A visual, intuitive, and experience-based approach to explaining stability of Control Systems

Abstract

Along with the technological advancements of this decade, a growing number of students have somewhat turned away from textbook-based traditional learning, while relying more on visual methods, such as web-based videos from other universities and learning platforms (e.g., The Khan Academy). Based on experience at Florida Atlantic University, we noticed that many students seek relevance of complicated and intangible heavy-math content to real life applications. Therefore, in order to keep pace with new learning styles of students, it is crucial to modernize teaching methods by supplementing the conventional teaching approaches with new and refreshing 'out-of-the-box' experiences. In addition, after many years of teaching Control Systems courses, we noticed that some students, while doing well in class assignments and exams, are missing understanding of basic key concepts. More specifically, they are all too often perplexed by the concept of stability. In order to address the question of how this became a pitfall for a grand majority of our students, we decided to introduce the material differently, i.e., to first establish the "aha" moment in students' minds, giving students something tangible to which they can relate - based on their own daily experiences. This was accomplished using visually pleasing, intuitive, hands-on examples, experiments, demonstrations and analogies that were introduced in a step-by-step manner, while connecting the concept of stability to other related concepts. These were followed by more traditional textbook-based math and physics explanations. We created a 21-minute YouTube video (https://www.youtube.com/watch?v=glM-gVp4FUM) aimed at sharing the ideas with students and professors at other universities with the hope that they will use the relevant parts in their learning and teaching. The video includes demonstrations, experiments, animation, stories, and real life examples, constantly connecting them to the concept of stability, while relating them to other concepts such as negative and positive feedback, and closed loop control. The concept of stability is introduced gradually, making sure there are no "discontinuities" in the presentation. It is of course also available to students beyond our university. In the first few days we noticed more than 200 viewers and a lot of highly encouraging feedback. In this paper we list the activities with the take-away for each. They are organized in the following way: 1. High level understanding (e.g., experimenting with Jenga-like tower: before, during and after its collapse) 2. Bounded Input Bounded Output (e.g., hearing screeching noise from speakers using an animation and an experiment; story-telling: adjusting water temperature while taking a shower) 3. Qualitative understanding of pole location and effects on stability (e.g., in class building and flying a paper airplane with varying locations of its center of mass) 4. Connection to the s-plane (e.g., visually relating poles locations to paper and actual airplanes) 5. Connection to open loop and closed loop (e.g., performing in class broom balancing acts and imitating a slow reaction of a street performer) 6. Relating to negative and positive feedback (e.g., balancing a horizontal stick) 7. Quantitative measurement of degrees of stability and instability (e.g., jumping a rope; driving in a narrow street) 8. Open challenge (e.g., engaging audience to come up with their own conclusion on demonstration) The video and this paper end with a challenge to the viewer to make sure he/she actually experience and further inquire about the concept of stability. We should notice here that this paper reports on larger scale on-going project that aims at explaining basic control system concepts in a similar manner.