Terminology
System

The term system is necessary to understand certain set of elements, their relationships and properties schematic sketch is shown in Figure 2.1 Understand the definition of a complete set of "S", which consists of a set of elements and sets their mutual relations. The system "S" has a set of inputs and a set of faults. System "S" turn on the external environment has a set of outputs. If the system "S" has some prescribed behavior in him a set of desired variables and a set of regulatory differences.

Fig. 2.1: System scheme

Image readers a general definition can be made on a technical example flying aircraft. The machine itself is composed of hundreds of parts, each with its own specific function. Furthermore, people in the aircraft, crew and passengers. Because the aircraft is moving in space and time, subject to external influences, such as temperature, wind direction and strength, etc. Other factors that can be described as failure can be sudden turbulence, lightning and aircraft equipment failure. Some of these defects may have a great influence on the main operation of the aircraft - the flight, such as engine failure. Others, such as failure toilets, strongly affect the mood among the passengers, but the main activity is not compromised. Between elements are created relationships, either on the basis of physical laws, social status, sympathy or antipathy. All these elements, states, relationships, values and external disturbances affect the outcome of a safe, happy years and achieving goals.

From the above example it is clear that the system may not only be a machine, but they can be distinguished systems of technical, physical, social, educational, mathematical, historical, social, and other livestock, as well as their combinations. This diversity systems shows that these systems are not easy to somehow split and described.

It may therefore be the mechanical systems, electronic systems, social systems, systems of botanical, zoological systems and of course, their combination. As an example, a technical system can be made car. If flying airliner described as a whole, can be seen as a technical-social system is a closed greenhouse botanical system, etc.

Systems can be classified according to the relationships between input and output variables to: static and dynamic, linear and non-linear, one-dimensional and multidimensional etc.

The numbers of input and output variables are divided systems:

- system with one input and one output signified SISO (single input, single output),
- system with several inputs and one output signified MISO (multi-input, single output),
- system with one input and several outputs signified SIMO (single input, multi-output),
- system with multiple inputs and multiple outputs signified MIMO (multi-input, multi-output).

Regarding the timing, and the sessions are divided systems:

- linear with time stable parameters - LTI (Linear Time Invariant System); example might be the relationship of voltage and current on the resistance,
- volatile linear with time parameters - LTNI (Non-Linear Time Invariant System); example might be the relationship of voltage and current on Photo-resistance,
- non-linear with time-stable parameters - NTI (Nonlinear Time Invariant System); example might be the relationship velocity discharge fluid through a hole at the bottom of an open tank,
- nonlinear unstable with time parameters - NTNI (Nonlinear Time-Invariant Non System); example might be the relationship between the number of births and marriages in society.

An example of a static system can be for example a voltage divider. The output voltage is defined by the size of resistors and input voltage. This relationship is described by the formula . In this respect there is no time dependency and is described only dependent on the input voltage. In contrast, the electric current flowing through the photo resistor depends not only on the supply voltage, but also on the intensity of the incident light. This means that in the course of 24 hours as a session and the system is dynamic.

Linear systems are systems in which all members work with the linear relationship between the output of the input force such as a hydraulic press according to the movement of the control piston. Nonlinear system has at least one member with a non-linear dependence between input and output. An example of a non-linear relation is air resistance a moving car.

A system with one input and one output can be imagined as a refrigerator. The input value is a quantity that represents the loss of heat in the cooling space. The output variable is the actual temperature in the refrigerator compartment. In contrast, flying plane has several inputs: wind speed and direction, outside air temperature, load weight, etc. The outputs are: the angle of horizontal and vertical flaps, throttle, etc.

In Table 1 are used symbols set, their values are then labeled with a lowercase letter.

Table 1: Used symbols
S = {P;R;U;Y;V} | P – elements set | R – relations set | U – inputs set
Y – outputs set | W – set points set | E – control deviations set | V – errors set

Variables of the system are: input (action) variable "u (t)" output variable "y (t)" state variables "x (t)", the error "e (t)" fault variable "v (t) "and the set point value" w (t) ".