The principles of control theory of automatic control...

Control principles of automatic control theory

The formation of specific principles of management began in technology. The theory of automatic control was developed, which was subsequently extended to a wider application and called the theory of automatic control. A great achievement of the theory of automatic control are the general principles of control developed in this theory, which are called fundamental and are sufficiently general. These principles are also being applied to management in socio-economic systems.

The main of these principles are as follows:

1. The principle of open, or software, control.

The essence of the principle is that the control is performed using a given algorithm or program.

Conditionally, this control principle is shown in Fig. 2.18, which shows: a device that generates a program or the law of functioning , control object, interference , output result , a device that is usually denoted by a special sign - a circle divided into sectors that generates a set of control actions or detecting the discrepancy between the result and the required result (as in Figure 2.18).

Fig. 2.18

In some cases, the control law generation unit and the control device are combined.

The circuit has the form of an open circuit, in which the main effect is transferred from the input to the output, performing the specified program (the law of functioning), which gave the principle a name. Under this control principle, the ζ • interference can distort the desired . Nevertheless, due to simplicity, this principle is widely used.

Example

According to the open principle, devices for starting a music box, tape recorder and other audio devices, machine tools with program control, conveyor control are built.

The similarity of this principle can be considered the management of the slave's work in the slave society at the initial stage of its development in the case of cruel slave owners who did not take into account the needs of the slave as a person who suppresses his human dignity and compels clearly to carry out the prescribed program.

2. The principle of compensation, or of disturbance management. This principle is also called the management principle of with anticipation.

In this way, a device is used that measures interference and produces compensating effects that correct the control law (Figure 2.19).

Fig. 2.19

A device of this kind is called a compensating device.

Example

The simplest example of such a principle are devices that provide voltage stabilization under DC oscillations. To date, many different compensation mechanisms have been developed in the theory of automatic control, according to the type of which subclasses of devices are singled out and even the principle of compensatory control in accordance with these types of devices is detailed.

This principle is used in enterprise planning: when designing plans, it is taken into account that the productivity of labor depends on the wear and tear of equipment, on the skills of workers, shifts, etc., and when calculating the time for executing planned tasks, appropriate adjustments are made in the form of wear coefficients equipment, shift factors, etc.

With regard to the management of society, we can assume that under the conditions of the feudal system the landowner tries to take into account to some extent the human needs of the serf worker in order to avoid riots or to win the love of serfs, which provided conditions for more effective work.

3. The principle of feedback, or deviation control.

The principle is illustrated in Fig. 2.20. The obtained values ​​are corrected on the basis of the deviation measurement Δy from the required result ytre6, called in automatic control theory setpoint & quot ;.

The concept of feedback is easily illustrated by examples of technical and electronic devices. However, when using this concept in relation to socio-economic systems, this concept is not always correctly interpreted.

Fig. 2.20

Often, they are limited only by fixing the mismatch Δ y between the required ytre6 and the actual value of the controlled parameter, and it is necessary to take into account and implement all the elements, without forgetting to close the feedback loop, generating the appropriate control actions in the feedback block , which correct the control law x (t).

Feedback can be:

negative - the opposing tendencies in the change of the output parameter, i.e. aimed at preserving, stabilizing the required value of the parameter (for example, stabilizing the output voltage, or in the systems of organizational management - the amount of output, etc.);

positive, preserving the trend of the changes occurring in the system of one or another output parameter (which is used in the development of generators of various kinds, in the modeling of developing systems).

An example of a system based on the use of stabilizing (negative) feedback in management is classical capitalism: feedback is provided by the regulation of the labor market, i.e. dismissal of workers in the case of overproduction of goods or, on the contrary, additional employment for work, if necessary, to increase the production of goods.

4. Combining the principles of feedback and control with anticipation.

To improve management, various ways of combining management principles (for example, the model of the type shown in Figure 2.21) are used.

Fig. 2.21

The combination of principles is also used in socio-economic systems. Since the implementation of the feedback principle is related to unemployment and social problems, the development of the capitalist system uses compensatory mechanisms in the form of social programs (unemployment benefits, etc.) that reduce the possibility of crises.

According to the principle of feedback, the main regulators of the human body function (when a person touches a hot iron, a person automatically pulls back his hand, etc.). This effect is similar to the operation of a thermostat (temperature regulator). But human regulators only work in early childhood on the principle of a thermostat. Later, when burned or stumbled several times, the child acquires a conditioned reflex, which protects him from pain, and the human regulators start working according to the principle called homeostasis, a simplified model of which can be a combination of control principles, shown in Fig. 2.21.

These principles also allow us to better understand the problem of adaptation.

Adaptation - in a broad sense, the ability of the system to adapt to changing environmental conditions, interference from the environment and influencing the system. Adaptation was also defined as the ability of the system to detect targeted adaptive behavior in complex environments [53].

Adaptation to an environment characterized by high uncertainty, allows the system to achieve goals in conditions of insufficient a priori information about the environment. If the system can not adapt to environmental changes, then it dies.

In the process of adaptation, the quantitative characteristics of the system (for example, the parameters of the autopilot when the dynamic characteristics of the aircraft change); structure of the system (for example, the lizard is capable of casting the tail if necessary, similarly, the ability to adjust the organizational structure is considered a useful characteristic of the enterprise and the organization ensuring their adaptability); correct the law of functioning, behavior of the system.

In developing systems, there are various forms of adaptation: system growth, tuning and self-adjustment, learning and self-learning, uniting systems into a collective and, on the contrary, decaying the system into separate parts, etc.

Highly organized adaptive systems have, in addition, the ability to change the external environment so that it is not necessary to change the behavior of the system, i.e. can adjust external conditions to achieve their goals.

Simple forms of adaptive behavior are observed in regulators, in technical systems with feedback. This principle of adaptation is illustrated in Fig. 2.20.

Example

Such a principle is applied, for example, in devices that provide voltage stabilization in the case of DC fluctuations in the on-board equipment of automatically controlled spacecrafts. * Y.

In more advanced models of adaptive behavior, a combination of the principles of feedback and compensating device is used (see Figure 2.21). With the help of such a model it is possible to explain the functioning of the main regulators of the human body, the formation of conditioned reflexes (for example, when the experience of touching a hot iron is accumulated, the person subsequently automatically jerks the hand, even if the iron is not hot, etc.).

The most developed theory of adaptation applied to technical systems was developed by I. Z. Tsypkin (see the references in [11]). He investigated various forms of regulation in technical systems and showed that control with anticipation (or compensatory control) can be considered a model of adaptive behavior. Moreover, in Tsypkin's theory, a device that measures interference and produces compensating effects that correct the control law is represented as an integrator or digger (for discrete noise) to accumulate interference to a level at which requires the correction of the law of management.

The combination of feedback and digitor principles (instead of the compensating device in Figure 2.18) is one of the homeostat models that was investigated in the first papers on modeling adaptation processes.

The problem of adaptation with respect to living, biological systems, and in particular, in the modeling of the brain, was studied

Have. R. Ashby [103]. In the future, the concept of adaptation, observed in biological systems and investigated first for technical systems, was applied to socio-economic systems.

The forms of adaptive behavior of socio-economic systems are very diverse. Adaptive behavior manifests itself in changing the behavior of the system in an unstable environment in order to maintain significant variables within certain boundaries, preserve the basic properties of the system or its structure.

Maintaining essential economic variables within certain limits (such as profit, profitability, output, sales, production costs, wages, etc.), the preservation of the basic properties of the system is sometimes called the economic homeostasis.

Later, the fact that the instability of the system can be affected not only by external interference, but also internal factors of instability of the system, with which one can also talk about adaptation and the need to create adaptive mechanisms.

Studies of non-linear developing systems with uncertainty showed that each system in its development passes through a maximum of adaptive possibilities, after which the breeding phase begins. As a result of these studies, M. B. Ignatiev the phenomenon of adaptation maximum was discovered.

The most complex form of adaptation is self-organizing systems. At the same time, the study of adaptation mechanisms leads to an analysis of complex problems of the contradiction of stability (controllability) and freedom of initiatives that play an important role in ensuring the development of the system and its adaptability to changing conditions (both external and internal), i.e. to the study of the problem of the stability of developing systems.

The models considered for clarification are presented in graphical form. However, they can also be represented by formal analytical methods that help to conduct research on the functioning and stability of systems. They are mainly used to study technical systems. But they can also be used to explain the principles of constructing and functioning objects of a more highly organized nature-for modeling animal and human reflexes, for regulating the parameters of living organisms (pressure, temperature, etc.), and even with some approximation for explaining the principles laid down in the basis of the corresponding formations of the social sphere.

Here there is an analogy with the action of the law of recapitulation E. Haeckel, according to which the stages through which the organism passes in the course of its development, repeat the evolutionary history of the group to which it refers. Apparently, therefore, in highly organized systems there are processes that can be displayed by methods and models developed for nonliving systems. This is also the basis for the possibility of applying mathematical methods for modeling certain processes in living systems.

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