An interactive CAD tool to teach and learn Nyquist criterion Ramon Costa-Castello * Jos´ e Luis Guzman ** Manuel Berenguel *** Sebastian Dormido **** * Universitat Politcnica de Catalunya (UPC) (e-mail: ramon.costa@upc.edu). ** Universidad de Almeria (UAL) (e-mail: joguzman@ual.es) *** Universidad de Almeria (UAL) (e-mail: beren@ual.es) **** Universidad Nacional de Educacin a Distancia (UNED) (e-mail: sdormido@dia.uned.es) Abstract: In his 1932 seminal paper “Regeneration Theory”, Harry Nyquist provided a rigorous set of measurable conditions by which to determine the stability of a feedback amplifier. Nyquist redefined feedback as a frequency-dependent phenomenon, and stability in terms of transient disturbances composed of different frequencies. Nyquists stabiliy criterion applies not only to feedback amplifiers, but to all feedback control systems. The contribution of Nyquist is now a fundamental part of current courses on Automatic Control that has been generalized in several different ways, to complex systems with many loops and to nonlinear systems. The paper describes an interactive CAD tool with the purpose to teach and learn Nyquist criterion. The tool has been developed using Sysquake, a Matlab-like language with fast execution and excellent facilities for interactive graphics, and is delivered as a stand-alone executable that is readily accessible to students and users in feedback control systems. Keywords: Nyquist’s criterion, Control education, Educational aids, Stability analysis, Interactive programs 1. INTRODUCTION The goal for any engineering course is to convey to student engineers the knowledge and skills which will make them valuable to industry. The job market calls for engineers with a broad understanding of the mathematics and the- ory underlying engineering concepts, but also, engineers who are able to apply those concepts with ingenuity and expediency. The second of these skills must be learned by repeated application of the concepts over a wide variety of test conditions. In doing so, the student acquires an intuition for the problems under study. For many years, the primary method of teaching engineering concepts has come in the form of classroom interaction and homework exer- cises. These methods do an adequate job of conveying the mathematics behind the scene but often leave the student lacking the intuition necessary to apply the concepts. The main stumbling block in the building of intuition about a concept is the students inability to visualise the ideas being learned. Many concepts have complex visual repre- sentations which can not be sufficiently explored through the normal classroom experience. For these reasons, a need arises for a set of applications which provide students the opportunity to visually and interactively explore the classroom concepts without use of pen and paper. In re- cent years there has been a growing demand within the educational community in general, and the one dedicated to the teaching of automatic control in particular, for the development of such modules, which provide the student a more complete control of their own learning process. With this kind of tools the students are not constrained to the examples given in the text of study. In addition, to do it in this way students improve their understanding and intuition on the subject. These types of technological de- velopments should be integrated as part of the educational contents. We have addressed these needs by developing a set of interactive cards that facilitate the learning of the relevant concepts of a basic automatic control course (Guzm´anS´ anchez et al., 2012). Each card gives the user full control of the learning process by providing hands- on manipulation of the concepts explored in a complete interactive way. The interactive cards are useful for both teachers and students. In the first case because they allow them to present the concepts in a visual and intuitive way and serve as support for the underlying theory. In the sec- ond case because they facilitate the understanding and the independent learning of basic automatic control concepts and the solution of numerous examples and scenarios that will test their skills and abilities. They can also be a useful platform to assess such learning. Somehow, it follows the idea of R. Bellman Bellman (1971) to look for a good trade off between theory and practice in learning 1 . In this paper we are going to present one of these interactive cards: the Nyquist criterion. The interactive cards are coded in Sysquake, a Matlab- like language with fast execution and excellent facilities for interactive graphics (Piguet, 2004), and is delivered 1 “Theory without application is like the smile of the Cheshire cat; application without theory is blind mans buff” 10th IFAC Symposium Advances in Control Education The International Federation of Automatic Control August 28-30, 2013. Sheffield, UK 978-3-902823-43-4/2013 © IFAC 55 10.3182/20130828-3-UK-2039.00049