Paper ID #16436 Visual and Intuitive Approach to Explaining Digitized Controllers Dr. Daniel Raviv, Florida Atlantic University Dr. Raviv is a Professor of Computer & Electrical Engineering and Computer Science at Florida Atlantic University. In December 2009 he was named Assistant Provost for Innovation and Entrepreneurship. With more than 25 years of combined experience in the high-tech industry, government and academia Dr. Raviv developed fundamentally different approaches to ”out-of-the-box” thinking and a breakthrough methodology known as ”Eight Keys to Innovation.” He has been sharing his contributions with profession- als in businesses, academia and institutes nationally and internationally. Most recently he was a visiting professor at the University of Maryland (at Mtech, Maryland Technology Enterprise Institute) and at Johns Hopkins University (at the Center for Leadership Education) where he researched and delivered processes for creative & innovative problem solving. For his unique contributions he received the prestigious Distinguished Teacher of the Year Award, the Faculty Talon Award, the University Researcher of the Year AEA Abacus Award, and the President’s Leadership Award. Dr. Raviv has published in the areas of vision-based driverless cars, green innovation, and innovative thinking. He is a co-holder of a Guinness World Record. His new book is titled: ”Everyone Loves Speed Bumps, Don’t You? A Guide to Innovative Thinking.” Dr. Daniel Raviv received his Ph.D. degree from Case Western Reserve University in 1987 and M.Sc. and B.Sc. degrees from the Technion, Israel Institute of Technology in 1982 and 1980, respectively. Paul Benedict Caballo Reyes, Florida Atlantic University Paul Benedict Reyes is an Electrical Engineering major in Florida Atlantic University who expects to graduate Spring 2016. His current interests are in wireless communications, power systems, and electrical machines. He holds leadership positions in organizations such as Tau Beta Pi and Asian Student Union. Mr. George Roskovich, Florida Atlantic University c American Society for Engineering Education, 2016 A Visual and Intuitive Approach to Explaining Digitized Controllers Daniel Raviv, Paul Benedict Reyes, and George Roskovich Department of Computer & Electrical Engineering and Computer Science Florida Atlantic University Emails: [email protected], [email protected], [email protected] Abstract In recent years, while teaching Control Systems and Digital Control Systems courses, we have noticed that some students do not fully understand the meaning of a “controller.” This may sound strange, especially when such students can solve problems, design controllers, and successfully pass the class. The observations made on this paper are based on our multiple years of experience in teaching the topics as well as several informal discussions with professors in other universities. It appears that some students miss the basic understanding that a controller (whether analog or digital) represents a transfer function (in the S-Domain or the Z-Domain) or a differential/difference equation so that, together with the dynamics of the plant and the rest of the system, it allows for desired closed loop behavior. This problem can be partially alleviated during laboratory experiments when students notice that a controller’s transfer function in the S-Domain can be practically implemented using hardware, which includes op-amps, capacitors, and resistors, and that this implementation is not unique. They can also witness the effect of changing the controller’s parameters on closed loop performance. The confusing issue for some is this: How can “software” (i.e., using difference equations, which are implemented using a micro-controller, including A/D and D/A converters) replace “hardware”? In other words, how can some lines of code yield similar input/output relationships obtained from an analog controller? This gap in understanding the similar time-response behavior of hardware and software implementations is what this paper tries to bridge. It is done in a visual, intuitive, step-by-step manner, elaborating on the pros and cons of transforming from the S-Domain to the Z-Domain, from Z-Domain to difference equations, and finally, from difference equations to implementable code. The paper uses examples of controllers and their possible representations, while clarifying and expanding on hardware implementations and their “semi-equivalent” software codes. This includes the use of the exact S to Z transformation (relevant only at sampling instants) and multiple S to Z approximations with appropriate justifications. The paper is an extension of on-going research that explains the meaning of sampling, digital computation, and reconstruction in digital control systems. It should be emphasized that the approach presented here does not attempt to replace material in existing textbooks. It simply presents supplementary visual and intuitive explanations that can help instructors and students to better understand topics in digital control systems. For clarification purposes, some explanations refer to existing textbook material. In order to explore the validity and usefulness of the new approach, a 40-minute presentation using visualization techniques was given to a Control Systems class followed by a questionnaire. Answers are based on a scale of “1” to “5,” “5” being strongly agree, “3” neutral, and “1” strongly disagree. The following is a brief summary of the results based on 20 responses: 50% of the students agreed and 30% strongly agreed that they better understand how a controller in hardware translates to software code. 55% strongly agree and 40% agree that visualization helped them understand the implementation of digital controllers. We are currently working on a more rigorous assessment to evaluate that students’ learning. 1. Introduction With the advent of the internet and growing accessibility through mobile devices, a tremendous amount of information is readily available to the new generation. “Rapid advances in information technology are reshaping the learning styles of many students.”1 The new generation’s perception of information is changing with this advancement in technology.6 Due to the increase in preference for visual media, instructors may notice it is harder for students to understand difficult concepts. Such a case is noted by Tyler DeWitt, a chemistry high school teacher and Ph.D. student at MIT.3Mr. DeWitt requests more effort should be made teaching concepts to young students. Mr. DeWitt’s realization came when he noticed his students missed key concepts although they were attending well planned lectures and completing assigned book reading. To remedy this, he engaged students with a different style of teaching that made the subject less intimidating and more fun. American astrophysicist Neil deGrasse Tyson mentions a similar problem during a speech given to the American Association of Physics Teachers.4He also highlighted the significance of educators relating to their students during lecture. For example, teachers can engage the students by making references about pop culture and relating it to the lecture. Much like what DeWitt and Tyson have noted, it has been observed at Florida Atlantic University that there are students who have already taken the Control Systems 1 class but are still having trouble understanding key concepts. Specifically, issues in understanding concepts arise when transitioning from analog controllers to digital controllers. Among the issues observed: 1. Understanding the deep meaning of the role of a controller in closed loop. 2. Conceptual understanding of transitioning from analog to digital controllers. For example, the idea that implemented code in a microprocessor (including of course signal sampling and reconstruction) can result in performance that is similar to analog hardware. 3. Understanding the justification behind the different transformations from the S-Domain to the Z-Domain. 4. Appreciating the fact that a digital controller can have different representations. For example, a controller’s Transfer Function can be represented in multiple ways. 5. Becoming aware of factors to be taken into consideration when dealing with digital controllers; the effect of sampling, approximations, computation delay, and reconstruction. This paper addresses these observations by offering a visual, intuitive, engaging, and less intimidating approach to explaining key concepts to students, with a focus on observations 2 and 3 (above). It should be noted that this approach is not meant to compete with textbooks but rather provide a supplement to help instructors introduce the material so that students can learn better and stay interested. 2. Observation 1: Understanding the Deep Meaning of the Role of Controller in Closed Loop We observed that some students do not have a deep understanding of a controller. Rather than shock the student with transfers functions and equations, analogy is employed to ease the process. Controller Design as an Art Designing a controller can be perceived as an art. Picture an artist who wants to make the color green. They have three primary colors: red, blue and yellow. On their palate, they start with yellow. Figure 1 – An Artist’s Palate As we know from elementary school, the artist needs to add blue to yellow to make green. Figure 2 – Palate with More Colors Designing controllers in Control Systems is similar to art. The controller’s “dynamics” are variably mixed to obtain a desired behavior.