John Mason Example Block Diagram Problem. March 24, 1997

Find T(s) = Y(s)/X(s) for the block diagram below.

Step 1: Series Connection - Multiply the values

Which yeilds:

Step 2: Parallel Connection - Add the values

Which yeilds:

Step 3: Feedback connection

Which yeilds:

Step 4: Series connection - Multiply

Which yeilds:

Step 5: Feedback Connection (The rest of the system)

Which yeilds:

Calculations below:

G1G3 + G1G2G4 G1(G3 + G2G4)

Y(s) = 1 + G1H1 = 1 + G1H1

1 + G1G3H2 + G1G2G4H2 1 + G1H1 + G1H2(G3 + G2G4)

1 + G1H1 1 + G1H1

Therefore,

Y(s) = G1(G3 + G2G4)

1 + G1H1 + G2H2(G3 + G2G4)