Education - A High School-Level Course in Feedback Control - A Matlab-Based Introduction Requiring Only Algebra and Trigonometry

JUNE 2007 « IEEE CONTROL SYSTEMS MAGAZINE 79 T he purpose of this article is to describe a control education and outreach effort being undertaken at the University of California, Santa Cruz (UCSC). The goal of our effort is to provide an introductory course on feedback control that is accessible to high school students and first-year undergraduate students. In the early stages of our effort, we found ample motivation in the literature for creating such a course. In 1998, an article from the “NSF/CSS Workshop on New Directions in Control Engineering Education” [1] made the following recommendations regarding needed reform in undergraduate control education: » “to provide practical experience in control systems engineering to first-year college students to stimulate future interest and introduce fundamental notions like feedback and the systems approach to engineering” » “to encourage the development of new courses and course materials that would significantly broaden the standard first introductory control systems course at the undergraduate level.” In 2003, a panel on future directions in control, dynamics, and systems provided a renewed vision of challenges and opportunities, along with recommendations to agencies and universities to ensure continued progress in areas of importance to the industrial and defense base [2]. One of the five primary recommendations is that the community and funding agencies invest in “new approaches to education and outreach for the dissemination of control concepts and tools to nontraditional audiences. As a first step toward implementing this recommendation, new courses and textbooks should be developed for both experts and nonexperts.” The panel also recommended the integration of software tools such as Matlab into these courses. Outreach motivation has also been provided from outside the control field. Ten years ago, feedback control was identified by the National Science Education Standards as being fundamental to understanding systems, and systems in turn was identified as a unifying concept for K–12 science education [3]. In 2005, the need for curricular material that motivates middle school and high school students to pursue advanced work in science and mathematics in the United States was underscored by the Committee on Prospering in the Global Economy of the 21st Century, a subcommittee of the National Academy of Sciences, National Academy of Engineering, and the Institute of Medicine [4]. This article presents an overview of an introductory course on feedback control amenable to traditional and nontraditional audiences. The course material is based on fundamental concepts in dynamical systems, modeling, stability analysis, robustness to uncertainty, feedback as it occurs naturally, and the design of feedback control laws to engineer desirable static and dynamic response. The course also includes an introduction to Matlab, provides Matlab exercises to reinforce concepts, and concludes with the design and application of a controller to achieve wall tracking with a kinematic robot experiment. The only prerequisite for the course is high school algebra, including basic trigonometry. During a fourweek period in the summer of 2005, the course was taken by a group of 17 talented high school students, ranging from ninth grade to 11th grade. By the end of the course (∼30 hours of lecture time), each student had successfully implemented a wall-tracking controller on a robot called Robobrain. The students acquired a basic understanding of the principles of feedback control and its importance in applications. The students also displayed a strong motivation to learn more advanced mathematics and engineering subjects. We focus on the course content as well as our first-hand experiences teaching the class. Our hope is that this information is useful to instructors interested in pursuing new approaches to outreach. All lecture material is freely available online for anyone to use, experiment with, and improve if desired [5]. The target audience for the course includes high school students, first-year undergraduates in engineering and science, and graduate and postdoctoral researchers seeking an introduction to dynamics and control. The material can be used to initiate collaboration between control theoreticians and biologists, for example, by helping the biologists learn the language and principles behind feedback control. By design, the course material provides explicit motivation for learning more advanced mathematics (including linear algebra, calculus, and differential equations) and physics. Since the only mathematical prerequisite is high school algebra and basic trigonometry, modeling is done entirely in discrete time and kept to low dimensions.