Rules for the conversion of structural schemes. negative connections. problem solving examples

A structural diagram of any complexity can be reduced to an equivalent single-loop (having one main feedback) or to an equivalent open-loop block diagram.

If there are a large number of elements in the system, a structural method is used, according to which the equation of the entire system is obtained on the basis of an algorithmic scheme using several simple rules.

The essence of the method is that by the known transfer functions of the individual elements of the system, which are the detecting links of unidirectional action, using the rules of the series, parallel and counter-parallel (with feedback) links of the links, they receive an equivalent transfer function or transfer function of the equivalent link. The result is a single-circuit closed chain consisting of several equivalent links.

Moreover, this chain can have multiple inputs and multiple outputs. Further, according to the single-circuit scheme, transfer functions between the open inputs and outputs of the system are recorded.

Structural transformations of the circuits are valid if they keep all the input and output signals of the system unchanged.

Schema conversion rules

1. If the node is transferred against the direction of the signal, then the portable branch should include elements with those transfer functions that are encountered along the path of the old and new points of the node's location.
2. If the node is transferred in the direction of the signal, then the portable branch should include elements with transfer functions inverse to the transfer functions of elements that occur along the path between the new and the old points of the node location.

Structural transformations of the circuits are valid if they keep all the input and output signals of the system unchanged.

The possibility of structural transformations of systems is provided by the principle of superposition and reversibility of signals:

(2.1) (2.1)

Rule 1: Permutation of the same type of elements (Table 2.1)

Table 2.1

Rearrange the node (adder or links)

Neighboring elements of the same type can be rearranged in places without changing anything in the scheme itself.

Rule 2: Transfer node from the output to the input of the adder (through the adder against the signal). Such a transfer is accompanied by duplication of the element (adder or link) (Fig. 2.1).

Fig. 2.1. Transfer node:

and - the transformed scheme; b - transformed circuit

Rule 3: Transferring a node through a link against the signal travel (Fig. 2.2).

Fig. 2.2. Transfer node through link:

and - the transformed scheme; b - transformed circuit

Rule 4: Transfer node and link through the adder. With such a transfer, it is necessary to install a subtractive device in the node branch (Fig. 2.3).

Fig. 2.3. Moving a node through the adder in the direction of the signal:

and - the transformed scheme; b - transformed circuit

Rule 5: Transfer the link through the adder in the direction of the signal (Fig. 2.4).

Fig. 2.4. Link transfer through adder:

and - the transformed scheme; b - transformed circuit

In this case, a dynamic link is added to the branch:

Rule 6: Transfer node through the link in the direction of the signal. With this transfer, an additional link with the reverse transfer function must be installed in the node branch (Fig. 2.5)

Fig. 2.5. Transfer node through link:

and - the transformed scheme; b - transformed circuit

Rule 7: Transfer the link through the adder against the signal. In this case, the link with the transfer function must be added to the portable branch (Fig. 2.6).

Fig. 2.6. Link transfer through adder:

and - the transformed scheme; b - transformed circuit

Block diagram of a closed two-loop system with negative feedback links (without cross-links)