What is the root locus method and how is it used in control design?

Root locus shows how closed-loop pole locations change as a parameter (usually gain K) varies from 0 to infinity. Locus starts at open-loop poles (K=0) and ends at open-loop zeros (K=infinity). Rules determine locus shape: number of branches, real-axis segments, asymptotes, breakaway/break-in points, and angle of departure/arrival. Designers use root locus to select gain for desired pole location (damping, speed) and assess stability. MATLAB and similar tools plot root locus automatically.