Given a system differential equation it is possible to derive a signal flow graph directly, but it is more convenient to go first derive the transfer function, and then go from the transfer function to the state space model, and then from the state space model to the signal flow graph.

Find a signal flow graph for the system described by the differential equation:

**Step 1: **Find the transfer function using the methods
described here (1DE ↔ TF)

**Step 2:** Find a state space representation using the
methods described here (TF ↔ SS). In this case we are using a CCF
form).

**Step 3:** Find a signal flow graph using the
methods described here (TF ↔ SFG).

This example is not yet finished

Repeat the previous example, but reverse the order (i.e., do step 3 (SFG → SS) then step 2 (SS → TF)then step 1 (TF → DE)).

Another option is to go directly from the Signal Flow Graph to the Transfer Function directly (using Mason's gain formula) and then go from the transfer function to the differential equation.

© Copyright 2005 to 2019 Erik Cheever This page may be freely used for educational purposes.

Erik Cheever Department of Engineering Swarthmore College