Transformation: Pole-Zero ↔ Signal Flow Graph

Given a pole-zero representation of a system 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.

Example: Pole-Zero→ Signal Flow Graph

Find a signal flow graph that represents the system with the following pole-zero description:

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Step 1: Find the transfer function using the methods described here (PZ ↔ 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 (SS ↔ SFG).

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Example: Signal Flow Graph → Pole-Zero

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


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

Erik Cheever       Department of Engineering         Swarthmore College