Structural transformation systems. Structural schemes. The main types of connection elements. Examples of tasks

A block diagram is a conventional graphic representation of a mathematical model of an automatic system (hereinafter referred to as the AU).

The structural diagram consists of images of elementary dynamic links in the form of rectangles, in which their transfer functions and switching elements are recorded (Table 1.1). An example of the simplest structural scheme is shown in Fig. 1.1.

Table 1.1

Elements of structural schemes

Fig. 1.1. The simplest structural diagram

The structural scheme differs from the functional one in that it gives a complete mathematical description of the system, but does not necessarily have to correspond to the very structure of the described system. The element of the structural scheme does not necessarily correspond to the real element of the automatic system.

Three basic types of compound elements.

1. When the elements are connected in series, the output signal of each preceding element is the input signal of the subsequent element (Fig. 1.2).

Fig. 1.2. Consistent connection of elements

The transfer function of the system:

(1.26)

2. Parallel connection of links is called such a connection, in which the output of all elements receives the same effect, and their output values ​​are algebraically summed (Fig. 1.3):

Fig. 1.3. Parallel connection of elements

The transfer function of the system:

(1.27)

3. A counter-parallel connection of two elements is called such a connection, in which the output signal of the second element arrives at the output of the second, and the output signal of the second element is algebraically summed with the common input signal. Diagram of the anti-parallel connection is shown in Fig. 1.4:

Fig. 1.4. Counter-parallel connection

Negative feedback transfer function:

(1.28)

Positive feedback transfer function:

(1.29)

W _p ( p ) is the transfer function of the open-loop system;

W _oc ( p ) - feedback transfer function;

Examples of problem solving