Control Systems classes cover many new topics and concepts. By the time instructors begin to teach design of controllers, students have already learned some analysis and synthesis tools such as Root Locus, Routh-Hurwitz criteria for stability, Bode plot and its relation to stability, and Nyquist plot and its stability criterion. The problem is that at this point in time, these topics can still be fragmented and partially disconnected in students' minds. Oftentimes, the relations between the topics are not fully clear.When it comes to design of feedback control systems, we have repeatedly found out that, despite continuous attempts to improve our teaching, there were still some problems in students' understanding. These include:•Connecting the concept of a controller to real-life, and to sensing-based daily examples •Understanding the true meaning of controller design and its implementation•"Translating" the plant model and the design specifications to different control tools, and inter-relating themIn this paper, we report on work in progress of an intuitive and visual approach to teaching design of controllers in a closed loop control system using a specific comprehensive third order system. For example, all explanations use different colors consistently to show stability (green), instability (red), and marginally stable (orange) systems on related plots. Table. In addition, this paper shows the effects of different controllers (P, I, D, PD, PI, and PID) and their relations to the desired performance. We intentionally show unsuccessful designs: this helps in explaining some pros and cons of different controllers. This is followed by a successful design of a controller. Lastly, we present multiple ways to observe and analyze the effect of the final controller design using multiple design tools, as well as MATLAB simulations. This also includes discussing design "rules of thumb" and how they are manifested in each tool.It should be noted that the material presented in this paper is not meant to replace existing textbooks chapters. It is merely an add-on to better explain, learn, and comprehend the topic of design, and see the bigger picture. This is work in progress. However, we have tested the approach a few times and received a very positive feedback from students. A more comprehensive assessment approach is planned for the near future.
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 foll...
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