The Root Locus Diagram

The following sections are included:

• The Root Locus—An Introduction

• Rules for Plotting the Root Locus

  • The Symmetry of the Root Locus

  • Branches on the Real Axis

  • The Asymptotic Behavior of the Branches

  • Departure of Branches from the Real Axis

  • A “Conservation Law”

  • The Behavior of Branches as They Leave Finite Poles or Enter Finite Zeros

  • A Group of Poles and Zeros Near the Origin

• Some (Semi-)Practical Examples

  • The Effect of Zeros in the Right Half-Plane

  • The Effect of Three Poles at the Origin

  • The Effect of Two Poles at the Origin

  • Variations on Our Theme

  • The Effect of a Delay on the Root Locus Plot

  • The Phase-lock Loop

  • Sounding a Cautionary Note—Pole-Zero Cancellation

• More on the Behavior of the Roots of Q(s)/K + P(s) = 0

• Exercises