By the end of this section, you should be able to

1. Use Root Locus method to design P and PD controller

2. Use Simulink to implement and test controllers numerically

This section introduces the root locus method, a core technique in control systems for visualizing how closed-loop poles move as the feedback gain K changes. Root locus gives you a practical bridge between a transfer function model and the time-domain behavior you care about, including stability, overshoot, and settling time. In the materials below you will work through the logic of selecting K, building and interpreting a root locus plot, and then using that plot to choose controller settings that meet performance targets. You will apply the method to design a proportional (P) controller and a proportional-derivative (PD) controller, with emphasis on selecting a desired pole location and understanding what that choice implies for transient response. You will also use Simulink to implement and test controllers numerically, so your hand analysis connects directly to simulation results and model validation. Use the table of contents below to jump between the overview topics, the P controller example, the desired pole selection workflow, the PD controller example, and the lecture code resources.