A unified approach for teaching root locus and bode compensator design

In an undergraduate controls course taught with a standard textbook, students often lose sight of the "forest" of control systems design because they struggle to master the numerous control system algorithm "trees" found in this textbook. As an alternative, the authors of this paper propose a design approach that is common for a large variety of compensators using both the more intuitive root locus design and the more practical Bode design methods. This approach is based on a simple procedure for root locus Proportional-Derivative (PD) design. In this paper, the Bode design procedures for three compensators: lead, PI, and Proportional-Integral-Derivative (PID) are developed from this simple PD design. Procedures for rate feedback, lag and PI-lead (practical PID) compensators have also been developed using this approach. The proposed Bode design procedures are very similar to the procedures developed for root locus design published previously. An example of a lead design from an undergraduate control system laboratory demonstrating this approach is presented.