Cascade regulation. Unrelated regulation Direct and indirect regulation

15.03.2020

Combined and separate spelling of “also” and “the same way”

Open lesson on the surrounding world on the topic "Crop production" (3rd grade)

Regulation is an artificial change in parameters and coolant flow in accordance with the actual needs of subscribers. Regulation improves the quality of heat supply, reduces excessive consumption of fuel and heat.

Depending on the point of implementation, there are:

1. central regulation - carried out at the heat source (CHP, boiler room);

2. group – at the central heating point or control center,

3. local – for ITP,

4. individual - directly on heat-consuming devices.

When the load is homogeneous, you can limit yourself to one central regulation. Central regulation is carried out according to the typical heat load, typical for the majority of subscribers in the area. Such a load can be either one type of load, for example heating, or two different types with a certain quantitative ratio, for example heating and hot water supply at a given ratio of the calculated values of these loads.

A distinction is made between connecting heating systems and hot water supply installations according to the principle of coupled and unconnected regulation.

With unrelated regulation, the operating mode of the heating system does not depend on the selection of water for hot water supply, which is achieved by installing the regulator in front of the heating system. In this case, the total water consumption for the subscriber installation is equal to the sum of the water consumption for heating and hot water supply. Increased water consumption in the supply main of the heating network leads to an increase in capital and operating costs in heating networks, an increase in capital and operating costs in heating networks, and an increase in electricity consumption for coolant transport.

Associated regulation makes it possible to reduce the total water consumption in heating networks, which is achieved by installing a flow regulator at the input of the subscriber installation and maintaining the flow of network water at the input constant. In this case, with an increase in water withdrawal for hot water supply, the consumption of network water for the heating system will decrease. The lack of fuel during the period of maximum water withdrawal is compensated by an increase in the consumption of network water for the heating system during the hours of minimum water withdrawal.

The connection of subscriber installations according to the principle of uncoupled regulation is used with central high-quality regulation for the heating load, and according to the principle of coupled regulation - with central regulation for the combined load.

For closed heat supply systems with a predominant (more than 65%) housing and communal load and with relation (15), central qualitative regulation of closed systems is used for the combined load of heating and hot water supply. In this case, the connection of hot water supply heaters for at least 75% of subscribers must be carried out according to a two-stage sequential scheme.

The temperature schedule of the central quality control for the combined load of heating and hot water supply (Figure 4) is built on the basis of the heating and household temperature schedule (Appendix).

Before entering the heating system, the network water passes through the upper stage heater, where its temperature drops from to . The water consumption for hot water supply is changed by the RT temperature regulator. Return water from the heating system enters the lower stage heater, where it cools from to . During hours of maximum water consumption, the temperature of the water entering the heating system decreases, which leads to a decrease in heat transfer. This imbalance is compensated during hours of minimum water consumption, when the heating system receives water at a temperature higher than required according to the heating schedule.

We determine the balance load of hot water supply, Q g b, MW, using the formula.

Issues covered in the lecture:

1. What consequences does the equality of the dynamics of direct and cross connections in the ASR of unrelated regulation lead to?

2. What operating frequencies are desirable to have in uncoupled control loops.

3. What is the complex coefficient of connectivity.

4. The principle of autonomy.

5. Condition of approximate autonomy.

Objects with multiple inputs and outputs that are mutually interconnected are called multi-connected objects.

The dynamics of multi-connected objects is described by a system of differential equations, and in Laplace-transformed form by a matrix of transfer functions.

There are two different approaches to automating multi-connected objects: unconnected control of individual coordinates using single-loop ACP; coupled regulation using multi-loop systems in which internal cross-connections of the object are compensated by external dynamic connections between individual control loops.

Figure 1 - Block diagram of unrelated regulation

In case of weak cross-couplings, the calculation of uncoupled regulators is carried out as for conventional single-circuit ACS, taking into account the main control channels.

If the cross-links are strong enough, then the stability margin of the system may be lower than the calculated one, which leads to a decrease in the quality of regulation or even loss of stability.

To take into account all the connections between the object and the controller, you can find an expression for the equivalent object, which has the form:

W 1 e (p) = W 11 (p) + W 12 (p)*R 2 (p)*W 21 (p) / . (1)

This is an expression for the controller R 1 (p), a similar expression for the controller R 2 (p).

If the operating frequencies of the two circuits are very different from each other, then their mutual influence will be insignificant.

The greatest danger is the case when all transfer functions are equal to each other.

W 11 (p) = W 22 (p) = W 12 (p) = W 21 (p). (2)

In this case, the setting of the P-regulator will be two times less than in a single-circuit ACP.

For a qualitative assessment of the mutual influence of control loops, a complex connectivity coefficient is used.

K St (ίω) = W 12 (ίω)*W 21 (ίω) / W 11 (ίω)*W 22 (ίω). (3)

It is usually calculated at zero frequency and the operating frequencies of both regulators.

The basis for building connected regulation systems is the principle of autonomy. In relation to an object with two inputs and outputs, the concept of autonomy means the mutual independence of the output coordinates U 1 and U 2 during the operation of two closed control systems.

Essentially, the autonomy condition consists of two invariance conditions: the invariance of the first output Y 1 with respect to the signal of the second controller X P 2 and the invariance of the second output Y 2 with respect to the signal of the first controller X P 1:

y 1 (t,x P2)=0; y 2 (t,x P1)=0; "t, x P1 , x P2 . (4)

In this case, the signal X P 1 can be considered as a disturbance for Y 2, and the signal X P 2 as a disturbance for Y 1. Then the cross channels play the role of disturbance channels (Figure 1.11.1 and Figure 1.11.2). To compensate for these disturbances, dynamic devices with transfer functions R 12 (p) and R 21 (p) are introduced into the control system, the signals from which are sent to the corresponding control channels or to the controller inputs.

By analogy with invariant ACP, the transfer functions of the compensators R 12 (p) and R 21 (p), determined from the autonomy condition, will depend on the transfer functions of the direct and cross channels of the object and will be equal to:

; , (5)

; . (6)

Just as in invariant ASRs, physical feasibility and technical implementation of approximate autonomy play an important role in constructing autonomous control systems.

The condition of approximate autonomy is written for real compensators, taking into account the operating frequencies of the corresponding regulators:

at w=0; w=w P2 , (7)

at w=0; w=w Р1. (8)

(a) – compensation of the impact from the second regulator in the first control loop

(b) – compensation of the impact from the first regulator in the second control loop

Figure 2 - Block diagrams of autonomous automated control systems

Figure 3 - Block diagram of an autonomous two-axis control system

Questions for self-control:

1. Definition and tasks of automation.

2. Modern process control system and stages of its development.

3. Management and regulation tasks.

4. Basic technical means of automation.

5. Technological process as a control object, main groups of variables.

6. Analysis of the technological process as a control object.

7. Classification of technological processes.

8. Classification of automatic control systems.

9. Control functions of automatic systems.

10. Selection of controlled quantities and regulatory influence.

11. Analysis of statics and dynamics of control channels.

12. Analysis of input influences, selection of controlled quantities.

13. Determination of the level of automation of technical equipment.

14. Control objects and their main properties.

15. Open-loop control systems. Advantages, disadvantages, scope, block diagram.

16. Closed control systems. Advantages, disadvantages, scope, block diagram and example of use.

17. Combined control systems. Advantages, disadvantages, scope, block diagram and example of use.

18. Theory of invariance of automatic control systems.

19. Combined ACP.

20. Typical compensators.

21. Calculation of compensator.

22. What is the condition of approximate invariance.

23. At what frequencies is the compensator calculated under the condition of partial invariance?

24. Condition for the physical realizability of invariant ATS.

25. Cascade control systems.

26. What is an equivalent object in a cascade ACS.

27. What explains the effectiveness of cascade automated control systems.

28. Methods for calculating cascade automated control systems.

29. ASR with additional impulse based on the derivative from an intermediate point.

30. Scope of application of ASR with additional impulse on the derivative.

31. Calculation of ASR with additional impulse based on the derivative.

32. Interconnected regulatory systems. Decoupled regulatory systems.

33. What consequences does the equality of the dynamics of direct and cross connections in the ASR of unrelated regulation lead to?

34. What operating frequencies are desirable to have in uncoupled control loops.

35. What is the complex coefficient of connectivity.

36. Associated regulation systems. Autonomous ACP.

37. The principle of autonomy.

38. Condition of approximate autonomy.

The block diagram of the disconnected control system for a two-dimensional object has the form:

Control error

Control action

Measured controlled quantities

Unmeasured outputs on main channels with transfer function and

Regulators with transfer functions and

Using discrete transfer functions of the controllers of the main and cross channels, we describe the system of disconnected control:

Let us transform system (2.0) by substitution, obtaining an equation for the connection between the system’s outputs and its inputs

(2.2)

In the first equation, we substitute the right side of the second equation:

(2.3)

Similarly, when substituting into the second equation instead of the right side of the first equation, one can obtain the dependence of the output on and .

From equation (2.3) it is clear that each controlled variable depends on both the first input of the system and the second input of the system. Let us show that the stability of the uncoupled system in this case decreases. To do this, we assume that the transfer functions of the object along the main and cross channels are equal to each other and the transfer functions of the regulators are equal to each other.

Then equation (2.3) will take the form:

(2.4)

If there are no cross connections in the object, then the output value depends only on the task in accordance with the following expression:

In accordance with the Nyquist criterion, in order for a closed-loop single-loop system to be stable (if an open-loop system is stable), it is necessary that the AFC hodograph of the open-loop system does not cover the point with coordinates . Based on this, in a disconnected control system, if taken equal to zero, this criterion will be the same, with the only difference being that the coordinates of the critical point will be . Thus, in an incoherent regulatory system, the area of stable regulation is narrowed, which reduces the stability of the system and worsens the quality of the transition process. If, when calculating the optimal settings of the controller in a non-coupled control system, internal cross-couplings are not taken into account, then the system may be unstable. To maintain the stability of a disconnected control system in the presence of internal connections, it is necessary to reduce the gain compared to the gain factors of the regulators in the absence of cross connections so much that the AFC hodograph of the open-loop system does not cover the point with coordinates .

Obviously, this can be achieved by significantly increasing the controller gain, i.e. speed of the regulator, which sharply worsens the quality of regulation. Therefore, with strong internal connections, the opportunity to obtain high quality regulation should be sought not in adjusting the structures and settings of unrelated regulators, but by “untying” internal connections through cross channels. Those. it is necessary to change the structure of the system itself. There are two ways to weaken or completely “untie” cross-links:

1. choosing unrelated or weakly related parameters as controlled quantities;

2. creation of a system of linked regulation, by introducing additional external compensating links between regulators into the ASR

The system of uncoupled regulation is simpler, more reliable and cheaper than systems of coherent regulation. They are feasible even in cases where communication control systems are technically infeasible. However, they are susceptible to disturbing influences and spread through main and cross channels, which can lead to deterioration in the quality of regulation and, in the best case, loss of stability. The advantages of incoherent control systems force us to look for ways to extend the scope of their application to objects with interconnected controlled quantities while maintaining satisfactory quality of regulation. The degree of connection between two controlled quantities can be determined using the transfer functions of the object along the main and cross channels. The degree of communication along the first main channel is equal to the ratio of its transfer function to the transfer function of the second main channel: . The degree of communication along the second cross channel is equal to the ratio of the transfer function of this channel to the transfer function of the first main channel: . General degree of connection between control variables: . Depending on the magnitude of the overall degree of connection, one of the following control options can be recommended:

With this connection of regulators, the channels will become the main ones and the overall degree of connection will be characterized by a new value. If it turns out that the overall degree of coupling of the values is less than 1, then a non-coupled control system can be applied;

3. with the ratio , the degree of connection is significant, which can significantly reduce the stability of a disconnected control system; in this case, it is necessary to eliminate or significantly weaken internal connections in the automated control system;

4. “decoupling” the regulation of quantities in the presence of cross connections is possible if the regulation of quantities with different dynamic characteristics is carried out, which reduces their interconnection through the process, for example, pressure regulators usually operate at higher frequencies, whereas temperature regulators, which determines their weak mutual influence Each other.

Approaches to setting up a disconnected control system can be as follows:

1. setup in single-circuit systems;

2. simultaneous optimization of regulators in a disconnected control system, taking into account the influence of the main and transition channels.

The first approach uses models of the main channels and corresponding regulators. From them, single-circuit control systems are compiled, in which the corresponding regulators are adjusted using one of the numerical methods. The advantage of this approach to setting up regulators is its simplicity and high speed.

From the system of equations for the relationship between the outputs of the object ( and ) and the inputs of the system ( and ) (2.3), (2.4) it follows that the controlled quantity depends not only on the dynamic properties of the main channel and the controller, but also on the dynamic properties of the second main channel, cross channels, and from the second regulator. The parameter is similar. Therefore, the control part of the system must be configured taking into account the dynamic properties of not only the corresponding main channel, but also taking into account the influence of the dynamics of cross-channels. Therefore, the disadvantage of this approach to tuning regulators is the non-optimality of the resulting tuning parameters.

Let's consider the second approach. The calculation of the transient process in a disconnected control system is carried out using the following system of finite-difference equations:

, where are the weighting coefficients for which the following conditions are met:

Quality indicators for the corresponding system output, used as optimization criteria. The larger weight is assigned to the quality indicator of the output whose regulation is most important.

When using convolution, the optimization problem is formed as follows: . When using the gradient method as a numerical optimization method, the optimization algorithm (algorithm diagram) will be the same as for a single-loop system. The difference will be that when calculating the transition process, the system of equations (3.0) and initial conditions (3.1) will be used. When calculating the partial derivatives of the criterion using optimal settings, one of the two approaches discussed above can be used (with and without the use of quasi-analytical recurrent dependencies). When using finite-difference equations, it is necessary to take partial derivatives of all equations of system (3.0) for all settings of both controllers. The initial conditions for calculating the numerical values of the resulting system of finite-difference equations must be set similarly to the initial conditions (3.1).

Currently, there are a whole variety of automatic control systems (ACS) or, as they are also called, automatic control systems (ACS). In this article we will consider some methods of regulation and types of automatic control systems.

Direct and indirect regulation

As is known, every automatic control system consists of a regulator and an object of regulation. The regulator has a sensitive element that monitors changes in the controlled variable depending on the value of the specified control signal. In turn, the sensitive element influences the regulatory body, which in turn changes the system parameters so that the values of the set and controlled quantities become the same. In the simplest regulators, the effect of the sensing element on the regulating organ occurs directly, that is, they are directly connected. Accordingly, such ACS are called direct control systems, and the regulators are called direct-acting regulators, as shown below:

In such a system, the energy required to move the valve that regulates the flow of water into the pool comes directly from the float, which will be the sensing element here.

In an indirect control system, to organize the movement of the control body, auxiliary devices are used that use additional energy sources for their operation. In such a system, the sensing element will act on the control of the auxiliary device, which, in turn, will move the control element to the desired position, as shown below:

Here the float (sensitive organ) acts on the contact of the excitation winding of the electric motor, which rotates the valve in the desired direction. Such systems are used when the power of the sensing element is not enough to control the operating mechanism or it is necessary to have a very high sensitivity of the measuring element.

Single-circuit and multi-circuit self-propelled guns

Modern ATS very often, almost always, have parallel correction devices or local feedbacks, as shown below:

ACS in which only one value is subject to regulation, and they have only one main feedback (one control loop) are called single-circuit. In such self-propelled guns, an impact applied to some point in the system can bypass the entire system and return to the original point after passing through only one bypass path:

And self-propelled guns, in which, in addition to the main circuit, there are also local or main feedback connections, are called multi-circuit. Conversely to single-circuit systems, in multi-circuit systems an impact applied to some point in the system can bypass the system and return to the point of application of the impact along several circuits of the system.

Systems of coupled and uncoupled automatic control

Systems in which several quantities are subject to regulation (multidimensional automatic control systems) can be divided into connected and unrelated.

Decoupled Regulatory Systems

Systems in which regulators designed to regulate different quantities that are unrelated to each other and can interact through a common control object are called unrelated control systems. Unrelated regulation systems are divided into independent and dependent.

In dependent variables, a change in one of the quantities to be controlled entails a change in the remaining quantities to be controlled. Therefore, in such devices, the various control parameters cannot be considered separately from each other.

An example of such a system would be an airplane with an autopilot, which has a separate rudder control channel. If the aircraft deviates from its course, the autopilot will cause the rudder to deflect. The autopilot will deflect the ailerons, and the deflection of the aileron and rudder will increase the aircraft's drag, causing the elevator to deflect. Thus, it is impossible to consider separately the processes of heading, pitch and lateral roll control, even though each of them has its own control channel.

In independent systems of unrelated regulation, the opposite is true; each of the quantities subject to regulation will not depend on changes in all the others. Such management processes can be considered separately from each other.

An example is an automatic control system for the angular velocity of a hydraulic turbine, where the voltage of the generator winding and the turbine speed are regulated independently of each other.

Linked regulation systems

In such systems, regulators of different quantities have connections among themselves that interact outside the object of regulation.

For example, consider the electric autopilot EAP, a simplified diagram of which is shown below:

Its purpose is to maintain the pitch, heading and roll of the aircraft at a given level. In this example, we will consider the functions of the autopilot related only to maintaining a given course, pitch, and roll.

The hydraulic semi-compass 12 serves as a sensitive element that monitors the deviation of the aircraft from the course. Its main part is a gyroscope, the axis of which is directed along a given course. When the plane begins to deviate from the course, the axis of the gyroscope begins to influence the sliders of the rheostatic course 7 and rotation 10 sensors connected by lever 11, while maintaining its position in space. The aircraft body, together with sensors 7 and 10, in turn, shift relative to the axis of the horoscope; accordingly, a difference arises between the position of the gyroscope and the aircraft body, which is detected by sensors 7 and 10.

The element that will perceive the deviation of the aircraft from the course specified in space (horizontal or vertical plane) will be the gyrovertical 14. Its main part is the same as in the previous case - the gyroscope, the axis of which is perpendicular to the horizontal plane. If the plane begins to deviate from the horizon, the pitch sensor slider 13 will begin to shift in the longitudinal axis, and when it deviates in the horizontal plane, the roll sensors 15-17 will begin to shift.

The bodies that control the aircraft are control rudders 1, height 18 and ailerons 19, and the performing elements that control the position of the rudders are the heading, pitch and roll steering machines. The operating principle of all three autopilot channels is completely similar. The steering gear of each steering wheel is connected to a potentiometric sensor. Main potentiometric sensor (see diagram below):

Connects to the corresponding feedback sensor via a bridge circuit. The bridge diagonal is connected to amplifier 6. When the aircraft deviates from the flight path, the slider of the main sensor will move and a signal will appear in the diagonal of the bridge. As a result of the appearance of the signal, the electromagnetic relay will be activated at the output of the amplifier 6, which will lead to the closure of the electromagnetic coupling circuit 4. The drum 3 of the machine, in the circuit of which the relay has activated, will engage with the shaft of the continuously rotating electric motor 5. The drum will begin to rotate and thereby wind or unwind ( depends on the direction of rotation) cables that rotate the corresponding rudder of the aircraft, and at the same time will move the brush of the feedback potentiometer (OS) 2. When the displacement value of the feedback potentiometer (OS) 2 becomes equal to the displacement value of the potentiometric sensor brush, the signal in the diagonal of this bridge will become equal to zero and the movement steering will stop. In this case, the aircraft's rudder will rotate to the position necessary to shift the aircraft to the specified course. As the mismatch is eliminated, the main sensor brush will return back to the middle position.

The output stages of the autopilot are identical, starting from amplifiers 6 and ending with the steering gears. But the entrances are a little different. The heading sensor slider is not connected rigidly to the gyro-compass, but with the help of a damper 9 and a spring 8. Because of this, we obtain not only a movement proportional to the displacement from the heading, but also an additional one, proportional to the first derivative of the deviation with respect to time. In addition, in all channels, in addition to the main sensors, additional sensors are provided that implement connected control along all three axes, that is, they coordinate the actions of all three rudders. This connection provides algebraic addition of the signals from the main and additional sensors at the input of amplifier 6.

If we consider the course control channel, then the auxiliary sensors will be roll and turn sensors, which are controlled manually by the pilot. In the roll channel there are additional rotation and rotation sensors.

The influence of control channels on each other leads to the fact that when the aircraft moves, a change in its roll will cause a change in pitch and vice versa.

It must be remembered that an automatic control system is called autonomous if it has such connections between its regulators that when one of the values changes, the rest will remain unchanged, that is, a change in one value does not automatically change the rest.

The basis for building connected regulation systems is principle of autonomy. In relation to an object with two inputs and outputs, the concept of autonomy means the mutual independence of output coordinates y 1 And y 2 when two closed control systems operate.

Essentially, the autonomy condition consists of two invariance conditions: invariance of the first output y 1 in relation to the signal of the second regulator X p2 and invariance of the second output y2. in relation to the signal of the first regulator X p1:

In this case the signal X p1 can be considered as a disturbance for y2, and the signal X p2 - how outrage for y 1. Then the cross channels play the role of disturbance channels (Fig. 1.35). To compensate for these disturbances, dynamic devices with transfer functions are introduced into the control system R 12 (p) And R 21 (r), the signals from which are sent to the corresponding regulation channels or to the inputs of the regulators.

By analogy with invariant ASRs, the transfer functions of compensators R 12 (p) And R 21 (r), determined from the autonomy condition, will depend on the transfer functions of the direct and cross channels of the object and, in accordance with expressions (1.20) and (1.20,a), will be equal to:

Just as in invariant ASRs, for the construction of autonomous control systems, an important role is played by physical feasibility and technical implementation approximate autonomy.

The condition of approximate autonomy is written for real compensators, taking into account the operating frequencies of the corresponding regulators:

In chemical technology, one of the most complex multi-connected objects is the rectification process. Even in the simplest cases - when separating binary mixtures - several interconnected coordinates can be identified in a distillation column (Fig. 1.36). For example, to regulate the process in the lower part of the column, it is necessary to stabilize at least two technological parameters that characterize the material balance in the liquid phase and in one of the components. For this purpose, the liquid level in the still and the temperature under the first plate are usually selected, and the flow of heating steam and the selection of the still product are used as control input signals. However, each of the regulatory influences affects both outputs: when the heating steam flow rate changes, the intensity of evaporation of the bottom product changes, and as a result, the liquid level and steam composition changes. Similarly, a change in the bottoms product selection affects not only the level in the bottoms, but also the reflux ratio, which leads to a change in the composition of the steam at the bottom of the column.

Rice. 1.35. Block diagrams of autonomous automated control systems: A– compensation of the impact from the second regulator in the first control loop; b– compensation of the impact from the first regulator in the second control loop; c – autonomous two-coordinate control system

Rice. 1.36. An example of a control system for an object with several inputs and outputs:

1 - distillation column; 2 – boiler; 3 – reflux condenser; 4 – reflux tank; 5 - Temperature regulator; 6,9 – level regulators; 7 – flow regulator; 8 – pressure regulator

To regulate the process in the upper part, you can select steam pressure and temperature as output coordinates, and the supply of refrigerant to the reflux condenser and reflux to reflux the column as regulating input parameters. Obviously, both input coordinates affect the pressure and temperature in the column during thermal and mass transfer processes.

Finally, considering the temperature control system simultaneously in the upper and lower parts of the column by supplying reflux and heating steam, respectively, we also obtain a system of unrelated control of an object with internal cross-links.