Systematic approach to modeling. Concept of system state Basic concepts and definitions
Biomedical significance of the topic
Thermodynamics is a branch of physical chemistry that studies any macroscopic systems whose state changes are associated with the transfer of energy in the form of heat and work.
Chemical thermodynamics is the theoretical basis of bioenergy - the science of energy transformations in living organisms and the specific features of the transformation of one type of energy into another in the process of life. In a living organism there is a close relationship between the processes of metabolism and energy. Metabolism is the source of energy for all life processes. The implementation of any physiological functions (movement, maintaining a constant body temperature, secretion of digestive juices, synthesis in the body of various complex substances from simpler ones, etc.) requires energy expenditure. The source of all types of energy in the body are nutrients (proteins, fats, carbohydrates), the potential chemical energy of which is converted into other types of energy during the metabolic process. The main way to release chemical energy necessary to maintain the vital activity of the body and carry out physiological functions is oxidative processes.
Chemical thermodynamics makes it possible to establish a connection between energy costs when a person performs certain work and the calorie content of nutrients, and makes it possible to understand the energetic essence of biosynthetic processes that occur due to the energy released during the oxidation of nutrients.
Knowledge of standard thermodynamic quantities for a relatively small number of compounds makes it possible to perform thermochemical calculations for the energy characteristics of various biochemical processes.
The use of thermodynamic methods makes it possible to quantify the energy of structural transformations of proteins, nucleic acids, lipids and biological membranes.
In the practical work of a doctor, thermodynamic methods are most widely used to determine the intensity of basal metabolism in various physiological and pathological conditions of the body, as well as to determine the calorie content of food products.
Problems of chemical thermodynamics
1. Determination of the energy effects of chemical and physicochemical processes.
2. Establishment of criteria for the spontaneous occurrence of chemical and physicochemical processes.
3. Establishment of criteria for the equilibrium state of thermodynamic systems.
Basic concepts and definitions
Thermodynamic system
A body or group of bodies separated from the environment by a real or imaginary interface is called a thermodynamic system.
Depending on the ability of a system to exchange energy and matter with the environment, isolated, closed and open systems are distinguished.
Isolated A system is a system that does not exchange either matter or energy with the environment.
A system that exchanges energy with the environment and does not exchange matter is called closed.
An open system is a system that exchanges both matter and energy with the environment.
System state, standard state
The state of a system is determined by the totality of its physical and chemical properties. Each state of the system is characterized by certain values of these properties. If these properties change, then the state of the system also changes, but if the properties of the system do not change over time, then the system is in a state of equilibrium.
To compare the properties of thermodynamic systems, it is necessary to accurately indicate their state. For this purpose, a concept has been introduced - a standard state, for which an individual liquid or solid is taken to be the physical state in which they exist at a pressure of 1 atm (101315 Pa) and a given temperature.
For gases and vapors, the standard state corresponds to a hypothetical state in which a gas at a pressure of 1 atm obeys the laws of ideal gases at a given temperature.
Values related to the standard state are written with the subscript “o” and the subscript indicates the temperature, most often 298K.
Equation of state
An equation that establishes a functional relationship between the values of properties that determine the state of a system is called an equation of state.
If the equation of state of a system is known, then to describe its state it is not necessary to know the numerical values of all properties of the system. For example, the Clapeyron–Mendeleev equation is the equation of state of an ideal gas:
where P is pressure, V is volume, n is the number of moles of an ideal gas, T is its absolute temperature and R is the universal gas constant.
It follows from the equation that to determine the state of an ideal gas it is enough to know the numerical values of any three of the four quantities P, V, n, T.
Status functions
Properties whose values during the transition of a system from one state to another depend only on the initial and final state of the system and do not depend on the transition path are called state functions. These include, for example, pressure, volume, temperature of the system.
Processes
The transition of a system from one state to another is called a process. Depending on the conditions of occurrence, the following types of processes are distinguished.
Circular or cyclic– a process, as a result of which the system returns to its original state. Upon completion of the circular process, changes in any function of the system state are equal to zero.
Isothermal– a process that occurs at a constant temperature.
Isobaric– a process that occurs at constant pressure.
Isochoric– a process in which the volume of the system remains constant.
Adiabatic– a process that occurs without heat exchange with the environment.
Equilibrium– a process considered as a continuous series of equilibrium states of the system.
Nonequilibrium– a process in which a system passes through nonequilibrium states.
Reversible thermodynamic process– a process after which the system and the systems interacting with it (the environment) can return to the initial state.
Irreversible thermodynamic process– a process after which the system and the systems interacting with it (the environment) cannot return to the initial state.
The latter concepts are discussed in more detail in the section “Thermodynamics of Chemical Equilibrium”.
Systems theory and system analysis Topic 6. State and functioning of systems Karasev E. M., 2014
Lecture outline 1. 2. 3. 4. 5. State of the system Static and dynamic properties of dynamic systems State space Stability of dynamic systems Conclusions Karasev E. M., 2014
1. System state The system is created in order to obtain the desired values (states) of its target outputs. The state of the system outputs depends on: o the values (states) of the input variables; o initial state of the system; o system functions. One of the main tasks of system analysis is to establish cause-and-effect relationships between the system’s outputs and its inputs and state. Karasev E. M., 2014
1. System status. State assessment The state of a system at a certain point in time is the set of its essential properties at that point in time. When describing the state of the system, you need to talk about: o the state of the inputs; o internal state; o state of system outputs. Karasev E. M., 2014
1. System status. State assessment The state of the system inputs is represented by a vector of input parameter values: X=(x 1, x 2, ..., xn) and is actually a reflection of the state of the environment. The internal state of the system is represented by a vector of values of its internal parameters (state parameters): Z = (z 1, z 2, ..., zv) and depends on the state of the inputs X and the initial state of the system Z 0: Z = F (Z 0, X). Karasev E. M., 2014
1. System status. State assessment The internal state is practically unobservable, but it can be estimated from the state of the outputs (values of the output variables) of the system Y = (y 1, y 2, ..., ym) due to the dependence Y = F 2(Z). In this case, we should talk about output variables in a broad sense: not only the output variables themselves, but also the characteristics of their change can act as coordinates reflecting the state of the system: speed, acceleration, etc. Karasev E. M., 2014
1. System status. State assessment Thus, the internal state of the system S at time t can be characterized by a set of values of its output coordinates and their derivatives at this time: St=(Yt, Y’’t, …). However, it should be noted that the output variables do not completely, ambiguously and untimely reflect the state of the system. Karasev E. M., 2014
1. System status. Process If a system is capable of transitioning from one state to another (for example, S 1 -> S 2 -> S 3> ...), then it is said that it has behavior and a process occurs in it. A process is a sequential change of states. In the case of a continuous change of states we have: P=S(t), and in the discrete case: P=(St 1, St 2, …, ). Karasev E. M., 2014
1. System status. Process In relation to the system, two types of processes can be considered: o o external process - a sequential change of influences on the system, i.e. a sequential change of environmental states; internal process is a sequential change in system states, which is observed as a process at the output of the system. Karasev E. M., 2014
1. System status. Static and dynamic systems A static system is a system whose state practically does not change during a certain period of its existence. A dynamic system is a system that changes its state over time. Clarifying definition: a system whose transition from one state to another does not occur instantly, but as a result of some process, is called dynamic. Karasev E. M., 2014
1. System status. Function of the system The properties of the system are manifested not only by the values of the output variables, but also by its function, therefore, determining the functions of the system is one of the main tasks of its analysis and design. The concept of function has different definitions: from general philosophical to mathematical. Karasev E. M., 2014
1. System status. System function General philosophical concept. Function is the external manifestation of the properties of an object. The system can be single- or multifunctional. Depending on the degree of impact on the external environment and the nature of interaction with other systems, functions can be distributed into increasing ranks: 1. passive existence, material for other systems; 2. maintenance of a higher order system; 3. opposition to other systems, environment; 4. absorption (expansion) of other systems and environment; 5. transformation of other systems and environments. Karasev E. M., 2014
1. System status. System function Mathematical concept. An element of a set Ey of arbitrary nature is called a function of an element x defined on a set Ex of arbitrary nature if each element x from the set Ex corresponds to a single element y from Ey. Karasev E. M., 2014
1. System status. System function Cybernetic concept. A system function is a method (rule, algorithm) for converting input information into output. The function of a dynamic system can be represented by a logical-mathematical model connecting the input (X) and output (Y) coordinates of the system, the “input-output” model: Y=F(X), where F is an operator called the operating algorithm. Karasev E. M., 2014
1. System status. System function In cybernetics, the concept of a “black box” is widely used - a cybernetic model in which the internal structure of an object is not considered (or nothing is known about it). In this case, the properties of an object are judged only on the basis of an analysis of its inputs and outputs. Sometimes the concept of a “gray box” is used when something is still known about the internal structure of an object. The task of system analysis is precisely to “lighten” the box - to turn black into gray, and gray into white. Karasev E. M., 2014
1. System status. System functioning Functioning is considered as the process of the system realizing its functions. From a cybernetic point of view: The functioning of a system is the process of processing input information into output. Mathematically, the functioning of the system can be written as follows: Y(t) = F(X(t)), i.e. the functioning of the system describes how the state of the system changes when the state of its inputs changes. Karasev E. M., 2014
1. System status. State of a system function The function of a system is its property, therefore we can talk about the state of the system at a given point in time, indicating its function, which is valid at that point in time. Thus, the state of the system can be considered in two aspects: o the state of its parameters and o the state of its function, which in turn depends on the state of the structure and parameters: St=(At, Ft) =(At, (Stt, At)) Karasev E.M., 2014
1. System status. State of the system function A system is called stationary if its function practically does not change during a certain period of its existence. For a stationary system, the response to the same impact does not depend on the moment of application of this impact. A system is considered non-stationary if its function changes over time. The nonstationarity of the system is manifested by its different reactions to the same disturbances applied in different periods of time. The reasons for the non-stationary nature of the system lie within it and consist in changes in the function of the system: structure (St) and/or parameters (A). Karasev E. M., 2014
1. System status. State of the system function Stationarity of the system in the narrow sense: A system is called stationary if all internal parameters do not change over time. A non-stationary system is a system with variable internal parameters. Karasev E. M., 2014
1. System status. Modes of a dynamic system Equilibrium mode (equilibrium state, equilibrium state) is a state of a dynamic system in which it can remain for as long as desired in the absence of external disturbing influences or under constant influences. Note: for economic and organizational systems the concept of “equilibrium” is rather conditionally applicable. Karasev E. M., 2014
1. System status. Modes of a dynamic system A transition regime (process) is understood as the process of movement of a dynamic system from some initial state to any of its steady modes - equilibrium or periodic. A periodic regime is a regime in which the system reaches the same states at regular intervals. Karasev E. M., 2014
2. Static and dynamic properties of dynamic systems Based on the dependence of the modeling object on time, static and dynamic characteristics of systems are distinguished, reflected in the corresponding models. Static models (static models) reflect the function of the system - the specific state of a real or designed system or the relationship of its parameters that do not change over time. Karasev E. M., 2014
2. Static and dynamic properties of dynamic systems Dynamic models (dynamics models) reflect the functioning of the system - the process of changing the states of a real or designed system. They show the differences between states, the sequence of changes in states, and the development of events over time. The main difference between static and dynamic models is the consideration of time: in statics it seems to not exist, but in dynamics it is the main element. Karasev E. M., 2014
2. 1 Static characteristics of systems In a narrow sense, the static characteristics of a system can include its structure. However, more often they are interested in the properties of the system for converting inputs into outputs in a steady state, when there are no changes in both input and output variables. such properties are defined as static characteristics. A static characteristic is the relationship between input and output quantities in steady state. A static characteristic can be represented by a mathematical or graphical model. Karasev E. M., 2014
2. 2 Dynamic characteristics of systems A dynamic characteristic is the system’s response to a disturbance (dependence of changes in output variables on input variables and on time). The dynamic characteristic can be represented by: o a mathematical model in the form of a differential equation (or system of equations) of the form: Karasev E. M., 2014
2. Dynamic characteristics of systems using a mathematical model in the form of a solution to a differential equation: a graphical model consisting of two graphs: a graph of changes in disturbance over time and a graph of the object’s reaction to this disturbance - a graphical dependence of the change in output over time. Karasev E. M., 2014
2. 3 Elementary dynamic links To facilitate the task of studying a complex dynamic system, it is divided into individual elements and differential equations are compiled for each of them. To display the dynamic properties of system elements, regardless of their physical nature, the concept of a dynamic link is used. A dynamic link is a part of a system or element described by a certain differential equation. A dynamic link can be represented by an element, a set of elements, or an automatic system as a whole. Karasev E. M., 2014
2. 3 Elementary dynamic links Any dynamic system can be conditionally decomposed into dynamic atoms - elementary dynamic links. To put it simply, an elementary dynamic link can be considered a link with one input and one output. An elementary link must be a directional link: the link transmits influence in only one direction - from input to output, so that a change in the state of the link does not affect the state of the previous link working at the input. Therefore, when dividing the system into links of directed action, a mathematical description of each link can be compiled without taking into account its connections with other links. Karasev E. M., 2014
2. 3 Elementary dynamic links All links are distinguished by the type of equations that determine the characteristics of the transient processes that arise in them under the same initial conditions and the same type of disturbance. To evaluate the behavior of an elementary link, test signals of a certain shape are usually supplied to its input. The following types of disturbing signals are most often used: o o o step effect; impulse impact; periodic signal. Karasev E. M., 2014
2. 3 Elementary dynamic links Stepped impact: A special case of stepwise impact is a single impact, which is described by the so-called unit function x(t) = 1(t): Karasev E. M., 2014
2. 3 Elementary dynamic links Impulse action (unit pulse or delta function) x(t) = δ(t): It should be noted that: Periodic signal: either in the form of a sine wave or in the form of a square wave. Karasev E. M., 2014
2. 4 Types of typical links and their transition functions The impact on the input of the system causes a change in its output y(t) - a transient process called the transition function. The transition (temporary) function is the reaction of the output variable of a link to a change in the input. In the future, we will consider typical links under a single step perturbation. Karasev E. M., 2014
2. 4 Types of typical links and their transition functions An inertia-free link (reinforcing, capacitive, scaling or proportional) is described by the equation: where k is the proportionality or gain coefficient. Karasev E. M., 2014
2. 4 Types of typical links and their transition functions The inertial link (aperidic, capacitive, relaxation) is described by the differential equation: Its transition process is described by the equation: where T is the time constant. Karasev E. M., 2014
2. 4 Types of typical links and their transition functions An ideal (inertia-free) differentiating link is described by a differential equation: At all points except zero, the value of y is equal to zero; at the zero point, y manages to increase to infinity in an infinitesimal time and return to zero. Karasev E. M., 2014
2. 4 Types of typical links and their transition functions A real differentiating link is described by a differential equation, in which, unlike an ideal link, an inertial term additionally appears: When a link is perturbed by a single stepwise action, the transition process in the link is described by the equation: Karasev E. M., 2014
2. 4 Types of typical links and their transition functions The real differentiating link is not elementary - it can be replaced by a connection of two links: ideal differentiating and inertial: Karasev E. M., 2014
2. 4 Types of typical links and their transition functions The integrating link (astatic, neutral) is described by the differential equation: The transition process in the link is described by the solution of this equation: Karasev E. M., 2014
2. 4 Types of typical links and their transition functions An oscillatory link is generally described by the following equation: An oscillatory link is obtained if it contains two capacitive elements capable of storing two types of energy and mutually exchanging these reserves. If during the process of oscillation the energy reserve received by the link at the beginning of the disturbance decreases, then the oscillations die out. At the same time: Karasev E. M., 2014
2. 4 Types of typical links and their transition functions An oscillatory link in general is described by the following equation: If, then instead of an oscillatory link, an aperiodic link of the second order is obtained. Karasev E. M., 2014
2. 4 Types of typical links and their transition functions An oscillatory link in general form is described by the following equation: When we obtain a conservative link with undamped oscillations. Karasev E. M., 2014
2. 4 Types of typical links and their transition functions The pure (transport) delay link repeats the shape of the input signal, but with a time delay: where τ is the delay time. Karasev E. M., 2014
3. State space Since the properties of a system are expressed by the values of its outputs, the state of the system can be defined as a vector of values of output variables Y = (y 1, ..., ym). Therefore, the behavior of the system (its process) can be displayed as a graph in an m-dimensional coordinate system. The set of possible states of the system Y is considered as the state space (or phase space) of the system, and the coordinates of this space are called phase coordinates. Karasev E. M., 2014
3. State space The point corresponding to the current state of the system is called a phase, or representing, point. The phase trajectory is the curve that the phase point describes when the state of the unperturbed system changes (with constant external influences). The set of phase trajectories corresponding to all possible initial conditions is called a phase portrait. Karasev E. M., 2014
3. State space The phase plane is a coordinate plane in which any two variables (phase coordinates) that uniquely determine the state of the system are plotted along the coordinate axes. Fixed (special or stationary) are points whose position in the phase portrait does not change over time. Singular points reflect equilibrium positions. Karasev E. M., 2014
3. State space We will assume that the values of the output coordinate are plotted on the abscissa axis of the phase plane, and the rate of its change is plotted on the ordinate axis. Karasev E. M., 2014
3. State space For phase trajectories of an unperturbed system, the following properties are valid: o only one trajectory passes through one point of the phase plane; o in the upper half-plane the representing point moves from left to right, in the lower half-plane - vice versa; o on the x-axis the derivative dy 2/dy 1=∞ everywhere except for the equilibrium points, therefore the phase trajectories intersect the x-axis (at non-singular points) at a right angle. Karasev E. M., 2014
4. Stability of dynamic systems Stability is understood as the property of a system to return to an equilibrium state or cyclic mode after eliminating the disturbance that caused the disruption of the latter. The state of stability (stable state) is the equilibrium state of the system to which it returns after removing the disturbing influences. Karasev E. M., 2014
4. Stability of dynamic systems Alexander Mikhailovich Lyapunov: A fixed point of a system a is called stable (or an attractor) if for any neighborhood N of point a there is some smaller neighborhood of this point N' such that any trajectory passing through N' remains in N for increasing t. Karasev E. M., 2014
4. Stability of dynamic systems Attractor - (from the Latin attraho - I attract to myself) - a region of stability where trajectories in phase space tend. A fixed point of a system a is called asymptotically stable if it is stable and, in addition, there exists a neighborhood N of this point where any trajectory passing through N tends to a as t tends to infinity. Karasev E. M., 2014
4. Stability of dynamical systems A fixed point of a system that is stable, but not asymptotically stable, is called neutrally stable. A fixed point of a system that is not stable is called unstable (or repeller). Repeller (from the Latin repello - I push away, drive away) is a region in phase space where trajectories, even starting very close to a singular point, are repelled from it. Karasev E. M., 2014
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The state of the system is determined by levels.
A level is the amount of mass, energy, information contained in a variable (block) or in the system as a whole at a given moment in time.
Levels do not remain constant, they undergo certain changes. The speed at which these changes occur is called tempo.
Rates determine the activity, intensity and speed of the processes of transformation, accumulation, transmission, etc. matter, energy, information flowing within the system.
Tempos and levels are interrelated, but their relationship is not clear-cut. On the one hand, rates generate new levels, which in turn influence rates, i.e. regulate them.
For example, the process of substance diffusion determines the transition of the system from level x 1 to level x 2 (the driving force of the mass transfer process). At the same time, the speed of this process (rate of mass transfer) depends on the mass of the indicated levels in accordance with the expression:
where: a is the mass transfer coefficient.
One of the most important characteristics of the system state is feedback.
Feedback is the property of a system (block) to respond to a change in one or more variables caused by an input influence, in such a way that, as a result of processes within the system, this change again affects the same or the same variables.
Feedback, depending on the method of influence, can be direct (when the reverse influence occurs without the participation of variables (blocks) - intermediaries) or contour (when the reverse influence occurs with the participation of variables (blocks) - intermediaries) (Fig. 3).
Rice. 3. Feedback principle
a – direct feedback; b – loop feedback.
Depending on the impact on primary changes in variables in the system, two types of feedback are distinguished:
§ Negative feedback, i.e. when an impulse received from the outside forms a closed circuit and causes attenuation (stabilization) of the initial impact;
§ Positive feedback, i.e. when an impulse received from the outside forms a closed circuit and causes an increase in the initial impact.
Negative feedback is a form of self-regulation that ensures dynamic balance in the system. Positive feedback in natural systems usually manifests itself in the form of relatively short-term bursts of self-destructive activity.
The predominantly negative nature of the feedback indicates that any change in environmental conditions leads to a change in the variables of the system and causes the system to transition to a new equilibrium state, different from the original one. This process of self-regulation is commonly called homeostasis.
The system’s ability to restore equilibrium is determined by two more characteristics of its state:
§ System stability, i.e. a characteristic indicating what magnitude of change in external influence (impact impulse) corresponds to the permissible change in the system variables, at which equilibrium can be restored;
§ System stability, i.e. a characteristic that determines the maximum permissible change in system variables at which equilibrium can be restored.
The goal of regulation in the system is formulated in the form of an extreme principle (the law of maximum potential energy): the evolution of the system goes in the direction of increasing the total energy flow through the system, and in a stationary state its maximum possible value is achieved (maximum potential energy).
Systematic approach to modeling
Concept of the system. The world around us consists of many different objects, each of which has various properties, and at the same time the objects interact with each other. For example, objects such as the planets of our solar system have different properties (mass, geometric dimensions, etc.) and, according to the law of universal gravitation, interact with the Sun and with each other.
The planets are part of a larger object - the Solar System, and the Solar System is part of our Milky Way galaxy. On the other hand, planets are made up of atoms of various chemical elements, and atoms are made up of elementary particles. We can conclude that almost every object consists of other objects, that is, it represents system.
An important feature of the system is its holistic functioning. A system is not a set of individual elements, but a collection of interconnected elements. For example, a computer is a system consisting of various devices, and the devices are interconnected both hardware (physically connected to each other) and functionally (information is exchanged between devices).
System is a collection of interconnected objects called system elements.
The state of the system is characterized by its structure, that is, the composition and properties of the elements, their relationships and connections with each other. The system maintains its integrity under the influence of various external influences and internal changes as long as it maintains its structure unchanged. If the structure of the system changes (for example, one of the elements is removed), then the system may cease to function as a whole. So, if you remove one of the computer devices (for example, a processor), the computer will fail, that is, it will cease to exist as a system.
Static information models. Any system exists in space and time. At each moment of time, the system is in a certain state, which is characterized by the composition of the elements, the values of their properties, the magnitude and nature of the interaction between the elements, and so on.
Thus, the state of the Solar system at any moment in time is characterized by the composition of the objects included in it (the Sun, planets, etc.), their properties (size, position in space, etc.), the magnitude and nature of the interaction with each other (gravitational forces, with the help of electromagnetic waves, etc.).
Models that describe the state of a system at a certain point in time are called static information models.
In physics, examples of static information models are models that describe simple mechanisms, in biology - models of the structure of plants and animals, in chemistry - models of the structure of molecules and crystal lattices, and so on.
Dynamic information models. The state of systems changes over time, that is, processes of change and development of systems. So, the planets move, their position relative to the Sun and each other changes; The Sun, like any other star, develops, its chemical composition, radiation, and so on change.
Models that describe the processes of change and development of systems are called dynamic information models.
In physics, dynamic information models describe the movement of bodies, in biology - the development of organisms or animal populations, in chemistry - the processes of chemical reactions, and so on.
Questions to Consider
1. Do computer components form a system: Before assembly? After assembly? After turning on the computer?
2. What is the difference between static and dynamic information models? Give examples of static and dynamic information models.
There are many concepts of a system. Let's consider the concepts that most fully reveal its essential properties (Fig. 1).
Rice. 1. Concept of system
“A system is a complex of interacting components.”
“A system is a set of interconnected operating elements.”
“A system is not just a collection of units... but a collection of relationships between these units.”
And although the concept of a system is defined in different ways, it usually means that a system is a certain set of interconnected elements that form a stable unity and integrity, which has integral properties and patterns.
We can define a system as something whole, abstract or real, consisting of interdependent parts.
System can be any object of living and inanimate nature, society, process or set of processes, scientific theory, etc., if they define elements that form unity (integrity) with their connections and interrelations between them, which ultimately creates a set of properties, inherent only to a given system and distinguishing it from other systems (property of emergence).
System(from the Greek SYSTEMA, meaning “a whole made up of parts”) is a set of elements, connections and interactions between them and the external environment, forming a certain integrity, unity and purposefulness. Almost every object can be considered as a system.
System– is a set of material and intangible objects (elements, subsystems) united by some kind of connections (informational, mechanical, etc.), designed to achieve a specific goal and achieving it in the best possible way. System is defined as a category, i.e. its disclosure is carried out through identifying the main properties inherent in the system. To study a system, it is necessary to simplify it while maintaining the basic properties, i.e. build a model of the system.
System can manifest itself as an integral material object, representing a naturally determined set of functionally interacting elements.
An important means of characterizing a system is its properties. The main properties of the system are manifested through the integrity, interaction and interdependence of the processes of transformation of matter, energy and information, through its functionality, structure, connections, and external environment.
Property– this is the quality of the object’s parameters, i.e. external manifestations of the method by which knowledge about an object is obtained. Properties make it possible to describe system objects. However, they can change as a result of the functioning of the system. Properties are external manifestations of the process by which knowledge about an object is obtained and it is observed. Properties provide the ability to describe system objects quantitatively, expressing them in units of a certain dimension. The properties of system objects can change as a result of its action.
The following are distinguished: main properties of the system :
· A system is a collection of elements . Under certain conditions, elements can be considered as systems.
· The presence of significant connections between elements. Under significant connections are understood as those that naturally and necessarily determine the integrative properties of the system.
· Presence of a specific organization, which is manifested in a decrease in the degree of uncertainty of the system compared to the entropy of the system-forming factors that determine the possibility of creating a system. These factors include the number of elements of the system, the number of significant connections that the element may have.
· Availability of integrative properties , i.e. inherent in the system as a whole, but not inherent in any of its elements separately. Their presence shows that the properties of the system, although they depend on the properties of the elements, are not completely determined by them. The system is not reduced to a simple set of elements; By decomposing a system into separate parts, it is impossible to understand all the properties of the system as a whole.
· Emergence – irreducibility of the properties of individual elements and the properties of the system as a whole.
· Integrity – this is a system-wide property, which consists in the fact that a change in any component of the system affects all its other components and leads to a change in the system as a whole; conversely, any change in the system affects all components of the system.
· Divisibility – it is possible to decompose the system into subsystems in order to simplify the analysis of the system.
· Communication skills. Any system operates in an environment, it experiences the influence of the environment and, in turn, influences the environment. Relationship between environment and system can be considered one of the main features of the functioning of the system, an external characteristic of the system that largely determines its properties.
· The system is inherent property to develop, adapt to new conditions by creating new connections, elements with their local goals and means of achieving them. Development– explains complex thermodynamic and information processes in nature and society.
· Hierarchy. Below the hierarchy refers to the sequential decomposition of the original system into a number of levels with the establishment of a relationship of subordination of the underlying levels to the higher ones. Hierarchy of the system is that it can be considered as an element of a higher order system, and each of its elements, in turn, is a system.
An important system property is system inertia, determining the time required to transfer the system from one state to another for given control parameters.
· Multifunctionality – the ability of a complex system to implement a certain set of functions on a given structure, which manifests itself in the properties of flexibility, adaptation and survivability.
· Flexibility – this is the property of a system to change the purpose of operation depending on the operating conditions or state of the subsystems.
· Adaptability – the ability of a system to change its structure and choose behavior options in accordance with new goals of the system and under the influence of environmental factors. An adaptive system is one in which there is a continuous process of learning or self-organization.
· Reliability – This is the property of a system to implement specified functions within a certain period of time with specified quality parameters.
· Safety – the ability of the system not to cause unacceptable impacts to technical objects, personnel, and the environment during its operation.
· Vulnerability – the ability to be damaged when exposed to external and (or) internal factors.
· Structurality – the behavior of the system is determined by the behavior of its elements and the properties of its structure.
· Dynamism is the ability to function over time.
· Availability of feedback.
Any system has a purpose and limitations. The goal of the system can be described by the target function U1 = F (x, y, t, ...), where U1 is the extreme value of one of the indicators of the quality of the system’s functioning.
System behavior can be described by the law Y = F(x), reflecting changes at the input and output of the system. This determines the state of the system.
State of the system is an instant photograph, or a snapshot of the system, a stop in its development. It is determined either through input interactions or output signals (results), or through macroparameters, macroproperties of the system. This is a set of states of its n elements and connections between them. The specification of a specific system comes down to the specification of its states, starting from its inception and ending with its death or transition to another system. A real system cannot be in any state. Her condition is subject to restrictions - some internal and external factors (for example, a person cannot live 1000 years). Possible states of a real system form in the space of system states a certain subdomain Z SD (subspace) - the set of permissible states of the system.
Equilibrium– the ability of a system, in the absence of external disturbing influences or under constant influences, to maintain its state for an indefinitely long time.
Sustainability is the ability of a system to return to a state of equilibrium after it has been removed from this state under the influence of external or internal disturbing influences. This ability is inherent in systems when the deviation does not exceed a certain established limit.
3. Concept of system structure.
System structure– a set of system elements and connections between them in the form of a set. System structure means structure, arrangement, order and reflects certain relationships, the mutual position of the components of the system, i.e. its structure and does not take into account the many properties (states) of its elements.
The system can be represented by a simple listing of elements, but most often when studying an object, such a representation is not enough, because it is necessary to find out what the object is and what ensures the fulfillment of its goals.
Rice. 2. System structure
The concept of a system element. A-priory element- It is an integral part of a complex whole. In our concept, a complex whole is a system that represents an integral complex of interconnected elements.
Element- a part of the system that is independent in relation to the entire system and is indivisible with this method of separating parts. The indivisibility of an element is considered as the inexpediency of taking into account its internal structure within the model of a given system.
The element itself is characterized only by its external manifestations in the form of connections and relationships with other elements and the external environment.
Communication concept. Connection– a set of dependencies of the properties of one element on the properties of other elements of the system. Establishing a connection between two elements means identifying the presence of dependencies in their properties. The dependence of the properties of elements can be one-sided or two-sided.
Relationships– a set of two-way dependencies of the properties of one element on the properties of other elements of the system.
Interaction– a set of interrelations and relationships between the properties of elements, when they acquire the nature of interaction with each other.
The concept of the external environment. The system exists among other material or intangible objects that are not included in the system and are united by the concept of “external environment” - objects of the external environment. The input characterizes the impact of the external environment on the system, the output characterizes the impact of the system on the external environment.
In essence, delineating or identifying a system is the division of a certain area of the material world into two parts, one of which is considered as a system - an object of analysis (synthesis), and the other - as the external environment.
External environment– a set of objects (systems) existing in space and time that are assumed to have an effect on the system.
External environment is a set of natural and artificial systems for which this system is not a functional subsystem.
Types of structures
Let's consider a number of typical system structures used to describe organizational, economic, production and technical objects.
Usually the concept of “structure” is associated with the graphic display of elements and their connections. However, the structure can also be represented in matrix form, the form of a set-theoretic description, using the language of topology, algebra and other systems modeling tools.
Linear (sequential) the structure (Fig. 8) is characterized by the fact that each vertex is connected to two neighboring ones. When at least one element (connection) fails, the structure is destroyed. An example of such a structure is a conveyor.
Ring the structure (Fig. 9) is closed; any two elements have two directions of connection. This increases the speed of communication and makes the structure more durable.
Cellular the structure (Fig. 10) is characterized by the presence of backup connections, which increases the reliability (survivability) of the functioning of the structure, but leads to an increase in its cost.
Multiply connected structure (Fig. 11) has the structure of a complete graph. Operational reliability is maximum, operational efficiency is high due to the presence of shortest paths, cost is maximum.
Star the structure (Fig. 12) has a central node, which acts as a center; all other elements of the system are subordinate.
Graphovaya structure (Fig. 13) is usually used when describing production and technological systems.
Network structure (net)- a type of graph structure that represents a decomposition of the system in time.
For example, a network structure can reflect the order of operation of a technical system (telephone network, electrical network, etc.), stages of human activity (in production - a network diagram, in design - a network model, in planning - a network model, network plan, etc. .d.).
Hierarchical structure is most widely used in the design of control systems; the higher the hierarchy level, the fewer connections its elements have. All elements except the upper and lower levels have both command and subordinate control functions.
Hierarchical structures represent a decomposition of a system in space. All vertices (nodes) and connections (arcs, edges) exist in these structures simultaneously (not separated in time).
Hierarchical structures in which each element of the lower level is subordinate to one node (one vertex) of the higher one (and this is true for all levels of the hierarchy) are called tree-like structures (structures "tree" type; structures on which tree order relationships are carried out, hierarchical structures with strong connections) (Figure 14, a).
Structures in which an element of a lower level can be subordinate to two or more nodes (vertices) of a higher level are called hierarchical structures with weak connections (Figure 14, b).
The designs of complex technical products and complexes, the structures of classifiers and dictionaries, the structures of goals and functions, production structures, and organizational structures of enterprises are presented in the form of hierarchical structures.
In general, the termhierarchy more broadly, it means subordination, the order of subordination of persons of lower position and rank to higher ones, it arose as the name of the “career ladder” in religion, is widely used to characterize relationships in the apparatus of government, army, etc., then the concept of hierarchy was extended to any coordinated order of objects according to subordination.
Thus, in hierarchical structures, it is only important to highlight the levels of subordination, and there can be any relationship between the levels and components within the level. In accordance with this, there are structures that use the hierarchical principle, but have specific features, and it is advisable to highlight them separately.
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