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.

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:

- a constant term, k=3,
- zeros at s=-1 and s=-2, and
- polese at s=-1+j, s=-1-j and s=-3.

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

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

Erik Cheever Department of Engineering Swarthmore College