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