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img Simplifying Block Diagrams

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.

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Fig 2.1B.1 Simplification using Brute Force

Simplification by Brute Force   img

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.


image/svg+xmlHGY++XF+_z1z2z3z4z1 = Y - z3z2 = F z1z3 = z2 + z4z4 = H XX = G z3z2 = F (Y - z3)z3 = F(Y - z3) + H XFY + H X1+FX = GFY + H X1+Fz3 = FG1 + F - GHX = Y
Fig 2.1B.2 Brute Force Method

Simplification using Equivalent Block Diagrams   img

The block diagram can also be simplified by replacing groups of block with equivalent simplified block (remind me). Continue simplifying the block diagram until one block remains.

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image/svg+xmlYX+_FG1-GH1GHGY++XF+_HGY++XF+_1GYXF+_G1-GH1GYXFG1+F-GH
Fig 2.1B.3 Simplification using Equivalent Block Diagrams