Block Diagram Reduction Rules

To form a control system the block are arranged together as required and the steps followed to obtain the transfer function are called Block Diagram Reduction Method.

Following are the rules to be followed during finding the transfer function of the system

Rule 1 : when more than one block is cascaded than overall transfer function is multiplication of all the transfer function .

G1(s) = C1(s)/ R(s) ; G2(s) = C2(s) / C1(s) ; G3(s) = C(s) / C2(s)

C(s) / R(s) = G1(s) . G2(s) . G3(s)

Rule 2 : When two or more input signal enters into system that point is known as Summing Point and the output coming out from summing point will be the sum of all the input entered through summing point .

Rule 3 : When there are two or more summing point than we can change the position of summing point with each other as shown below in fig .

Rule 4 : When one or more blocks are connected in parallel to other block than the final equivalent transfer function can be find as following

C(s) = R(s) G1(s) + R(s) G2(s) + R(s) G3(s)

C(s) = R(s) [ G1(s) + G2(s) + G3(s) ]

C(s) /R(s) = G1(s) + G2(s) + G3(s)

Rule 5 : When take off point is shifted from position before block to a position after block than a block is added having gain equals to reciprocal of current gain as shown below.

Rule 6 : When take off point is shifted from a position after block to a position before the block than a block is added having gain equals to current gain as shown below .

Rule 7 : When a summing point is shifted from a position before a block to position after the block , a block is added to summing point having gain equals to current gain .

Rule 8 : When a summing point is shifted from a position after a block to a position before the block , a block is added having gain equals to reciprocal of current gain .

Rule 9 : when a take off point is shifted from a position before a summing point to position after the summing point , it takes place as shown in below fig.

Rule 10 : Shifting a take off point from a position after a summing point to position before summing point is shown in below fig.

Rule 11 : Elimination of summing point in closed loop system is done as shown in below fig .

As we know a complex control system is difficult to analyze as various factors are associated with it. In this article, we will see how to easily analyze a control system, and it is only possible by using block diagram reduction rules. This representation of a system involves summing points, functional blocks, etc., connected through branches which makes the analysis easy, simple, and step by step, crystal clear.

We will start our Article with Methods of Block Diagram Reduction Rules, and Then we will go through all the rules of Block Reduction, At last, we will Solve a Problem block diagram reduction technique.