Block Diagram Reduction Techniques

  • Determine the overall transfer function of an interconected system, using block diagram reduction techniques.

Rule 1: Blocks in cascade (series):

Blocks in Series

Rule 2: (Combining blocks in parallel):

Blocks in Parallel

Rule 3: (Eliminating a feedback loop):

Eliminating a Feedback Loop

Solved Examples

Solved Example:


Find the equivalent transfer function, T(s) = C(s)/R(s), for the system shown in Figure.


The transfer function will be given by: \begin{align*} T(s) = \dfrac{C(s)}{R(s)} &= \dfrac{G(s)}{1 + G(s) H(s)}\\ &= \dfrac{\left(\dfrac{1}{s}\right)}{1 + \left(\dfrac{1}{s}\right) (5)}\\ &= \dfrac{\left(\dfrac{1}{s}\right)}{\left(1 + \dfrac{5}{s}\right)}\\ &= \dfrac{1}{s+5} \end{align*}

Correct Answer: A