5. Transfer Function

\[\frac{Y(s)}{X(s)} = \frac{K_p}{\tau_p s+1} = \frac{\text{Laplace transform of output deviation}}{\text{Laplace transform of output deviation}} = G(s)\] The above ratio is called the transfer function, \(G(s)\), of the system. In examining physical systems, we usually attempt to obtain a transfer function.



Procedure for obtaining the transfer function for a process:

  1. Write the appropriate balance equations (usually mass or energy balances for a chemical process).

  2. Linearize terms if necessary.

  3. Write the balance equations in deviation variable form.

  4. Take Laplace transform for the linear balance equations.

  5. Rearrange the resulting transformed equation into the transfer function form (i.e., the output divided by the input).