The transfer function of the PI controller. Regulators and regulation schemes

1.   A device for regulating the progress of machines, the operation of mechanisms. R. volume. Regulatory - related to the regulator, regulators.

2. reschedule  That which regulates, guides the development of something Science - p. progress.

regulator  - T.F. Efremova New Dictionary of the Russian language. Interpretive word-formation

  what is a regulator

regulator

regul iT

m

1) A device for regulating the action of smth. (cars, machinery, etc.).

2) That which directs, regulates the development of smth.

regulator  - D.N. Ushakov Big Dictionary of Modern Russian

  what is a regulator

regulator

REGULATOR, REGULATOR, ·husband.

1.   Same as the traffic controller (spec. New,). Traffic regulator (policeman).

2.   Automatic device for regulating the progress of machines or their parts (tech.). Current regulator. Steam regulator.

|   reschedule What serves to regulate, order something ( · The book.). The correct financial policy of the Soviet government in the interests of the workers is a reliable regulator of trade.

regulator  - Small Academic Dictionary of the Russian language

  what is a regulator

regulator

BUT, m

Device, device for regulating the operation of mechanisms and their parts.

Speed ​​control.

- Unscrew the regulator, live! he shouted. --- The engine, devoid of control, slowly delayed the course.  N. Ostrovsky, How the steel was tempered.

2. reschedule   Book

What regulates, directs smth.

Bazarov, everywhere and in everything, acts only in the way he wants or as it seems to him advantageous ---. He does not recognize any regulator, no moral law, no principle, either over himself or outside himself or within himself.  Pisarev, Bazarov.

The instinct of accumulation in the old society was a permanent regulator of consumption.  Makarenko, A book for parents.

regulator  - Comprehensive dictionary of foreign words of the Russian language

  what is a regulator

regulator

MODERATOR or REGULATOR

(lat.) Drive in cars, serving to reduce or enhance movement; device in the piano to control the power of sound.

REGULATOR

(new-lat., from lat. regula). 1) a projectile with any machine that equalizes its movement, its course, and, if necessary, accelerates or slows it down. 2) the executor of the decisions, the executor in the criminal court of Sev.-Amer. States

(Source: "Dictionary of foreign words that are part of the Russian language." Chudinov, AN, 1910)

REGULATOR

1) device in k.-n. the car, accelerating or slowing down its movement and work; 2) in the portable. sense - c.-n. phenomenon or force in general, bringing order and correctness to a certain region.

The term `dictionary regulator`

regulator

stabilizer, control device, controller, sensor; signaling device, gearbox, balancer

Dictionary of Russian Synonyms

m. 1) A device for regulating the action of smth. (cars, machinery, etc.). 2) That which directs, regulates the development of smth.

regulator

-but , m

Speed ​​control.

- Unscrew the regulator, live! he shouted. --- The engine, devoid of control, slowly delayed the course.  N. Ostrovsky, How the steel was tempered.

2. reschedule book

Bazarov, everywhere and in everything, acts only in the way he wants or as it seems to him advantageous ---. He does not recognize any regulator, no moral law, no princes ...

(lat.) Drive in cars, serving to reduce or enhance movement; device in the piano to control the power of sound.

(new-lat., from lat. regula). 1) a projectile with any machine that equalizes its movement, its course, and, if necessary, accelerates or slows it down. 2) the executor of the decisions, the executor in the criminal court of Sev.-Amer. States

(Source: "Dictionary of foreign words included in the Russian language". Chudinov, AN, 1910)

1) device in k.-n. the car, accelerating or slowing down its movement and work; 2) in the portable. sense - c.-n. phenomenon or force in general, bringing order and correctness to a certain region.

Regulator `Kuznetsova Dictionary of Explanation`

regulator

REGULATOR   -but; m

1.   Device, device for regulating the operation of mechanisms and their parts. R. speed. Turn the volume knob.

2. Book  What regulates, directs smth. R. prices. Moral r. R. human relations.

Great Dictionary of Russian language. - 1st ed.: SPb .: Norint  S.A. Kuznetsov. 1998

A, m. 1. A device for regulating something n. (specialist.). 2. That which regulates, guides the development of something. R. prices.

regulator, m. 1. Same as the traffic controller (special. new,). Traffic regulator (policeman). 2. An automatic device for regulating the progress of machines or their parts. Current regulator. Steam regulator. || reschedule What serves to regulate, ordering something n. (book). The correct financial policy of the Soviet government in the interests of the workers is a reliable regulator of trade.

(inosk.) - the manager, the installer of the order (hint at regulator  - projectile at the machine for the equation of action) - leveler

Wed  The manager has an overwhelming influence on the case and ... I will say it bluntly: the influence has become difficult, it is necessary to get rid of it ... How? to invite regulator  in the form of a companion.

A.A. Sokolov. Secret. 32.

Wed  Régulateur (régula, rule, regularis, straight) is an equalizer that gives correctness.

Regulator

automatic (from lat. regulo - I am putting in order, adjusting), a device (a set of devices), through which the regulation is carried out automatically . Using the sensor - Sensor -   A system, depending on the principle of regulation, measures either a regulated value or a disturbing action and, using a converter or computing device, in accordance with the law of regulation, produces an effect on the regulator of the object. Adjustable corrective devices may also be part of a relay to ensure the stability and the required quality of the control process, and amplifiers that increase the output power of the output R. to a value sufficient to actuate the actuator, which ...

REGULATOR

the fields Kа l g e b ra and u c h and x h and c e l is the number R K-, which, by definition, is equal to 1 if Kes is a field or an imaginary quadratic zero expansion, and in other cases it is, where r -  group rank   E  field units K (see   Algebraic Number, Algebraic Number Theory),   but   -dimensional volume of the main parallelepiped r-dimensional lattice in

(from lat. regulo - directing, ordering), a gene encoding the structure of the repressor, the function of which is to control the transcription of the operon. Mutations in P. that inactivate the repressor lead to constitutive (that is, independent of the presence of the effector) transcription of the operon and, accordingly, to constitutive synthesis of the enzymes encoded by the operon. Such mutations are, as a rule, recessive in contrast to similar mutations of the operator. (see Operon).

A device or mechanism (also in a figurative sense), by means of which it is kept constant, changes, moves in the desired direction a certain quantity, position or process.

REGULATOR

(from the Latin. regulo - I put in order, I set up, the regula is the norm, the rule) automatic - the device (complex of devices), by means of which automatic regulation(see fig.). With the help of feeling. element (sensor) R. measures or adjustable value, or a disturbing effect, and by converting or calculating. devices in accordance with regulatory law produces an impact on the regulatory body of the object of regulation. The regulating effect can be given to the regulator of the object or directly with the senses. element R. (direct action of the regulator), or after a preliminary. gain (indirect action regulator). RVs may also include compensating devices that serve to ensure sustainability and the required quality ...

REGULATORS AND REGULATORY SCHEMES

Andrey Kazantsev

What is a regulator? This term comes from the theory of automated control. A regulator is a device that monitors the operation of the control object and, constantly analyzing its state, produces a specific control action (control signal).

  Figure 1 shows the classical scheme of the control loop taken from the textbook on the theory of automatic control.

Fig. 1. Classic control loop.

Obviously, the regulator itself is a stupid thing. However, it begins to be beneficial when it is included in the control loop and adjusted to the required control characteristics (the terms “control” and “control” are used here as synonyms). In the general case, each control loop can be considered as a certain system consisting directly of the control object itself and the regulator, which through an actuator can influence the controlled parameter of the object. The regulator is operated on the basis of a constant analysis of an adjustable parameter characterizing the state of an object, for which a sensor is connected to the regulator input. Informational communication between the sensor, which measures the adjustable parameter, and the regulator input is called feedback. This forms a closed control loop, and the control system itself is called closed. In general, the notion of “feedback” (feedback) is a fundamental category in control theory. It is thanks to the presence of feedback with the object that it becomes possible to implement really high-quality, one can say sighted control.

How is the controller implemented in modern ACSs? Enough of government phrases, now everything is in order. The definition of the regulator given above was taken from the encyclopedia and, frankly, not very successful. A regulator is not necessarily a separate device. The fact is that in modern ACSs, the regulator functions are implemented as part of the control application program at the controller level. So one industrial controller can programmatically implement up to thousands of regulators. This is a modern approach to building control systems; Nevertheless, local regulators, made in the form of individual devices, are still actively used today where such powerful functionality is not required. Do not shoot the gun on the sparrows!

What are the regulators? Completely different: limit on / off control (on / off control), proportional control (P-control), control with timer or delay (timer control, delay control), etc. The apotheosis of the development of regulators was the emergence of a proportional-integro-differential controller (PID controller, PID in English), which in many cases allowed to achieve optimal control quality, and which will be discussed further. In modern automated process control systems, PID regulation is a fundamental element in managing continuous processes, the basis of all fundamentals.

How does the PID regulator work? The PID controller is a link in the feedback control loop used to maintain the specified value of the parameter being measured. The PID controller measures the deviation of a stabilized quantity from a given value (the so-called setpoint) and generates a control signal that is the sum of three terms, the first of which is proportional to this deviation, the second is proportional to the integral of the deviation and the third is proportional to the derivative of the deviation. If some of the components of the items are not used, then the regulator is respectively called proportional-integral, proportional-differential, proportional, etc. Figure 2 shows a simplified functional diagram of the PID controller:

Fig. 2. Functional diagram of the PID controller.

e (t) is the deviation of the measured value from the setpoint (error);
  u (t) is the control action generated by the regulator.

Figure 3 shows a more typical image of the PID controller in the form of a single functional unit, which is typical of an industrial control system.

Fig. 3. Simplified image of the PID controller in the form of a single functional unit.

The purpose of the PID controller is to maintain a certain PV value at a given SP value by changing another OP value, where

PV - measured value (process value);
  SP - the specified value of the measured parameter (setpoint, setpoint);
  OP - control action (output);
  The difference (SP-PV) is called an error or a mismatch.

As already mentioned, the output signal OP is defined by three terms:

OP = P + DI + TI = KP * (SP-PV) + KDI * d (SP-PV) / dt + KTI * (SP-PV) dt;

where KP, KDI, KTI are the gains respectively proportional (proportional), differential (derivative) and integral (integral) component.

However, in most real-world systems, a slightly different output formula is used, in which the proportional coefficient is behind the bracket:

OP = Pp * ((SP-PV) + PD * d (SP-PV) / dt + PI * (SP-PV) dt),

where Pp = 1 / KP (proportional band); PD = KDI (differentiation constant); PI = 1 / KTI (integration constant).

Now we analyze the meaning of each component.

Proportional component.

The proportional component seeks to eliminate the direct error (SP-PV) in the value of the stabilized quantity observed at a given point in time. The value of this component is directly proportional to the deviation of the measured value from the setpoint (SP-PV). So if the input signal is setpoint, i.e. PV = SP, then the proportional component is zero.

When using only a proportional controller, the value of the regulated value is never set to the specified value (PVust PV SP). There is a so-called static error, which is equal to such a deviation of the controlled variable, which provides an output signal that stabilizes the output value at precisely this value. For example, in the temperature controller, the output signal OP, which regulates the power of the heater, gradually decreases as the temperature PV approaches the setpoint SP:

with PV → SP, OP → 0.

The system is stabilized at a certain OP value at which the power of the heater is equal to the heat loss. In this case, the temperature cannot reach the setpoint, since in this case the heater power will become zero (OP = 0), and it will begin to cool, and with it the temperature will also fall.

As the proportionality factor (gain) increases, the static error decreases, but too much gain can cause self-oscillations, and with a further increase in the ratio, the system can lose stability and go “into the spacing”.

Integral component.

To eliminate the static error, the integral component is introduced. It allows the regulator to "learn" from previous experience. If the system does not experience external disturbances, then after a while the regulated value stabilizes at a given value. With stabilization (PV = SP), the proportional component will be zero, and the output signal will be fully provided by the integral component. With a constant mismatch value (SP-PV), the integral component is a linearly increasing value with time.

Physically, the integral component represents a delay in the response of the regulator to a change in the magnitude of the mismatch, introducing some inertia into the system, which can be useful for controlling objects with high sensitivity.

Differential component.

The differential component counteracts the expected deviations of the controlled variable, as if anticipating the object's behavior in the future. These deviations can be triggered by external disturbances or a delay in the influence of the regulator on the system.

The faster the controlled variable deviates from the setpoint, the stronger the reaction created by the differential component. When the mismatch becomes constant, the differential component no longer affects the control signal.

The process of setting the PID controller consists mainly of setting the setpoint and the values ​​of the above three factors. There are several mathematical methods for calculating the optimal coefficients of the PID controller on the basis of ensuring the greatest stability of the system. However, in practice, the adjustment of the regulator is carried out empirically (so-called “by the eye”). In modern automated process control systems, so-called self-adjusting PID-regulators are often used, which, by applying a single exposure to the object and analyzing the response, automatically expose sufficiently good coefficients, if not optimal. Moreover, there are algorithms adapted PID-regulation, involving automatic adjustment (adjustment) of the control coefficients in the control process. With their help, it is possible to achieve very high quality control even in highly nonlinear systems, however, for some reason, technologists still regard this functionality with great suspicion.

Application.

What are PID controls used for? It is better to explain with an example. Suppose there is an abstract process. The water in the tank must be heated and maintained at a certain temperature. For heating water using a gas burner located under the tank. The intensity of combustion is regulated by the gas supply valve. Figure 4 shows how this can be organized using PID control.

Fig. 4. An example of the use of a PID controller.

The temperature setpoint is set manually by the operator. The regulator, analyzing the difference between the setpoint and the temperature sensor reading, generates a signal to control the gas supply control valve to the burner.

As noted, the quality of control is highly dependent on the adjustment of the controller coefficients. Figure 5 shows the system behavior when the PID is configured incorrectly.

Fig. 5. Transient with poor PID settings.

Here the operator decided to change the setting. As can be seen from the figure, the regulator is not able to work correctly, and there is a diverging oscillatory process. The system is clearly not stable.

Figure 6 shows the transition process with the correct controller settings. The operator again changes the temperature setting, but this time the regulator works correctly. There is some overshoot, but in general the process quickly converges.

Fig. 6. Transient with good PID settings.

Consider the complex schemes for the use of PID-regulators.

Cascade control (cascade control).

Classic example. The heater of the furnace (burner in our case) has excess power, and the heating object (billet) can overheat on the one hand, and remain cold on the other. If such a heating mode is unacceptable, then single-loop control will not be enough. To ensure uniform heating of the object, it is necessary to measure the temperature already in two places: near the heater and in the coldest place. In this case, the controller should contain two PID - links connected in series. The first PID link (called the master), to the input of which the temperature value in a cold place is fed, will produce the setpoint value for the second link (called the slave). The temperature near the heater is supplied to the input of the slave link (see Figure 7).

Fig. 7. Example of cascade control.

Such a structure of regulation of two by means of series-connected PID-regulators, which has two inputs for measurement parameters and one control output, is called cascade. For effective control, it is necessary that the slave PID controller is faster than the master.

Figure 8 shows another system.

Fig. 8. Another example of cascade control.

The temperature inside the jacketed tank is controlled in a cascade. The master PID controller (Tc1) responds to changes in temperature in the tank, but its output is not directly connected to the valve regulating the incoming flow of heat transfer fluid. Output Tc1 sets the setpoint for the slave regulator Tc2, and Tc2 controls the temperature of the heat transfer fluid in the pump circuit using a valve. Thus, Tc2 deals with all temperature fluctuations around the pump, which can be transmitted from the source of heat carrier.

With this cascade, all incoming disturbances and temperature fluctuations will be determined and processed by the Tc2 controller before they affect the temperature directly in the tank. Knowledge of impending disturbances and vibrations before they directly affect the control object allows the system to take preventive actions. This approach to the organization of management is called proactive regulation.

Ratio management (ratio control).

  Sometimes the stabilization of a relationship between two or more process variables is more significant than the stabilization of their absolute values. In such cases, proportional control systems are used.

Usually, the process variables for which a given ratio should be maintained are the consumption values ​​of the components or the volume values, which is most typical for combustion processes (for example, the direction of fuel to the burner nozzles). In Figure 9, the amount of fuel in control circuit 2 is maintained in the ratio of FAC with the amount of air in circuit 1, which is set by the setpoint SP1.

Fig. 9. Relationship management.

Relationship management is most often used in the following processes:

1. The mixture of two or more streams of substances for the production of mixtures of a given chemical composition;
  2. The mixture of two or more substances for the production of mixtures with desired physical properties;
  3. Maintain a given fuel / air ratio to achieve an optimal combustion process.

Practice.

Enough theory! How does a real PID controller look like? As already noted, in modern ACSs, the PID controller is implemented as a software functional unit running in the controller. Figure 10 shows a PID control block taken from the development environment of a real control system. Pay attention to how many different parameters are in the block (more than 30). But don't let that bother you, in practice no more than ten of them require careful adjustment.

Fig. 10. Configuration of the PID controller function block. Click on the image to enlarge.

We list the most important parameters of the block:

1. SP - setpoint value;
  2. PV - the value of the regulated value;
  3. OP is the value of the output signal (control signal);
  4. SL - input for setting the setting in automatic mode;
  5. RemoteSP - input for setting the setting in remote mode;
  6. Mode - input for setting the mode of the regulator;
  7. XP - the proportional component coefficient;
  8. TD - the coefficient of the differential component;
  9. TI - coefficient of the integral component;
  10. SL_Track - input to enable tracking mode.

Earlier we examined in detail the first three parameters, so we will not dwell on them. Very interesting is the parameter Mode. The fact is that the regulator can work in at least three modes of setting: automatic (automatic), remote (remote) and manual (manual).

1. Automatic mode is most often used; In this mode, the controller setpoint is set manually by the operator using the SL input.

2. When operating in remote mode, the setpoint is programmatically generated in another function block and sent to the input of the RemoteSP controller.

3. When working in manual mode, the operator has the ability to directly set the value of the control signal by manipulating the output of the OP; in this mode, the regulator suspends the generation of the OP control action using the PID algorithm.

Example. Suppose we have a container with water, equipped with a heater. At the moment, the water temperature is maintained at 80 C. In this case, we have:

PV is the current water temperature measured by the sensor;
  SP is the current setting set by the operator;
  OP - heater power control signal;

Let at the moment PV = SP = 80 ° C, i.e. there is no mismatch. At the same time, OP = 65% (the heater operates at 65% of its rated power), and the PID controller is in automatic mode. Now, for whatever reason, the operator decides to switch the regulator to manual mode and sets the new value OP = 20%. Due to the decrease in heating power, after some time the water temperature drops to 35 ° C. Now PV = 35 ° C, SP = 80 ° C, OP = 20%. Imagine what happens if the regulator is turned back into automatic mode. The mismatch will become equal to SP-PV = 80-35 = 45 ° C, and, therefore, the proportional component will be equal to XP * 45/100. At the moment the regulator enters the automatic mode, this value of P * 45/100 (together with other components) is transmitted to the OP output and causes an abrupt change in the control signal, respectively, by P * 45/100%. Such a sharp (hopping) change in the control signal is called a “shock.” How will the heating element respond? Probably not the best way. Although with the heating element, most likely, nothing will happen. Much worse if as actuator  stands the positioning device.

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