1. Block diagrams & Signal flow graphs
Automatic control
1. modeling
Lesson 5
Block diagrams
&
Signal flow graphs

2. Automatic Control by Meiling CHEN
block
pickoff point
summer
Automatic Control by Meiling CHEN

3. Automatic Control by Meiling CHEN

4. Automatic Control by Meiling CHEN

5. Automatic Control by Meiling CHEN

6. Automatic Control by Meiling CHEN
original
equivalent
Automatic Control by Meiling CHEN

7. Automatic Control by Meiling CHEN
original
equivalent G G G G
Automatic Control by Meiling CHEN

8. Automatic Control by Meiling CHEN
original
equivalent G G G G G
Automatic Control by Meiling CHEN

9. Automatic Control by Meiling CHEN
Example 1
Automatic Control by Meiling CHEN

10. Automatic Control by Meiling CHEN
Example 2
Automatic Control by Meiling CHEN

11. Automatic Control by Meiling CHEN
Signal flow graphs
Automatic control
Automatic Control by Meiling CHEN

12. Automatic Control by Meiling CHEN

13. Automatic Control by Meiling CHEN
Mason’s Rule
Mason’s gain rule is as follows: the transfer function of a system with signal-input, signal-output flow graphs is
Δ=1-(sum of all loop gains)+(sum of products of gains of all combinations if 2 nontouching loops)- (sum of products of gains of all combinations if 3 nontouching loops)+…
A path is any succession of branches, from input to output, in the direction of the arrows, that does not pass any node more than once.
A loop is any closed succession of branches in the direction of the arrows that does not pass any node more than once.
Automatic Control by Meiling CHEN

14. Automatic Control by Meiling CHEN
Example 3
Automatic Control by Meiling CHEN

15. Automatic Control by Meiling CHEN
Example 4
find
Automatic Control by Meiling CHEN