Advances in undergraduate control education: the analytical design approach

Introductory undergraduate control courses in the USA are generally limited to trial-and-error design techniques, based largely on the Nyquist stability criterion and root-locus analysis. The corresponding theory is well over fifty years old. Very little is presented on analytic design, where one has an existence theorem, and a computable algorithm to find a solution when one exists. One reason for the lack of analytic design in introductory courses is the level of mathematics required to understand much of this theory. Here we summarize some of the existing analytic design techniques, and their mathematical pre-requisites, and then we propose the interpolation approach for analytic design, as one requiring the least amount of mathematics.