T he block diagram shown in Fig 2.1B.1 can be simplified to a single transfer function using either of the two methods discussed in Section 2.1. The goal is to find a single transfer function relating the input Y to the output X. In this example it is implied that all variables or functions are functions of the Laplace variable,s. Thus G is G(s), etc.
In the brute force method, we add a variable to the output of each block, write the equation relating input to output for each block and eliminate the unwanted variables from the equations.
The block diagram can also be simplified by replacing groups of block with equivalent simplified block. Continue simplifying the block diagram until one block remains.