Control Theory #34 — Pole-Zero Analysis (Worked Example 11)

Instructor: Dr. Süleyman Burak ÇELİK

In this worked example, we analyze two transfer functions from their pole-zero diagrams. We write the transfer functions, determine relative degrees, check stability, and match a state space model to the correct system matrix. Topics covered: - Part (a): Writing transfer functions from pole-zero plots with K = -2 - Part (b): Relative degree calculation (poles minus zeros) - Part (c): Stability analysis (all poles in left half plane) - Part (d): Matching eigenvalues of candidate A matrices to G2 poles Key results: - G1(s) = -2(s-0.2)/(s+0.2), relative degree 0 - G2(s) = 2(s-0.2)/[(s+0.2)(s^2+0.8s+0.25)], relative degree 2 - Both stable, zero at +0.2 is non-minimum phase (no effect on stability) - State space match: A1 (eigenvalues = poles of G2) Every step shown clearly — no shortcuts. Playlist: Control Theory - AcEdumy GitHub: https://github.com/acedumy