# Feedback control system Block diagram

In addition to that, the diagram also shows there is a feedback path through which output signal C(s) is fed back and compared with the input R(s) and the difference between input and output E(s) = R(s) – C(s) is acting as actuating signal or error signal. In each block of diagram, the output and input are related together by transfer function. Where, transfer function where, C(s) is the output and R(s) is the input of that particular block. A complex control system consists of several blocks. Each of them has its own transfer function. But overall transfer function of the system is the ratio of transfer function of final output to transfer function of initial input of the system. This overall transfer function of the system can be obtained by simplifying the control system by combining this individual blocks, one by one. Technique of combining of these blocks is referred as **block diagram reduction technique**. For successful implementation of this technique, some rules for block diagram reduction to be followed. Let us discuss these rules, one by one for reduction of block diagram of control system.

If the transfer function of input of control system is R(s) and corresponding output is C(s), and the overall transfer function of the control system is G(s), then the control system can be represented as

### Take off Point of Block Diagram

when we need to apply one or same input to more than one blocks, we use**take off point**. A point is where the input gets more than one paths to propagate. This to be noted that the input does not get divided at a point, hence input propagates through all the paths connected to that point without affecting its value. Hence, by take off point same input signals can be applied to more than one systems or blocks. Representation of a common input signal to more than one blocks of control system is done by a common point as shown in the figure below with point X.