Improvement for Root Locus Method Teaching by Introducing New Applications

The root locus method is one of the fundamental methods in classical control theory, which, however, has not received considerable attention in modern control theory. The gap of the root locus method's utility between classical control theory and modern control theory has thus become an important issue, especially in the teaching of the root locus method for undergraduate students. In this paper, we propose an improvement for root locus method teaching by introducing new applications of the root locus method from the study on near-controllability and controllability of discrete-time bilinear systems. In the new applications, the root locus method is used to prove near-controllability and controllability, instead of verifying stability. Since controllability is one of the fundamental concepts in modern control theory, the new applications can help the students better understand the root locus techniques from the classical control theory point of view to the modern control theory point of view. Examples are given to illustrate the proposed improvement for root locus method teaching, which can be used in textbooks, exercises, and courses.