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Visual and Intuitive Approach to Explaining Digitized Controllers

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2016 ASEE Annual Conference & Exposition


New Orleans, Louisiana

Publication Date

June 26, 2016

Start Date

June 26, 2016

End Date

August 28, 2016





Conference Session

Circuits & Systems Education II

Tagged Division

Electrical and Computer

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Paper Authors


Daniel Raviv Florida Atlantic University

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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 professionals 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.

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Paul Benedict Caballo Reyes Florida Atlantic University

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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.

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George Roskovich Florida Atlantic University

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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. 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.

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.

Raviv, D., & Reyes, P. B. C., & Roskovich, G. (2016, June), Visual and Intuitive Approach to Explaining Digitized Controllers Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.27184

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