New Orleans, Louisiana
June 26, 2016
June 26, 2016
August 28, 2016
Electrical and Computer
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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