Control Process-Block Diagram

Transfer Functions
 
 
Definition:
The relationship from an input signal, u, to an output signal, y, in the Laplace transform domain.

1. Equation form: L[y] = G(s) L[u]
2. Block Diagram form:

Block Diagram Equivalence:

1. Series:
    is equivalent to    
2. Parallel:
      is equivalent to:    
3. Positive Feedback:
    is equivalent to:    
4. Negative Feedback:

is equivalent to

Additional Rules:

1. Summing Junctions
   
2. For the transfer functions of multiple inputs: u₁, u₂, etc., to output y, use superposition. That is, for the transfer function of u₁ to y, disregard the effects u₂, u₃ etc.

Example 1:
 



 



is equivalent to: