Transformation: Differential Equation ↔ Pole-Zero

Given a system differential equation it is possible to derive a pole-zero model directly, but it is more convenient to go first derive the transfer function, and then go from the transfer function to the pole-zero model.

Example: Diff Eq → Pole-Zero

Find a pole-zero model 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 pole-zero representation using the methods described here (TF ↔ PZ).  The pole-zero representation consists of:

Example: Pole-Zero → Diff Eq

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


References

© Copyright 2005 to 2015 Erik Cheever    This page may be freely used for educational purposes.

Erik Cheever       Department of Engineering         Swarthmore College