linear differential equations of the 1st - 2nd order with delay, which are obtained by processing experimental or calculated transient functions through different channels of influence. To solve the problems of optimal control of static modes, finite ratios are used, obtained from the equations of the material and energy balance of the TOU, or the regression equation. In the 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-project research, methods of analysis of automatic control systems are used, studied in the discipline "Theory of automatic control", and methods for constructing mathematical models, which are presented in the course "Computer modeling of objects and control systems". The results obtained at the stage of pre-project R&D are used at the stage preliminary development of process control systems, during which the following works are performed: Selection of the criterion and mathematical formulation of the TOU optimal control problem, 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 built; Development of the functional and algorithmic structure of the process control system; Determining the amount of information about the state of the TOU and VC resources (speed, storage capacity) necessary to implement all the functions of the APCS; Preliminary selection of KTS, primarily UVK; Preliminary calculation of the technical and economic efficiency of process control systems. The central place among the works of this stage is occupied by the mathematical formulation of the problem. chi optimal control of TOU. The remaining tasks of this stage (except for the calculation of technical and economic efficiency) are related to the system engineering synthesis of automated process control systems, in which the analogy method is widely used. The accumulated experience in the development of automated process control systems for 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 TEP, integration and averaging, etc.), as well as typical functions of local automation systems implemented in the automated process control system programmatically (signaling, emergency blocking, regulation with using model laws under the NCU, etc.). The final stage of the conceptual design of the automated process control system is preliminary calculation of technical and economic efficiency the system being developed. It is performed by specialists in economics, however, the initial data for them should be prepared by specialists in automation, so let's consider some key points. The main indicator of the economic efficiency of APCS is the annual economic effect from its implementation, which is calculated by the formula E= (FROM 2 - S 2) - (C 1 - S 1) - En(K 2 - K 1) , where C1 And C2- annual sales volumes of products in wholesale prices before and after the introduction of automated process control systems, thousand rubles; S1 And S2- the cost of production before and after the implementation of the system, thousand rubles; K1 And K2- capital expenditures for ATC before and after the commissioning of the automated process control system, thousand rubles; En– normative sectoral coefficient of efficiency of capital investments in automation and computer equipment, rub/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 its cost. The improvement of these economic indicators is most often achieved by reducing the consumption of raw materials, materials and energy per unit of output due to more accurate maintenance of the optimal technological regime, increasing product quality (grade and, accordingly, prices), increase in equipment productivity by reducing the loss of working time due to unscheduled process shutdowns caused by control errors, etc. At the stage of pre-project R&D, production reserves should be identified that can be used thanks to the use of an automation system. 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 errors of the operating personnel due to untimely detection of pre-emergency situations, then the use of an automated process control system that implements the functions of forecasting 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 the volume of sales and a decrease in the cost of production. 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 is developed, the smaller the reserves, as a rule. However, not all identified (potential) reserves of economic efficiency can be used after the introduction of automated process control systems. The actual efficiency turns out to be less than the potential one due to the non-ideality of the APCS, which manifests itself, in particular, in the incomplete adequacy of the TOU mathematical model, 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 failures of elements of hardware and software, due to which the quality of performance of individual functions and process control systems as a whole decreases, etc. The real effect usually ranges from 25 to 75% of the potential, and, as a rule, the greater the potential effect, the less it is implemented. The main indicator of the technical and economic efficiency of the APCS is the payback period of the system, which is determined by the formula = K 2 - K 1 . (C 2 - S 2) - (C 1 - S 1) It should be no more than the standard, which for the chemical industry is 3 The final stage of the first stage of creating an automated process control system is the development of terms of reference for the design of the system, which should include a complete list of functions, a feasibility study for the development of an automated process control system, a list and scope of research and a schedule for creating the system. When developing non-standard APCS, the first stage accounts for approximately 25% of the total labor intensity, including 15% for pre-project R&D. When replicating automated process control systems, the first stage can be excluded or significantly reduced. The next stage in the creation of a non-standard process control system is the development technical project, during which the main technical solutions are made that implement the required technical specifications. Work at this stage is carried out by research and design organizations. The main content of R&D is the development and deepening of pre-project R&D, in particular, the refinement of mathematical models and formulations of optimal control problems, checking, using computer simulation, the performance and efficiency of algorithms selected for the implementation of the most important information and control functions of APCS. The functional and algorithmic structures of the system are being specified, information links between functions and algorithms are being worked out, and the organizational structure of the APCS is being developed. A very important and time-consuming stage at the TP stage is the development of special software for the system. According to available estimates, the labor intensity of creating special software was close to the total volume of pre-project R&D and amounted to 15% of the total labor costs for the creation of process control systems. At the TP stage, the composition of the CTS is finally selected and calculations are performed to assess the reliability of the implementation of the most important functions of the APCS and the system as a whole. The total labor costs for design are approximately 30% of the costs for the creation of automated process control systems. At the stage of implementation of automated process control systems, installation and commissioning works are carried out, the sequence and content of which are studied in the corresponding course. Labor costs at this stage are about 30% of the total system costs. When developing prototypes of automated process control systems to be further replicated at the same type of TOU, it is important to analyze the functioning of the system, during which the effectiveness of the decisions taken during its creation is checked and the actual technical and economic efficiency of the automated process control system is determined. Any chemical production is a sequence of three main operations 1. preparation of raw materials; 2. actual chemical transformation; 3. selection of target products. This sequence of operations is included in a single complex chemical-technological system (CTS). A modern chemical enterprise, plant or combine, as a large-scale system, consists of a large number of interconnected subsystems, between which there are subordination relations in the form hierarchical structures 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 single whole to obtain a given product or intermediate. Structural diagrams of the regulated object xv(u)⎨ xv(z) One of the stages of designing control systems for technological ⎫ processes - the choice of structure meters of regulators. And the structure of the sys- Rice. 1.1. Structural diagram of the object of regulation. process as an object of regulation. topics, and the parameters of the regulators are determined by the properties of the 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 totality will be denoted by the vector y). These variables in the process of regulation 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 the technology and the capabilities of the control system. As a rule, the variables included in the vector y, are measured directly, but sometimes they can be calculated using the plant model from other directly measured variables. Vector y often called the vector of controlled variables. 2. Variables, by changing which the control system can influence the object for the purpose of control. The set of these variables is denoted by the vector xp(or u) regulatory actions. Usually, changes in the costs of material flows or energy flows serve as regulatory influences. 3. Variables whose changes are not related to the impact of the regulatory system. These changes reflect the influence of external conditions on the regulated object, changes in the characteristics of the object itself, etc. They are called disturbing influences and are denoted by the vector xv or 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 the disturbing effect allows you 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 flow at the outlet of the apparatus; regulating influences can be a change in the steam flow rate in the reactor jacket, a change in the catalyst flow rate and the flow rate of the reaction mixture; disturbing influences are changes in the composition of the raw material, the pressure of the heating steam, and if the pressure If the heating steam pressure is not difficult to measure, then the composition of the raw material in many cases can be measured with low accuracy or insufficiently quickly. The analysis of the technological process as an object of automatic control involves the assessment of its static and dynamic properties for each of the channels from any possible control action to any possible controlled parameter, as well as the assessment of similar characteristics through the channels of communication of 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., to decide which regulatory action should be used to control one or another state parameter. As a result, in many cases (by no means always) it is possible to isolate the control loops for each of the regulated values, i.e., to obtain a set of single-loop control systems. An important element of the synthesis of the ACP of the technological process is the calculation of a single-loop control system. In this case, it is required to choose a structure and find the numerical values of the controller parameters. As a rule, the following typical structures of control devices are used (typical control laws): proportional (P) controller (R(p) = -S1); integral (I) controller (R(p) = -S0/p); proportional-integral (PI) control law (R(p) = -S1 - S0/p) and, finally, proportional-integral-derivative (PID) law (R(p) = -S1 - S0/p - S2 p ). When calculating the system, they check the possibility of using the simplest regulation law, each time assessing the quality of regulation, and if it does not meet the requirements, they switch to more complex laws or use the so-called circuit quality improvement methods. In the theory of automatic control, various methods have been developed for calculating the ASR for given quality criteria, as well as methods for assessing the quality of transient processes for given parameters of the object and the controller. At the same time, along with accurate methods that require a lot of time and manual labor, approximate methods have been developed that make it possible to relatively quickly evaluate the operating parameters of the controller or the quality of transient processes (the Ziegler–Nichols method for calculating controller settings; approximate formulas for estimating integral quadratic criterion, etc.). It might be useful to read:
Exchange of information with adjacent and superior automated control systems. Control functions provide
In connection with the introduction of microprocessor technology, the distributed technical structure of automated process control systems is becoming more widespread, i.e. divided into a number of autonomous subsystems - local technological control stations, geographically distributed over technological control areas. Each local subsystem is of the same type
Rice. 3. Technical structure of the CTS APCS for operation in the mode of direct digital control.
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