Wednesday, September 2, 2015

Block Diagram Algebra

The transfer function for the input output behaviour of a linear system or element of a linear system is given by
G(s) = C(s)/R(s)
where R(S )-Laplace transform  of the input variable  and 
C(S)-Laplace transform of  the  output variable 

A control system may have many number of components  connected to each  other  and each components have its own transfer function .To show this different transfer function of each component a block diagram is generally referred .
block diagram of  a system is pictorial representation or convenient graphical representation of the input -output behaviour i.e. transfer function of each component and of the flow signals . The block diagram depicts the interrelationship  between different system components .The block diagram  representation is more advantageous than mathematical representation as it identical the flow of signal of the actual system more realistically .
The block itself shows transfer function and it is a system of mathematical  operation on the input signal to the block that produces output signal .The flow  of information is unidirectional from input to the output with the output being equal to the result of product of input and output transfer function. The blocks are connected by lines with arrows indicating the unidirectional flow of information. The arrowhead which points toward the block designates the input and the arrowhead coming out of the block that is leading away from the block represents the output. Such arrows are referred to as signal.
Block Diagram Algebra - Figure
Block Diagram Algebra - Figure

The above figure shows that the signal into the block represents the input R(s) and the signal leading away from the block represents the output C(s), while the block itself represents the transfer function.
Summing Point - Figure
Summing Point

Summing Point :- The figure (b) shows the summing operation. The plus indicated that the signal a and b are to be added. The quantities being added have the same dimension and units. Figure (a) shows the differencing operation. The plus and minus sign indicates that the two signals a and b are to be subtracted. If the circle with cross symbol is not shown with any sign convention, by default the two signals are added.
Branch Point :- It is a point from which the signal from block goes concurrently to other block.
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