1. Block diagram reduction

2. Block reduction rules
It is important to note that blocks can be connected in series only if the output of one block is not affected by the next following block. If there are cascaded blocks, we can replace them by their multiply in one block. Any simple feedback loops can be reduced to one block.
Complicated block diagram can be treated step by step to reduce it using the following rules:

3. Rule (1): Negative feedback

4. Rule (2): Cascade blocks

5. Rule (3): Parallel blocks

6. Rule (4): Moving signal backward

7. Rule (5): Moving signal forward

8. Rule (6): Moving summing point

9. Rule (7): Moving summing point

10. Rule (8): Order of summing points

12. Example 2

13. Example 3

15. Example 4
Consider the diagram below

16. Reduce cascaded block
Reduce feedback block in internal loop

17. Remove next feedback block in internal loop

19. Example 5

20. Example 6